Contact: dima dot [LAST NAME] at gmail dot com

### Research areas

- Inverse problems
- Applied harmonic analysis
- Mathematical super-resolution
- Numerical analysis

### Preprints

- R. Katz, G. Giordano, and D. Batenkov, “Data-driven identification of reaction-diffusion dynamics from finitely many non-local noisy measurements by exponential fitting,” Arxiv.2404.09503.

[Bibtex]`@article{katz2024, author = {Katz, Rami and Giordano, Giulia and Batenkov, Dmitry}, date = {2024-04-15}, date-modified = {2024-04-24 11:27:20 -0400}, eprint = {2404.09503}, eprintclass = {math}, eprinttype = {arxiv}, journal = {arXiv.2404.09503}, pubstate = {preprint}, title = {Data-Driven Identification of Reaction-Diffusion Dynamics from Finitