RG Plonka-Hoch (Mathematical Signal and Image Processing)

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  • 2023 | Journal Article | Research Paper
    ​ ​X-let’s Atom Combinations for Modeling and Denoising of OCT Images by Modified Morphological Component Analysis​
    Razavi, R. ; Plonka, G.   & Rabbani, H.​ (2023) 
    IEEE Transactions on Medical Imaging,.​ DOI: https://doi.org/10.1109/TMI.2023.3320977 
    ​Details  DOI 
  • 2023 | Journal Article
    ​ ​From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation​
    Derevianko, N. ; Plonka, G.   & Petz, M.​ (2023) 
    IMA Journal of Numerical Analysis,.​ DOI: https://doi.org/10.1093/imanum/drab108 
    ​Details  DOI 
  • 2023 | Journal Article
    ​ ​Spline representation and redundancies of one-dimensional ReLU neural network models​
    Plonka, G. ; Riebe, Y.   & Kolomoitsev, Y. ​ (2023) 
    Analysis and Applications, 21(01) pp. 127​-163​.​ DOI: https://doi.org/10.1142/S0219530522400103 
    ​Details  DOI 
  • 2023 | Journal Article | 
    ​ ​ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application​
    Derevianko, N. ; Plonka, G.   & Razavi, R. ​ (2023) 
    Numerical Algorithms,.​ DOI: https://doi.org/10.1007/s11075-022-01432-6 
    ​Details  DOI 
  • 2022 | Conference Paper
    ​ ​Automatic Classification of Macular Diseases from OCT Images Using CNN Guided with Edge Convolutional Layer​
    Esfahani, E. N.; Daneshmand, P. G.; Rabbani, H. & Plonka, G. ​ (2022)
    pp. 3858​-3861. ​44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC)​, Glasgow, Scotland. DOI: https://doi.org/10.1109/EMBC48229.2022.9871322 
    ​Details  DOI  PMID  PMC 
  • 2022 | Conference Paper
    ​ ​Detection of Retinal Abnormalities in OCT Images Using Wavelet Scattering Network​
    Baharlouei, Z.; Rabbani, H. & Plonka, G. ​ (2022)
    pp. 3862​-3865. ​2022 44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC)y Society. Annual International Conference​, Glasgow, Scotland. DOI: https://doi.org/10.1109/EMBC48229.2022.9871989 
    ​Details  DOI  PMID  PMC 
  • 2022 | Journal Article
    ​ ​Approximation by quasi-interpolation operators and Smolyak's algorithm​
    Kolomoitsev, Y. ​ (2022) 
    Journal of Complexity, 69 art. S0885064X2100056X​.​ DOI: https://doi.org/10.1016/j.jco.2021.101601 
    ​Details  DOI 
  • 2022 | Preprint
    ​ ​On generalized $K$-functionals in $L_p$ for $0​
    Kolomoitsev, Y.  & Lomako, T.​ (2022). DOI: https://doi.org/10.48550/ARXIV.2211.12564 
    ​Details  DOI 
  • 2022 | Preprint
    ​ ​Sharp $L_p$-error estimates for sampling operators​
    Kolomoitsev, Y.  & Lomako, T.​ (2022). DOI: https://doi.org/10.48550/ARXIV.2202.05034 
    ​Details  DOI 
  • 2022 | Journal Article
    ​ ​Frame soft shrinkage operators are proximity operators​
    Geppert, J. A. & Plonka, G. ​ (2022) 
    Applied and Computational Harmonic Analysis, 57 pp. 185​-200​.​ DOI: https://doi.org/10.1016/j.acha.2021.12.001 
    ​Details  DOI 
  • 2022 | Journal Article
    ​ ​Retinal optical coherence tomography image analysis by a restricted Boltzmann machine​
    Ezhei, M.; Rabbani, H. & Plonka, G. ​ (2022) 
    Biomedical Optics Express, 13(9) pp. 4539​-4558​.​ DOI: https://doi.org/10.1364/BOE.458753 
    ​Details  DOI  WoS 
  • 2022 | Conference Paper
    ​ ​Combining Non-Data-Adaptive Transforms for OCT Image Denoising by Iterative Basis Pursuit​
    Razavi, R. ; Rabbani, H. & Plonka, G. ​ (2022)
    pp. 2351​-2355. ​2022 IEEE International Conference on Image Processing (ICIP)​, Bordeaux, France. DOI: https://doi.org/10.1109/ICIP46576.2022.9897319 
    ​Details  DOI 
  • 2022 | Journal Article
    ​ ​Reconstruction of Connected Digital Lines Based on Constrained Regularization​
    Lashgari, M.; Rabbani, H.; Plonka, G.   & Selesnick, I.​ (2022) 
    IEEE Transactions on Image Processing, 31 pp. 5613​-5628​.​ DOI: https://doi.org/10.1109/TIP.2022.3197991 
    ​Details  DOI 
  • 2022 | Journal Article
    ​ ​Exact reconstruction of extended exponential sums using rational approximation of their Fourier coefficients​
    Derevianko, N.   & Plonka, G. ​ (2022) 
    Analysis and Applications, 20(3) pp. 543​-577​.​ DOI: https://doi.org/10.1142/S0219530521500196 
    ​Details  DOI 
  • 2022 | Journal Article | 
    ​ ​Uniform approximation by multivariate quasi-projection operators​
    Kolomoitsev, Y.   & Skopina, M.​ (2022) 
    Analysis and Mathematical Physics, 12(2) art. 68​.​ DOI: https://doi.org/10.1007/s13324-022-00665-x 
    ​Details  DOI 
  • 2021 | Journal Article | 
    ​ ​Exact reconstruction of sparse non-harmonic signals from their Fourier coefficients​
    Petz, M.; Plonka, G. & Derevianko, N.​ (2021) 
    Sampling Theory, Signal Processing, and Data Analysis, 19(1).​ DOI: https://doi.org/10.1007/s43670-021-00007-1 
    ​Details  DOI 
  • 2021 | Journal Article | 
    ​ ​Deterministic Sparse Sublinear FFT with Improved Numerical Stability​
    Plonka, G. & von Wulffen, T.​ (2021) 
    Results in Mathematics, 76(2).​ DOI: https://doi.org/10.1007/s00025-020-01330-0 
    ​Details  DOI  arXiv 
  • 2021 | Preprint
    ​ ​Sparse grid approximation in weighted Wiener spaces​
    Kolomoitsev, Y. ; Lomako, T.& Tikhonov, S.​ (2021). DOI: https://doi.org/10.48550/ARXIV.2111.06335 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Approximation properties of periodic multivariate quasi-interpolation operators​
    Kolomoitsev, Y.   & Prestin, J.​ (2021) 
    Journal of Approximation Theory, 270 art. 105631​.​ DOI: https://doi.org/10.1016/j.jat.2021.105631 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Hardy–Littlewood and Ulyanov inequalities​
    Kolomoitsev, Y.   & Tikhonov, S.​ (2021) 
    Memoirs of the American Mathematical Society, 271(1325).​ DOI: https://doi.org/10.1090/memo/1325 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Optimal Rank‐1 Hankel Approximation in the Spectral Norm for Matrices with Multiple Largest Eigenvalue​
    Knirsch, H.​ (2021) 
    Proceedings in Applied Mathematics and Mechanics, 21(1).​ DOI: https://doi.org/10.1002/pamm.202100012 
    ​Details  DOI 
  • 2021 | Book Chapter
    ​ ​Modifications of Prony’s Method for the Recovery and Sparse Approximation with Generalized Exponential Sums​
    Keller, I.& Plonka, G. ​ (2021)
    In:​Fasshauer, Gregory E.; Neamtu, Marian; Schumaker, Larry L.​ (Eds.), Approximation Theory XVI pp. 123​-152. ​Cham: ​Springer. DOI: https://doi.org/10.1007/978-3-030-57464-2_7 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Approximation by multivariate quasi-projection operators and Fourier multipliers​
    Kolomoitsev, Y.   & Skopina, M.​ (2021) 
    Applied Mathematics and Computation, 400 art. 125955​.​ DOI: https://doi.org/10.1016/j.amc.2021.125955 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​The Difference between Optimal Rank‐1 Hankel Approximations in the Frobenius Norm and the Spectral Norm​
    Knirsch, H.; Petz, M. & Plonka, G. ​ (2021) 
    Proceedings in Applied Mathematics and Mechanics, 20(1).​ DOI: https://doi.org/10.1002/pamm.202000085 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Asymptotics of the Lebesgue constants for bivariate approximation processes​
    Kolomoitsev, Y.   & Lomako, T.​ (2021) 
    Applied Mathematics and Computation, 403 art. 126192​.​ DOI: https://doi.org/10.1016/j.amc.2021.126192 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Iterative Sparse FFT for M‐sparse Vectors: Deterministic versus Random Sampling​
    Plonka, G.   & von Wulffen, T.​ (2021) 
    Proceedings in Applied Mathematics and Mechanics, 20(1).​ DOI: https://doi.org/10.1002/pamm.202000134 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Rational Functions for the Reconstruction of Exponential Sums from their Fourier Coefficients​
    Petz, M.; Plonka, G.   & Derevianko, N. ​ (2021) 
    Proceedings in Applied Mathematics and Mechanics, 21(1).​ DOI: https://doi.org/10.1002/pamm.202100078 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Optimal rank-1 Hankel approximation of matrices: Frobenius norm and spectral norm and Cadzow's algorithm​
    Knirsch, H.; Petz, M. & Plonka, G. ​ (2021) 
    Linear Algebra and its Applications, 629 pp. 1​-39​.​ DOI: https://doi.org/10.1016/j.laa.2021.07.004 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Statistical modeling of retinal optical coherence tomography using the Weibull mixture model​
    Jorjandi, S.; Amini, Z.; Plonka, G.   & Rabbani, H.​ (2021) 
    Biomedical Optics Express, 12(9) pp. 5470​.​ DOI: https://doi.org/10.1364/BOE.430800 
    ​Details  DOI 
  • 2021 | Journal Article
    ​ ​Asymptotics of the Lebesgue constants for a $d$-dimensional simplex​
    Kolomoitsev, Y.   & Liflyand, E.​ (2021) 
    Proceedings of the American Mathematical Society, 149(7) pp. 2911​-2926​.​ DOI: https://doi.org/10.1090/proc/15438 
    ​Details  DOI 
  • 2020 | Journal Article | 
    ​ ​Parseval Proximal Neural Networks​
    Hasannasab, M.; Hertrich, J.; Neumayer, S.; Plonka, G.; Setzer, S. & Steidl, G.​ (2020) 
    The Journal of Fourier Analysis and Applications, 26(4).​ DOI: https://doi.org/10.1007/s00041-020-09761-7 
    ​Details  DOI 
  • 2020 | Book Chapter
    ​ ​One-Dimensional Discrete-Time Phase Retrieval​
    Beinert, R.& Plonka, G. ​ (2020)
    In:​Salditt, Tim; Egner, Alexander; Luke, D. Russell​ (Eds.), Nanoscale Photonic Imaging pp. 603​-627.  DOI: https://doi.org/10.1007/978-3-030-34413-9_24 
    ​Details  DOI 
  • 2020 | Journal Article
    ​ ​Approximation by sampling-type operators in $L_p$-spaces​
    Kolomoitsev, Y.   & Skopina, M.​ (2020) 
    Mathematical Methods in the Applied Sciences, 43(16) pp. 9358​-9374​.​ DOI: https://doi.org/10.1002/mma.6222 
    ​Details  DOI 
  • 2020 | Preprint
    ​ ​Adaptive sampling recovery of functions with higher mixed regularity​
    Derevianko, N.  & Ullrich, T.​ (2020). DOI: https://doi.org/10.48550/ARXIV.2004.03556 
    ​Details  DOI 
  • 2020 | Journal Article
    ​ ​Approximation of Gaussians by spherical Gauss-Laguerre basis in the weighted Hilbert space​
    Derevianko, N.   & Prestin, J.​ (2020) 
    Electronic Transactions on Numerical Analysis, 52 pp. 249​-269​.​
    ​Details 
  • 2020 | Journal Article
    ​ ​Properties of moduli of smoothness inLp(Rd)​
    Kolomoitsev, Y.   & Tikhonov, S.​ (2020) 
    Journal of Approximation Theory, 257 art. 105423​.​ DOI: https://doi.org/10.1016/j.jat.2020.105423 
    ​Details  DOI 
  • 2020 | Journal Article
    ​ ​Approximation by periodic multivariate quasi-projection operators​
    Kolomoitsev, Y.; Krivoshein, A. & Skopina, M.​ (2020) 
    Journal of Mathematical Analysis and Applications, 489(2) art. 124192​.​ DOI: https://doi.org/10.1016/j.jmaa.2020.124192 
    ​Details  DOI 
  • 2020 | Journal Article | 
    ​ ​The Generalized Operator Based Prony Method​
    Stampfer, K. & Plonka, G. ​ (2020) 
    Constructive Approximation, 52(2) pp. 247​-282​.​ DOI: https://doi.org/10.1007/s00365-020-09501-6 
    ​Details  DOI 
  • 2020 | Journal Article | 
    ​ ​Smoothness of functions versus smoothness of approximation processes​
    Kolomoitsev, Y.   & Tikhonov, S. Y.​ (2020) 
    Bulletin of Mathematical Sciences, 10(3) art. 2030002​.​ DOI: https://doi.org/10.1142/S1664360720300029 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​A higher order Faber spline basis for sampling discretization of functions​
    Derevianko, N.   & Ullrich, T.​ (2019) 
    Journal of Approximation Theory, 257 pp. 105449​.​ DOI: https://doi.org/10.1016/j.jat.2020.105449 
    ​Details  DOI 
  • 2019 | Journal Article | Research Paper
    ​ ​A Tree-based Dictionary Learning Framework​
    Budinich, R. & Plonka, G. ​ (2019) 
    International Journal of Wavelets, Multiresolution and Information Processing, 18(5) art. 2050041​.​ DOI: https://doi.org/10.1142/S0219691320500411 
    ​Details  DOI  arXiv 
  • 2019 | Journal Article
    ​ ​On an orthogonal bivariate trigonometric Schauder basis for the space of continuous functions​
    Derevianko, N. ; Myroniuk, V. & Prestin, J.​ (2019) 
    Journal of Approximation Theory, 238 pp. 67​-84​.​ DOI: https://doi.org/10.1016/j.jat.2017.05.007 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Real sparse fast DCT for vectors with short support​
    Bittens, S. & Plonka, G. ​ (2019) 
    Linear Algebra and its Applications, 582 pp. 359​-390​.​ DOI: https://doi.org/10.1016/j.laa.2019.08.006 
    ​Details  DOI 
  • 2019 | Thesis | Doctoral Thesis
    ​ ​Sparse Fast Trigonometric Transforms​
    Bittens, S.​ (2019)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2019 | Journal Article
    ​ ​Reconstruction of Non‐Stationary Signals by the Generalized Prony Method​
    Keller, I.; Plonka, G.   & Stampfer, K.​ (2019) 
    Proceedings in Applied Mathematics and Mechanics, 19(1).​ DOI: https://doi.org/10.1002/pamm.201900358 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Reconstruction of stationary and non-stationary signals by the generalized Prony method​
    Plonka, G. ; Stampfer, K. & Keller, I.​ (2019) 
    Analysis and Applications, 17(2) pp. 179​-210​.​ DOI: https://doi.org/10.1142/S0219530518500240 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Optimal approximation with exponential sums by a maximum likelihood modification of Prony’s method​
    Zhang, R. & Plonka, G. ​ (2019) 
    Advances in Computational Mathematics, 45(3) pp. 1657​-1687​.​ DOI: https://doi.org/10.1007/s10444-019-09692-y 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Sparse power factorization: balancing peakiness and sample complexity​
    Geppert, J.; Krahmer, F.   & Stöger, D.​ (2019) 
    Advances in Computational Mathematics, 45(3) pp. 1711​-1728​.​ DOI: https://doi.org/10.1007/s10444-019-09698-6 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Quasi-projection operators in the weighted $L_p$ spaces​
    Kolomoitsev, Y.   & Skopina, M.​ (2018) 
    Applied and Computational Harmonic Analysis, 52 pp. 165​-197​.​ DOI: https://doi.org/10.1016/j.acha.2020.01.003 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Computation of Adaptive Fourier Series by Sparse Approximation of Exponential Sums​
    Plonka, G.   & Pototskaia, V.​ (2018) 
    The Journal of Fourier Analysis and Applications, 25(4) pp. 1580​-1608​.​ DOI: https://doi.org/10.1007/s00041-018-9635-1 
    ​Details  DOI 
  • 2018 | Monograph
    ​ ​Numerical Fourier Analysis​ ​
    Plonka-Hoch, G. ; Potts, D.; Steidl, G.& Tasche, M.​ (2018)
    Cham​: Birkhauser Verlag GmbH, Imprint of Springer Nature. DOI: https://doi.org/10.1007/978-3-030-04306-3 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain​
    Beinert, R.   & Plonka, G. ​ (2018) 
    Applied and Computational Harmonic Analysis, 45(3) pp. 505​-525​.​ DOI: https://doi.org/10.1016/j.acha.2016.12.002 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Sparse fast DCT for vectors with one-block support​
    Bittens, S. & Plonka, G. ​ (2018) 
    Numerical Algorithms, 82(2) pp. 663​-697​.​ DOI: https://doi.org/10.1007/s11075-018-0620-1 
    ​Details  DOI 
  • 2018 | Conference Paper
    ​ ​Sparse Power Factorization With Refined Peakiness Conditions​
    Stoger, D.; Geppert, J. & Krahmer, F.​ (2018)
    pp. 816​-820. ​IEEE/SP Workshop on Statistical Signal Processing (SSP)​, Freiburg im Breisgau. DOI: https://doi.org/10.1109/SSP.2018.8450850 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​A deterministic sparse FFT for functions with structured Fourier sparsity​
    Bittens, S.; Zhang, R. & Iwen, M. A.​ (2018) 
    Advances in Computational Mathematics, 45(2) pp. 519​-561​.​ DOI: https://doi.org/10.1007/s10444-018-9626-4 
    ​Details  DOI 
  • 2018 | Journal Article
    ​ ​Sparse graph-regularized dictionary learning for suppressing random seismic noise​
    Liu, L. ; Ma, J. & Plonka, G. ​ (2018) 
    Geophysics, 83(3) pp. V215​-V231​.​ DOI: https://doi.org/10.1190/geo2017-0310.1 
    ​Details  DOI 
  • 2017 | Journal Article | 
    ​ ​Sparse Phase Retrieval of One-Dimensional Signals by Prony's Method​
    Beinert, R. & Plonka, G. ​ (2017) 
    Frontiers in Applied Mathematics and Statistics, 3.​ DOI: https://doi.org/10.3389/fams.2017.00005 
    ​Details  DOI 
  • 2017 | Journal Article
    ​ ​Image Compression with the Region Based Easy Path Wavelet Transform​
    Budinich, R.​ (2017) 
    Proceedings in Applied Mathematics and Mechanics, 17(1) pp. 831​-832​.​ DOI: https://doi.org/10.1002/pamm.201710383 
    ​Details  DOI 
  • 2017 | Thesis | Doctoral Thesis
    ​ ​Application of AAK theory for sparse approximation​
    Pototskaia, V.​ (2017)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2017 | Journal Article
    ​ ​Seismic data interpolation and denoising by learning a tensor tight frame​
    Liu, L. ; Plonka, G.   & Ma, J.​ (2017) 
    Inverse Problems, 33(10) pp. 105011​.​ DOI: https://doi.org/10.1088/1361-6420/aa7773 
    ​Details  DOI 
  • 2017 | Journal Article | Research Paper
    ​ ​Sparse FFT for Functions with Short Frequency Support​
    Bittens, S.​ (2017) 
    Dolomites Research Notes on Approximation, 10(Special Issue) pp. 43​-55​.​
    ​Details 
  • 2017 | Journal Article
    ​ ​Sparse phase retrieval of structured signals by Prony's method​
    Beinert, R. & Plonka, G. ​ (2017) 
    Proceedings in Applied Mathematics and Mechanics, 17(1) pp. 829​-830​.​ DOI: https://doi.org/10.1002/pamm.201710382 
    ​Details  DOI 
  • 2017 | Journal Article
    ​ ​Application of the AAK theory and Prony-like Methods for sparse approximation of exponential sums​
    Pototskaia, V. & Plonka, G. ​ (2017) 
    Proceedings in Applied Mathematics and Mechanics, 17(1) pp. 835​-836​.​ DOI: https://doi.org/10.1002/pamm.201710385 
    ​Details  DOI 
  • 2017 | Conference Paper
    ​ ​Refined performance guarantees for Sparse Power Factorization​
    Geppert, J. A.; Krahmer, F.   & Stoger, D.​ (2017)
    pp. 509​-513. ​2017 International Conference on Sampling Theory and Applications (SampTA)​, Tallinn, Estonia. DOI: https://doi.org/10.1109/SAMPTA.2017.8024391 
    ​Details  DOI 
  • 2017 | Journal Article
    ​ ​Deterministic sparse FFT for M-sparse vectors​
    Plonka, G. ; Wannenwetsch, K. ; Cuyt, A. & Lee, W.-s.​ (2017) 
    Numerical Algorithms, 78(1) pp. 133​-159​.​ DOI: https://doi.org/10.1007/s11075-017-0370-5 
    ​Details  DOI 
  • 2017 | Journal Article
    ​ ​A region-based easy-path wavelet transform for sparse image representation​
    Budinich, R.​ (2017) 
    International Journal of Wavelets, Multiresolution and Information Processing, 15(05) pp. 1750045​.​ DOI: https://doi.org/10.1142/S021969131750045X 
    ​Details  DOI 
  • 2017 | Journal Article
    ​ ​Characterization of Local Besov Spaces via Wavelet Basis Expansions​
    Derevianko, N. ; Myroniuk, V. & Prestin, J.​ (2017) 
    Frontiers in Applied Mathematics and Statistics, 3.​ DOI: https://doi.org/10.3389/fams.2017.00004 
    ​Details  DOI 
  • 2017 | Journal Article
    ​ ​A sparse fast Fourier algorithm for real non-negative vectors​
    Plonka, G.   & Wannenwetsch, K. ​ (2017) 
    Journal of Computational and Applied Mathematics, 321 pp. 532​-539​.​ DOI: https://doi.org/10.1016/j.cam.2017.03.019 
    ​Details  DOI 
  • 2016 | Journal Article | Research Paper | 
    ​ ​Using sparsity information for iterative phase retrieval in x-ray propagation imaging​
    Pein, A.; Loock, S.; Plonka-Hoch, G.   & Salditt, T. ​ (2016) 
    Optics Express, 24(8) art. 8332​.​ DOI: https://doi.org/10.1364/oe.24.008332 
    ​Details  DOI  PMID  PMC 
  • 2016 | Journal Article
    ​ ​Non-negativity constraints in the one-dimensional discrete-time phase retrieval problem​
    Beinert, R. ​ (2016) 
    Information and Inference, pp. iaw018​.​ DOI: https://doi.org/10.1093/imaiai/iaw018 
    ​Details  DOI 
  • 2016 | Journal Article
    ​ ​Pseudo-inverses of difference matrices and their application to sparse signal approximation​
    Plonka, G. ; Hoffmann, S. & Weickert, J.​ (2016) 
    Linear Algebra and its Applications, 503 pp. 26​-47​.​ DOI: https://doi.org/10.1016/j.laa.2016.03.033 
    ​Details  DOI 
  • 2016 | Thesis | Doctoral Thesis
    ​ ​Deterministic Sparse FFT Algorithms​
    Wannenwetsch, K.​ (2016)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2016 | Journal Article
    ​ ​One-Dimensional Phase Retrieval with Additional Interference Intensity Measurements​
    Beinert, R. ​ (2016) 
    Results in Mathematics, 72(1-2) pp. 1​-24​.​ DOI: https://doi.org/10.1007/s00025-016-0633-9 
    ​Details  DOI 
  • 2016 | Journal Article
    ​ ​Asymmetric chirplet transform — Part 2: Phase, frequency, and chirp rate​
    Boßmann, F. & Ma, J.​ (2016) 
    Geophysics, 81(6) pp. V425​-V439​.​ DOI: https://doi.org/10.1190/geo2015-0696.1 
    ​Details  DOI  WoS 
  • 2016 | Thesis | Doctoral Thesis
    ​ ​Phase Retrieval with Sparsity Constraints​
    Loock, S.​ (2016)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2016 | Preprint
    ​ ​Application of the AAK theory for sparse approximation of exponential sums​
    Plonka-Hoch, G.  & Pototskaia, V.​ (2016)
    ​Details  arXiv 
  • 2016 | Journal Article
    ​ ​Sparse approximation by Prony's method and AAK theory​
    Plonka-Hoch, G.   & Pototskaia, V.​ (2016) 
    Oberwolfach Reports, 33 pp. 16​-19​.​
    ​Details 
  • 2016 | Journal Article
    ​ ​Iterative Phase Retrieval with Sparsity Constraints​
    Loock, S. & Plonka-Hoch, G. ​ (2016) 
    Proceedings in Applied Mathematics and Mechanics, 16(1) pp. 835​-836​.​ DOI: https://doi.org/10.1002/pamm.201610406 
    ​Details  DOI 
  • 2015 | Journal Article
    ​ ​Relation between total variation and persistence distance and its application in signal processing​
    Plonka-Hoch, G.   & Zheng, Y.​ (2015) 
    Advances in Computational Mathematics, 42(3) pp. 651​-674​.​ DOI: https://doi.org/10.1007/s10444-015-9438-8 
    ​Details  DOI 
  • 2015 | Journal Article
    ​ ​Ambiguities in One-Dimensional Discrete Phase Retrieval from Fourier Magnitudes​
    Beinert, R.   & Plonka-Hoch, G. ​ (2015) 
    Journal of Fourier Analysis and Applications, 21(6) pp. 1169​-1198​.​ DOI: https://doi.org/10.1007/s00041-015-9405-2 
    ​Details  DOI 
  • 2015 | Conference Paper
    ​ ​Discrete Green’s Functions for Harmonic and Biharmonic Inpainting with Sparse Atoms​
    Hoffmann, S.; Plonka-Hoch, G.   & Weickert, J.​ (2015)
    In:Tai, Xue-Cheng​ (Ed.), ​Energy minimization methods in computer vision and pattern recognition pp. 169​-182. ​10th international conference, EMMCVPR 2015​, Hong Kong.
    Cham​: Springer Nature. DOI: https://doi.org/10.1007/978-3-319-14612-6_13 
    ​Details  DOI 
  • 2015 | Thesis | Doctoral Thesis
    ​ ​Application of persistent homology in signal and image denoising​
    Zheng, Y.​ (2015)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2015 | Journal Article
    ​ ​Linear Widths of the Classes S^Ω_{p,θ}B of Periodic Functions of Many Variables​
    Derevianko, N.   & Cheremshyns’ka, O. I.​ (2015) 
    Transactions of Institute of Mathematics of NAS of Ukraine, 12(4) pp. 165​-185​.​
    ​Details 
  • 2015 | Journal Article
    ​ ​A Partial Derandomization of PhaseLift Using Spherical Designs​
    Gross, D.; Krahmer, F. & Kueng, R.​ (2015) 
    Journal of Fourier Analysis and Applications, 21(2) pp. 229​-266​.​ DOI: https://doi.org/10.1007/s00041-014-9361-2 
    ​Details  DOI  WoS 
  • 2015 | Journal Article
    ​ ​Fast Subspace Approximation Via Greedy Least-Squares​
    Iwen, M. A. & Krahmer, F.​ (2015) 
    Constructive Approximation, 42(2) pp. 281​-301​.​ DOI: https://doi.org/10.1007/s00365-014-9273-z 
    ​Details  DOI  WoS 
  • 2015 | Encyclopedia Article
    ​ ​Curvelets​
    Plonka, G.  & Ma, J.​ (2015)
    In:Engquist, B.​ (Ed.), Encyclopedia of Applied and Computational Mathematics pp. 320​-321. 
    Berlin​: Springer.
    ​Details 
  • 2015 | Journal Article
    ​ ​Asymmetric chirplet transform for sparse representation of seismic data​
    Bossmann, F. & Ma, J.​ (2015) 
    Geophysics, 80(6) pp. WD89​-WD100​.​ DOI: https://doi.org/10.1190/GEO2015-0063.1 
    ​Details  DOI  WoS 
  • 2015 | Thesis | Doctoral Thesis
    ​ ​Ambiguities in one-dimensional phase retrieval from Fourier magnitudes​
    Beinert, R.​ (2015)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2015 | Journal Article
    ​ ​Deterministic sparse FFT algorithms​
    Plonka-Hoch, G.   & Wannenwetsch, K. ​ (2015) 
    Proceedings in Applied Mathematics and Mechanics, 15(1) pp. 667​-668​.​ DOI: https://doi.org/10.1002/pamm.201510323 
    ​Details  DOI 
  • 2015 | Journal Article
    ​ ​Prony's Method for Multivariate Signals​
    Peter, T.; Plonka-Hoch, G.   & Schaback, R. ​ (2015) 
    Proceedings in Applied Mathematics and Mechanics, 15(1) pp. 665​-666​.​ DOI: https://doi.org/10.1002/pamm.201510322 
    ​Details  DOI 
  • 2015 | Journal Article
    ​ ​Ambiguities in one-dimensional phase retrieval of structured functions​
    Beinert, R.   & Plonka-Hoch, G. ​ (2015) 
    Proceedings in Applied Mathematics and Mechanics, 15(1) pp. 653​-654​.​ DOI: https://doi.org/10.1002/pamm.201510316 
    ​Details  DOI 
  • 2015 | Journal Article
    ​ ​A deterministic sparse FFT algorithm for vectors with small support​
    Plonka-Hoch, G.   & Wannenwetsch, K. ​ (2015) 
    Numerical Algorithms, 71(4) pp. 889​-905​.​ DOI: https://doi.org/10.1007/s11075-015-0028-0 
    ​Details  DOI 
  • 2015 | Journal Article
    ​ ​Reconstruction of polygonal shapes from sparse Fourier samples​
    Wischerhoff, M. & Plonka-Hoch, G. ​ (2015) 
    Journal of Computational and Applied Mathematics, 297 pp. 117​-131​.​ DOI: https://doi.org/10.1016/j.cam.2015.11.013 
    ​Details  DOI 
  • 2015 | Journal Article | Research Paper
    ​ ​Computing and analyzing recoverable supports for sparse reconstruction​
    Kruschel, C. & Lorenz, D. A.​ (2015) 
    Advances in Computational Mathematics, 41(6) pp. 1119​-1144​.​ DOI: https://doi.org/10.1007/s10444-015-9403-6 
    ​Details  DOI  WoS 
  • 2015 | Journal Article | 
    ​ ​Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized X-ray CT​
    Jørgensen, J.; Kruschel, C. & Lorenz, D. A.​ (2015) 
    Inverse Problems in Science and Engineering, 23(8) pp. 1283​-1305​.​ DOI: https://doi.org/10.1080/17415977.2014.986724 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​Phase retrieval for Fresnel measurements using a shearlet sparsity constraint​
    Loock, S. & Plonka-Hoch, G. ​ (2014) 
    Inverse Problems, 30(5) art. 055005​.​ DOI: https://doi.org/10.1088/0266-5611/30/5/055005 
    ​Details  DOI 
  • 2014 | Thesis | Doctoral Thesis
    ​ ​Generalized Prony Method​
    Peter, T.​ (2014)
    Der Andere Verlag.
    ​Details 
  • 2014 | Journal Article
    ​ ​An RIP-Based Approach to Sigma Delta Quantization for Compressed Sensing​
    Feng, J.-M. & Krahmer, F.​ (2014) 
    IEEE Signal Processing Letters, 21(11) pp. 1351​-1355​.​ DOI: https://doi.org/10.1109/LSP.2014.2336700 
    ​Details  DOI  WoS 
  • 2014 | Journal Article
    ​ ​Prony methods for recovery of structured functions​
    Plonka-Hoch, G.   & Tasche, M.​ (2014) 
    GAMM-Mitteilungen, 37(2) pp. 239​-258​.​ DOI: https://doi.org/10.1002/gamm.201410011 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​Estimations of Linear Widths of the Classes B^Ω_{p,θ} of Periodic Functions of Many Variables in the Space L_q​
    Derevianko, N. ​ (2014) 
    Ukrainian Mathematical Journal, 66(7) pp. 1013​-1027​.​
    ​Details 
  • 2014 | Journal Article
    ​ ​Suprema of Chaos Processes and the Restricted Isometry Property​
    Krahmer, F.; Mendelson, S. & Rauhut, H.​ (2014) 
    Communications on Pure and Applied Mathematics, 67(11) pp. 1877​-1904​.​ DOI: https://doi.org/10.1002/cpa.21504 
    ​Details  DOI  WoS 
  • 2014 | Thesis | Doctoral Thesis
    ​ ​Reconstruction of Structured Functions from Sparse Fourier Data​
    Wischerhoff, M.​ (2014)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2014 | Thesis | Doctoral Thesis
    ​ ​Model based defect reconstruction in ultrasonic non-destructive testing​
    Boßmann, F.​ (2014)
    Uelvesbüll​: Der Andere Verlag.
    ​Details 
  • 2014 | Journal Article
    ​ ​Estimates of Linear Widths of the Classes H^Ω_p of Periodic Functions of Many Variables in the Space L_q​
    Derevianko, N. ​ (2014) 
    Transactions of Institute of Mathematics of NAS of Ukraine, 11(3) pp. 128​-145​.​
    ​Details 
  • 2014 | Journal Article
    ​ ​Sparse matrices in frame theory​
    Krahmer, F.; Kutyniok, G. & Lemvig, J.​ (2014) 
    Computational Statistics, 29(3-4) pp. 547​-568​.​ DOI: https://doi.org/10.1007/s00180-013-0446-1 
    ​Details  DOI  WoS 
  • 2014 | Journal Article
    ​ ​Local Sampling and Approximation of Operators with Bandlimited Kohn-Nirenberg Symbols​
    Krahmer, F. & Pfander, G. E.​ (2014) 
    Constructive Approximation, 39(3) pp. 541​-572​.​ DOI: https://doi.org/10.1007/s00365-014-9228-4 
    ​Details  DOI  WoS 
  • 2014 | Book Chapter
    ​ ​Adaptive Approximation Algorithms for Sparse Data Representation​
    Guillemard, M.; Heinen, D. ; Iske, A.; Krause-Solberg, S.& Plonka-Hoch, G. ​ (2014)
    In: Extraction of Quantifiable Information from Complex Systems pp. 281​-302. ​Cham: ​Springer. DOI: https://doi.org/10.1007/978-3-319-08159-5_14 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​Approximation of the Classes H p Ω of Periodic Functions of Many Variables in the Space L p​
    Derev’yanko, N. V. ​ (2014) 
    Ukrainian Mathematical Journal, 66(5) pp. 707​-718​.​ DOI: https://doi.org/10.1007/s11253-014-0966-z 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing​
    Krahmer, F.; Saab, R. & Yilmaz, O.​ (2014) 
    Information and Inference, 3(1) pp. 40​-58​.​ DOI: https://doi.org/10.1093/imaiai/iat007 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​Stable and Robust Sampling Strategies for Compressive Imaging​
    Krahmer, F. & Ward, R.​ (2014) 
    IEEE Transactions on Image Processing, 23(2) pp. 612​-622​.​ DOI: https://doi.org/10.1109/TIP.2013.2288004 
    ​Details  DOI  PMID  PMC  WoS 
  • 2013 | Thesis | Master Thesis
    ​ ​Methoden zur Bildrekonstruktion aus unvollständigen Mengen von Waveletkoeffizienten​
    Pototskaia, V.​ (2013)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2013 | Thesis | Master Thesis
    ​ ​Multilevel Gauß-Newton Methoden zur Phasenrekonstruktion​
    Beinert, R.​ (2013)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2013 | Journal Article
    ​ ​A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators​
    Peter, T. & Plonka-Hoch, G. ​ (2013) 
    Inverse Problems, 29(2) art. 025001​.​ DOI: https://doi.org/10.1088/0266-5611/29/2/025001 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Optimal representation of piecewise Hölder smooth bivariate functions by the Easy Path Wavelet Transform​
    Plonka-Hoch, G. ; Iske, A. & Tenorth, S.​ (2013) 
    Journal of Approximation Theory, 176 pp. 42​-67​.​ DOI: https://doi.org/10.1016/j.jat.2013.08.002 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Trigonometric Widths of Classes of Periodic Functions of Many Variables​
    Derevianko, N. ​ (2013) 
    Ukrainian Mathematical Journal, 64(8) pp. 1185​-1198​.​
    ​Details 
  • 2013 | Journal Article
    ​ ​Real function reconstruction from sparse Fourier samples​
    Wischerhoff, M.​ (2013) 
    Proceedings in Applied Mathematics and Mechanics, 13(1) pp. 491​-492​.​ DOI: https://doi.org/10.1002/pamm.201310238 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Spectral Properties of Two-slanted Matrices​
    Berg, L. & Plonka-Hoch, G. ​ (2013) 
    Results in Mathematics, 35(3-4) pp. 201​-215​.​ DOI: https://doi.org/10.1007/bf03322813 
    ​Details  DOI 
  • 2013 | Journal Article
    ​ ​Sparsity and spectral properties of dual frames​
    Krahmer, F. ; Kutyniok, G. & Lemvig, J.​ (2013) 
    Linear Algebra and its Applications, 439(4) pp. 982​-998​.​ DOI: https://doi.org/10.1016/j.laa.2012.10.016 
    ​Details  DOI  WoS 
  • 2013 | Journal Article | 
    ​ ​How many Fourier samples are needed for real function reconstruction?​
    Plonka-Hoch, G.   & Wischerhoff, M.​ (2013) 
    Journal of Applied Mathematics and Computing, 42(1-2) pp. 117​-137​.​ DOI: https://doi.org/10.1007/s12190-012-0624-2 
    ​Details  DOI 
  • 2012 | Journal Article
    ​ ​Representation of sparse Legendre expansions​
    Peter, T.; Plonka-Hoch, G.   & Roşca, D.​ (2012) 
    Journal of Symbolic Computation, 50 pp. 159​-169​.​ DOI: https://doi.org/10.1016/j.jsc.2012.06.002 
    ​Details  DOI 
  • 2012 | Journal Article
    ​ ​Compressive Video Sampling With Approximate Message Passing Decoding​
    Ma, J.; Plonka-Hoch, G.   & Hussaini, M. Y.​ (2012) 
    IEEE Transactions on Circuits and Systems for Video Technology, 22(9) pp. 1354​-1364​.​ DOI: https://doi.org/10.1109/tcsvt.2012.2201673 
    ​Details  DOI 
  • 2012 | Journal Article
    ​ ​Ortho-projective Widths of Classes of Periodic Functions of Many Variables​
    Derevianko, N. ​ (2012) 
    Transactions of Institute of Mathematics of NAS of Ukraine, 9(2) pp. 146​-156​.​
    ​Details 
  • 2012 | Journal Article
    ​ ​SqFreeEVAL: An (almost) optimal real-root isolation algorithm​
    Burr, M. A. & Krahmer, F.​ (2012) 
    Journal of Symbolic Computation, 47(2) pp. 153​-166​.​ DOI: https://doi.org/10.1016/j.jsc.2011.08.022 
    ​Details  DOI 
  • 2012 | Journal Article
    ​ ​Lower bounds for the error decay incurred by coarse quantization schemes​
    Krahmer, F. & Ward, R.​ (2012) 
    Applied and Computational Harmonic Analysis, 32(1) pp. 131​-138​.​ DOI: https://doi.org/10.1016/j.acha.2011.06.003 
    ​Details  DOI 
  • 2012 | Journal Article
    ​ ​Approximation by k-sparse sums of eigenfunctions of linear operators​
    Peter, T. & Plonka-Hoch, G. ​ (2012) 
    Oberwolfach Reports, 31 pp. 16​-18​.​
    ​Details 
  • 2012 | Journal Article
    ​ ​Optimally Sparse Image Representation by the Easy Path Wavelet Transform​
    Plonka, G. ; Tenorth, S. & Iske, A.​ (2012) 
    International Journal of Wavelets, Multiresolution and Information Processing, 10(1) art. 1250007​.​ DOI: https://doi.org/10.1142/S0219691311004493 
    ​Details  DOI  WoS 
  • 2012 | Journal Article
    ​ ​Root-Exponential Accuracy for Coarse Quantization of Finite Frame Expansions​
    Krahmer, F.; Saab, R. & Ward, R.​ (2012) 
    IEEE Transactions on Information Theory, 58(2) pp. 1069​-1079​.​ DOI: https://doi.org/10.1109/TIT.2011.2168942 
    ​Details  DOI 
  • 2012 | Journal Article | 
    ​ ​Sparse Deconvolution Methods for Ultrasonic NDT​
    Boßmann, F.; Plonka-Hoch, G. ; Peter, T.; Nemitz, O. & Schmitte, T.​ (2012) 
    Journal of Nondestructive Evaluation, 31(3) pp. 225​-244​.​ DOI: https://doi.org/10.1007/s10921-012-0138-8 
    ​Details  DOI 
  • 2012 | Journal Article | 
    ​ ​An Area Preserving Projection from the Regular Octahedron to the Sphere​
    Roşca, D. & Plonka-Hoch, G. ​ (2012) 
    Results in Mathematics, 62(3-4) pp. 429​-444​.​ DOI: https://doi.org/10.1007/s00025-012-0286-2 
    ​Details  DOI 
  • 2012 | Journal Article | 
    ​ ​Wavelet Shrinkage on Paths for Denoising of Scattered Data​
    Heinen, D.   & Plonka-Hoch, G. ​ (2012) 
    Results in Mathematics, 62(3-4) pp. 337​-354​.​ DOI: https://doi.org/10.1007/s00025-012-0285-3 
    ​Details  DOI 
  • 2011 | Thesis | Doctoral Thesis
    ​ ​Adaptive Waveletmethoden zur Approximation von Bildern​
    Tenorth, S.​ (2011)
    Georg-August-Universität Göttingen. 
    ​Details 
  • 2011 | Thesis | Master Thesis
    ​ ​Modeling and Analysis of Calibrating Cone-Beam-CT​
    Kruschel, C.​ (2011)
    TU Braunschweig, Institut for Analysis and Algebra. 
    ​Details 
  • 2011 | Journal Article
    ​ ​Uniform spherical grids via equal area projection from the cube to the sphere​
    Roşca, D. & Plonka-Hoch, G. ​ (2011) 
    Journal of Computational and Applied Mathematics, 236(6) pp. 1033​-1041​.​ DOI: https://doi.org/10.1016/j.cam.2011.07.009 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​On the computation of Gramian matrices for refinable bases on the interval​
    Primbs, M.​ (2011) 
    International Journal of Wavelets, Multiresolution and Information Processing, 6(3) pp. 459​-479​.​ DOI: https://doi.org/10.1142/S0219691308002422 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​An optimal family of exponentially accurate one-bit Sigma-Delta quantization schemes​
    Deift, P.; Krahmer, F. & Güntürk, C. S.​ (2011) 
    Communications on Pure and Applied Mathematics, 64(7) pp. 883​-919​.​ DOI: https://doi.org/10.1002/cpa.20367 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​New and Improved Johnson–Lindenstrauss Embeddings via the Restricted Isometry Property​
    Krahmer, F. & Ward, R.​ (2011) 
    SIAM Journal on Mathematical Analysis, 43(3) pp. 1269​-1281​.​ DOI: https://doi.org/10.1137/100810447 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​Optimally Sparse Frames​
    Casazza, P. G.; Heinecke, A.; Krahmer, F. & Kutyniok, G.​ (2011) 
    IEEE Transactions on Information Theory, 57(11) pp. 7279​-7287​.​ DOI: https://doi.org/10.1109/TIT.2011.2160521 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​Curvelet-Wavelet Regularized Split Bregman Iteration for Compressed Sensing​
    Plonka, G.   & Ma, J.​ (2011) 
    International Journal of Wavelets, Multiresolution and Information Processing, 9(1) pp. 79​-110​.​ DOI: https://doi.org/10.1142/S0219691311003955 
    ​Details  DOI  WoS 
  • 2011 | Journal Article
    ​ ​Nonlinear approximation by sums of exponentials and translates​
    Peter, T.; Potts, D. & Tasche, M.​ (2011) 
    SIAM Journal on Scientific Computing, 33(4) pp. 1920​-1947​.​ DOI: https://doi.org/10.1137/100790094 
    ​Details  DOI  WoS 
  • 2011 | Book Chapter
    ​ ​Some Notes on Two-Scale Difference Equations​
    Berg, L.& Plonka-Hoch, G. ​ (2011)
    In: Functional Equations and Inequalities pp. 7​-29. ​Dordrecht: ​Springer. DOI: https://doi.org/10.1007/978-94-011-4341-7_2 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​A New Hybrid Method for Image Approximation Using the Easy Path Wavelet Transform​
    Plonka, G. ; Tenorth, S. & Rosca, D.​ (2011) 
    IEEE Transactions on Image Processing, 20(2) pp. 372​-381​.​ DOI: https://doi.org/10.1109/TIP.2010.2061861 
    ​Details  DOI 
  • 2010 | Thesis | Diploma Thesis
    ​ ​Behandlung von Poisson- und Gamma-Störungen in digitalen Bildern mit Hilfe von Splitting-Methoden​
    Wischerhoff, M.​ (2010)
    Universität Duisburg-Essen, Fachbereich Mathematik. 
    ​Details 
  • 2010 | Thesis | Diploma Thesis
    ​ ​Bildapproximation mittels Wedgelets​
    Heinen, D.​ (2010)
    Universität Duisburg-Essen, Fachbereich Mathematik. 
    ​Details 
  • 2010 | Journal Article
    ​ ​The Curvelet Transform​
    Ma, J. & Plonka-Hoch, G. ​ (2010) 
    IEEE Signal Processing Magazine, 27(2) pp. 118​-133​.​ DOI: https://doi.org/10.1109/msp.2009.935453 
    ​Details  DOI 
  • 2010 | Book Chapter
    ​ ​A survey on L2-approximation orders from shift-invariant spaces​
    Jetter, K.& Plonka-Hoch, G. ​ (2010)
    In:​Dyn, N.; Leviatan, D.; Levin, D.; Pinkus, A.​ (Eds.), Multivariate Approximation and Applications pp. 73​-111. ​Cambridge University Press. DOI: https://doi.org/10.1017/cbo9780511569616.005 
    ​Details  DOI 
  • 2010 | Journal Article
    ​ ​A New Sparse Representation of Seismic Data Using Adaptive Easy-Path Wavelet Transform​
    Ma, J.; Plonka-Hoch, G.   & Chauris, H.​ (2010) 
    IEEE Geoscience and Remote Sensing Letters, 7(3) pp. 540​-544​.​ DOI: https://doi.org/10.1109/lgrs.2010.2041185 
    ​Details  DOI 
  • 2010 | Journal Article
    ​ ​Easy Path Wavelet Transform on Triangulations of the Sphere​
    Plonka-Hoch, G.   & Roşca, D.​ (2010) 
    Mathematical Geosciences, 42(7) pp. 839​-855​.​ DOI: https://doi.org/10.1007/s11004-009-9263-z 
    ​Details  DOI 
  • 2010 | Journal Article
    ​ ​New Stable Biorthogonal Spline-Wavelets on the Interval​
    Primbs, M.​ (2010) 
    Results in Mathematics, 57(1-2) pp. 121​-162​.​ DOI: https://doi.org/10.1007/s00025-009-0008-6 
    ​Details  DOI 
  • 2010 | Conference Paper
    ​ ​Image approximation by a hybrid method based on the Easy Path Wavelet Transform​
    Plonka-Hoch, G. ; Tenorth, S. & Roşca, D.​ (2010)
    In:Matthews, Michael B.​ (Ed.), ​Conference record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, 2009 pp. 442​-446. ​Asilomar Conference on Signals, Systems and Computers​, Pacific Grove, California.
    Piscataway, NJ​: Institute of Electrical and Electronics Engineers (IEEE). DOI: https://doi.org/10.1109/acssc.2009.5469855 
    ​Details  DOI 
  • 2010 | Journal Article
    ​ ​Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation​
    Krommweh, J.​ (2010) 
    Journal of Visual Communication and Image Representation, 21(4) pp. 364​-374​.​ DOI: https://doi.org/10.1016/j.jvcir.2010.02.011 
    ​Details  DOI 
  • 2010 | Journal Article
    ​ ​Tetrolet shrinkage with anisotropic total variation minimization for image approximation​
    Krommweh, J. & Ma, J.​ (2010) 
    Signal Processing, 90(8) pp. 2529​-2539​.​ DOI: https://doi.org/10.1016/j.sigpro.2010.02.022 
    ​Details  DOI 
  • 2009 | Thesis | Diploma Thesis
    ​ ​Entwicklung einer automatisierten Auswertung von bildgebenden Ultraschallverfahren​
    Boßmann, F.​ (2009)
    Universität Duisburg-Essen, Fachbereich Mathematik. 
    ​Details 
  • 2009 | Thesis | Diploma Thesis
    ​ ​Parameterbestimmung bei anharmonischen Fouriersummen mittels approximativer Prony-Methode​
    Peter, T.​ (2009)
    Universität Rostock, Institut für Mathematik. 
    ​Details 
  • 2009 | Journal Article
    ​ ​Directional Haar wavelet frames on triangles​
    Krommweh, J. & Plonka-Hoch, G. ​ (2009) 
    Applied and Computational Harmonic Analysis, 27(2) pp. 215​-234​.​ DOI: https://doi.org/10.1016/j.acha.2009.03.002 
    ​Details  DOI 
  • 2009 | Journal Article
    ​ ​A Digital Diffusion-Reaction Type Filter for Nonlinear Denoising​
    Plonka-Hoch, G. ​ (2009) 
    Results in Mathematics, 53(3-4) pp. 371​-381​.​ DOI: https://doi.org/10.1007/s00025-008-0348-7 
    ​Details  DOI 
  • 2009 | Conference Paper
    ​ ​Sparse Data Representation on the Sphere using the Easy Path Wavelet Transform​
    Plonka-Hoch, G.   & Roşca, D.​ (2009)
    In:Fesquet, L.; Torresani, B.​ (Eds.), ​SAMPTA'09, International Conference on SAMPling Theory and Applications. 
    ​Details 
  • 2009 | Book Chapter
    ​ ​Image approximation by adaptive tetrolet transform​
    Krommweh, J.​ (2009)
    In:​Fesquet, L.; Torresani, B.​ (Eds.), Sampling Theory and Applications (SampTA'09) pp. 81​-84. 
    ​Details 
  • 2009 | Journal Article
    ​ ​Computing with Curvelets: From Image Processing to Turbulent Flows​
    Ma, J. & Plonka-Hoch, G. ​ (2009) 
    Computing in Science & Engineering, 11(2) pp. 72​-80​.​ DOI: https://doi.org/10.1109/mcse.2009.26 
    ​Details  DOI 
  • 2009 | Journal Article
    ​ ​The Easy Path Wavelet Transform: A New Adaptive Wavelet Transform for Sparse Representation of Two-Dimensional Data​
    Plonka-Hoch, G. ​ (2009) 
    Multiscale Modeling & Simulation, 7(3) pp. 1474​-1496​.​ DOI: https://doi.org/10.1137/080719248 
    ​Details  DOI 
  • 2009 | Thesis | Doctoral Thesis
    ​ ​Novel Schemes for Sigma-Delta Modulation: Improved Exponential Accuracy to Low-Complexity Design​
    Krahmer, F.​ (2009)
    New York University. 
    ​Details 
  • 2009 | Journal Article
    ​ ​The Method of Stable Completion in the Classical Wavelet Context​
    Primbs, M.​ (2009) 
    Results in Mathematics, 53(3-4) pp. 391​-398​.​ DOI: https://doi.org/10.1007/s00025-008-0350-0 
    ​Details  DOI 
  • 2009 | Journal Article
    ​ ​Nonlinear and adaptive frame approximation schemes for elliptic PDEs: Theory and numerical experiments​
    Dahlke, S.; Fornasier, M.; Primbs, M.; Raasch, T. & Werner, M.​ (2009) 
    Numerical Methods for Partial Differential Equations, 25(6) pp. 1366​-1401​.​ DOI: https://doi.org/10.1002/num.20407 
    ​Details  DOI 
  • 2009 | Journal Article
    ​ ​Tight frame characterization of multiwavelet vector functions in terms of the polyphase matrix​
    Krommweh, J.​ (2009) 
    International Journal of Wavelets, Multiresolution and Information Processing, 7(1) pp. 9​-21​.​
    ​Details 
  • 2009 | Journal Article
    ​ ​An Orthonormal Basis of Directional Haar Wavelets on Triangles​
    Krommweh, J.​ (2009) 
    Results in Mathematics, 53(3-4) pp. 323​-331​.​ DOI: https://doi.org/10.1007/s00025-008-0343-z 
    ​Details  DOI 
  • 2009 | Conference Paper
    ​ ​Nonlinear locally adaptive wavelet filter banks​
    Plonka-Hoch, G.   & Tenorth, S.​ (2009)
    In:Fesquet, L.; Torresani, B.​ (Eds.), ​SAMPTA'09, International Conference on SAMPling Theory and Applications. 
    ​Details 
  • 2008 | Thesis | Diploma Thesis
    ​ ​Verallgemeinerte Rudin-Osher-Fatemi-Regularisierung zur Signalentstörung​
    Tenorth, S.​ (2008)
    Universität Duisburg-Essen, Fachbereich Mathematik. 
    ​Details 
  • 2008 | Journal Article
    ​ ​Nonlinear Regularized Reaction-Diffusion Filters for Denoising of Images With Textures​
    Plonka-Hoch, G. ​ (2008) 
    IEEE Transactions on Image Processing, 17(8) pp. 1283​-1294​.​ DOI: https://doi.org/10.1109/tip.2008.925305 
    ​Details  DOI 
  • 2008 | Journal Article
    ​ ​Uncertainty in time–frequency representations on finite Abelian groups and applications​
    Krahmer, F.; Pfander, G. E. & Rashkov, P.​ (2008) 
    Applied and Computational Harmonic Analysis, 25(2) pp. 209​-225​.​ DOI: https://doi.org/10.1016/j.acha.2007.09.008 
    ​Details  DOI 
  • 2007 | Journal Article
    ​ ​Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion​
    Ma, J. & Plonka-Hoch, G. ​ (2007) 
    IEEE Transactions on Image Processing, 16(9) pp. 2198​-2206​.​ DOI: https://doi.org/10.1109/tip.2007.902333 
    ​Details  DOI 
  • 2007 | Journal Article
    ​ ​Convergence of an Iterative Nonlinear Scheme for Denoising of Piecewise Constant Images​
    Plonka-Hoch, G.   & Ma, J.​ (2007) 
    International Journal of Wavelets, Multiresolution and Information Processing, 05(06) pp. 975​-995​.​ DOI: https://doi.org/10.1142/s0219691307002142 
    ​Details  DOI 
  • 2007 | Journal Article
    ​ ​Numerical stability of biorthogonal wavelet transforms​
    Plonka-Hoch, G. ; Schumacher, H. & Tasche, M.​ (2007) 
    Advances in Computational Mathematics, 29(1) pp. 1​-25​.​ DOI: https://doi.org/10.1007/s10444-007-9034-7 
    ​Details  DOI 
  • 2006 | Journal Article
    ​ ​A Multiscale Wavelet-Inspired Scheme for Nonlinear Diffusion​
    Plonka-Hoch, G.   & Steidel, G.​ (2006) 
    International Journal of Wavelets, Multiresolution and Information Processing, 04(01) pp. 1​-21​.​ DOI: https://doi.org/10.1142/s0219691306001063 
    ​Details  DOI 
  • 2006 | Journal Article
    ​ ​A new factorization technique of the matrix mask of univariate refinable functions​
    Plonka-Hoch, G.   & Ron, A.​ (2006) 
    Numerische Mathematik, 87(3) pp. 555​-595​.​ DOI: https://doi.org/10.1007/pl00005424 
    ​Details  DOI 
  • 2005 | Journal Article
    ​ ​Worst-case error analysis of lifting-based fast DCT-algorithms​
    Primbs, M.​ (2005) 
    IEEE Transactions on Signal Processing, 53(8) pp. 3211​-3218​.​ DOI: https://doi.org/10.1109/TSP.2005.851114 
    ​Details  DOI 
  • 2004 | Journal Article
    ​ ​Fast and numerically stable algorithms for discrete cosine transforms​
    Plonka-Hoch, G.   & Tasche, M.​ (2004) 
    Linear Algebra and its Applications, 394 pp. 309​-345​.​ DOI: https://doi.org/10.1016/j.laa.2004.07.015 
    ​Details  DOI 
  • 2004 | Book Chapter
    ​ ​Numerical stability of fast trigonometric and orthogonal wavelet transforms​
    Plonka-Hoch, G.  & Tasche, M.​ (2004)
    In:​Neamtu, M.; Saff, E.B.​ (Eds.), Advances in Constructive Approximation: Vanderbilt pp. 393​-419. ​Brentwood: ​Nashboro Press.
    ​Details 
  • 2003 | Journal Article
    ​ ​Properties of locally linearly independent refinable function vectors​
    Plonka, G.   & Zhou, D.-X.​ (2003) 
    Journal of Approximation Theory, 122(1) pp. 24​-41​.​ DOI: https://doi.org/10.1016/s0021-9045(03)00036-4 
    ​Details  DOI 
  • 2003 | Journal Article
    ​ ​Invertible integer DCT algorithms​
    Plonka, G.   & Tasche, M.​ (2003) 
    Applied and Computational Harmonic Analysis, 15(1) pp. 70​-88​.​ DOI: https://doi.org/10.1016/s1063-5203(03)00032-0 
    ​Details  DOI 
  • 2003 | Journal Article
    ​ ​Construction of Multiscaling Functions with Approximation and Symmetry​
    Plonka-Hoch, G.   & Strela, V.​ (2003) 
    SIAM Journal on Mathematical Analysis, 29(2) pp. 481​-510​.​ DOI: https://doi.org/10.1137/s0036141096297182 
    ​Details  DOI 
  • 2002 | Journal Article
    ​ ​Convergence of Cascade Algorithms in Sobolev Spaces for Perturbed Refinement Masks​
    Chen, D.-R. & Plonka, G. ​ (2002) 
    Journal of Approximation Theory, 119(2) pp. 133​-155​.​ DOI: https://doi.org/10.1006/jath.2002.3682 
    ​Details  DOI 
  • 2002 | Book Chapter
    ​ ​How many holes can locally linearly independent refinable function vectors have?​
    Plonka-Hoch, G. ​ (2002)
    In:​Levesley, J.; Anderson, I. J.; Mason, J. C.​ (Eds.), Algorithms for Approximation IV pp. 378​-393. ​The University of Huddersfield.
    ​Details 
  • 2001 | Journal Article
    ​ ​A global method for invertible integer DCT and integer wavelet algorithms​
    Plonka, G. ​ (2001) 
    Applied and Computational Harmonic Analysis, 16(2) pp. 90​-110​.​ DOI: https://doi.org/10.1016/j.acha.2003.10.004 
    ​Details  DOI 
  • 1998 | Journal Article
    ​ ​Compactly supported solutions of two-scale difference equations​
    Berg, L. & Plonka, G. ​ (1998) 
    Linear Algebra and its Applications, 275-276 pp. 49​-75​.​ DOI: https://doi.org/10.1016/s0024-3795(97)10012-x 
    ​Details  DOI 
  • 1998 | Book Chapter
    ​ ​From wavelets to multiwavelets​
    Plonka-Hoch, G.  & Strela, V.​ (1998)
    In:​Daehlen, Morten; Lyche, Tom; Schumaker, Larry. L.​ (Eds.), Mathematical Methods of Curves and Surfaces II pp. 1​-25. ​Nashville: ​Vanderbilt University Press.
    ​Details 
  • 1997 | Book Chapter
    ​ ​Stability of translates of scaling vectors​
    Plonka-Hoch, G. ​ (1997)
    In:​Sydow, Achim​ (Ed.), Computational Mathematics pp. 81​-86. ​Berlin: ​Wissenschaft & Technik Verlag.
    ​Details 
  • 1997 | Preprint
    ​ ​Refinement of Vectors of Bernstein Polynomials​
    Berg, L.& Plonka-Hoch, G. ​ (1997)
    ​Details 
  • 1997 | Book Chapter
    ​ ​On stability of scaling vectors​
    Plonka-Hoch, G. ​ (1997)
    In:​Mehauté, A. Le; Rabut, C.; Schumaker, L. L.​ (Eds.), Surface Fitting and Multiresolution Methods pp. 295​-324. ​Nashville: ​Vanderbilt University Press,.
    ​Details 
  • 1997 | Conference Paper
    ​ ​Necessary and Sufficient Conditions for Orthonormality of Scaling Vectors​
    Plonka-Hoch, G. ​ (1997)
    In:Nürnberger, Günther; Schmidt, Jochen W.; Walz, Guido​ (Eds.), ​Multivariate Approximation and Splines pp. 205​-218. ​Interna­tional conference on "Multivariate Approximation and Splines"​, Mannheim.
    Basel​: Birkhäuser. DOI: https://doi.org/10.1007/978-3-0348-8871-4_17 
    ​Details  DOI 
  • 1997 | Journal Article
    ​ ​Approximation Order Provided by Refinable Function Vectors​
    Plonka-Hoch, G. ​ (1997) 
    Constructive Approximation, 13(2) pp. 221​-244​.​ DOI: https://doi.org/10.1007/s003659900039 
    ​Details  DOI 
  • 1997 | Journal Article
    ​ ​Regularity of refinable function vectors​
    Cohen, A.; Daubechies, I. & Plonka-Hoch, G. ​ (1997) 
    The Journal of Fourier Analysis and Applications, 3(3) pp. 295​-324​.​ DOI: https://doi.org/10.1007/bf02649113 
    ​Details  DOI 
  • 1996 | Journal Article
    ​ ​Generalized spline wavelets​
    Plonka-Hoch, G. ​ (1996) 
    Constructive Approximation, 12(1) pp. 127​-155​.​ DOI: https://doi.org/10.1007/bf02432858 
    ​Details  DOI 
  • 1995 | Book Chapter
    ​ ​Factorization of refinement masks of function vectors​
    Plonka-Hoch, G. ​ (1995)
    In:​Chui, C. K.; Shumaker, L. L.​ (Eds.), Wavelets and Multilevel Approximation pp. 317​-324. ​Singapore: ​World Scientific Publishing Co.
    ​Details 
  • 1995 | Journal Article
    ​ ​On the Computation of Periodic Spline Wavelets​
    Plonka-Hoch, G.   & Tasche, M.​ (1995) 
    Applied and Computational Harmonic Analysis, 2(1) pp. 1​-14​.​ DOI: https://doi.org/10.1006/acha.1995.1001 
    ​Details  DOI 
  • 1995 | Preprint
    ​ ​Approximation Properties of Multi-Scaling Functions: A Fourier Approach​
    Plonka-Hoch, G. ​ (1995)
    ​Details 
  • 1995 | Journal Article
    ​ ​On the construction of wavelets on a bounded interval​
    Plonka-Hoch, G. ; Selig, K. & Tasche, M.​ (1995) 
    Advances in Computational Mathematics, 4(1) pp. 357​-388​.​ DOI: https://doi.org/10.1007/bf02123481 
    ​Details  DOI 
  • 1994 | Journal Article
    ​ ​Periodic Spline Interpolation with Shifted Nodes​
    Plonka, G. ​ (1994) 
    Journal of Approximation Theory, 76(1) pp. 1​-20​.​ DOI: https://doi.org/10.1006/jath.1994.1001 
    ​Details  DOI 
  • 1994 | Book Chapter
    ​ ​Spline wavelets with higher defect​
    Plonka-Hoch, G. ​ (1994)
    In:​Laurent, P. J.; Mehauté, A. Le; Schumaker, L. L.​ (Eds.), Wavelets, Images, and Surface Fitting pp. 387​-398. ​Boston: ​AKPeters.
    ​Details 
  • 1994 | Journal Article
    ​ ​Cardinal Hermite Spline Interpolation with Shifted Nodes​
    Plonka-Hoch, G.   & Tasche, M.​ (1994) 
    Mathematics of Computation, 63(208) art. 645​.​ DOI: https://doi.org/10.2307/2153287 
    ​Details  DOI 
  • 1994 | Journal Article
    ​ ​Optimal shift parameters for periodic spline interpolation​
    Plonka-Hoch, G. ​ (1994) 
    Numerical Algorithms, 6(2) pp. 297​-316​.​ DOI: https://doi.org/10.1007/bf02142676 
    ​Details  DOI 
  • 1994 | Journal Article
    ​ ​Two-scale symbol and autocorrelation symbol for B-splines with multiple knots​
    Plonka-Hoch, G. ​ (1994) 
    Advances in Computational Mathematics, 3(1-2) pp. 1​-22​.​ DOI: https://doi.org/10.1007/bf02431993 
    ​Details  DOI 
  • 1994 | Book Chapter
    ​ ​A Unified Approach to Periodic Wavelets​
    Plonka-Hoch, G.  & Tasche, M.​ (1994)
    In:​Chui, Charles K.; Montefusco, Laura; Puccio, Luigia​ (Eds.), Wavelets: Theory, Algorithms, and Applications pp. 137​-151. ​San Diego, California: ​Academic Press. DOI: https://doi.org/10.1016/b978-0-08-052084-1.50012-0 
    ​Details  DOI 
  • 1993 | Journal Article
    ​ ​An efficient algorithm for periodic Hermite spline interpolation with shifted nodes​
    Plonka-Hoch, G. ​ (1993) 
    Numerical Algorithms, 5(1) pp. 51​-62​.​ DOI: https://doi.org/10.1007/bf02109283 
    ​Details  DOI 
  • 1993 | Preprint
    ​ ​Nonperiodic Hermite spline interpolation​
    Plonka-Hoch, G. ​ (1993)
    ​Details 
  • 1992 | Journal Article
    ​ ​Efficient Algorithms for Periodic Hermite Spline Interpolation​
    Plonka-Hoch, G.   & Tasche, M.​ (1992) 
    Mathematics of Computation, 58(198) pp. 693​-703​.​ DOI: https://doi.org/10.2307/2153209 
    ​Details  DOI 

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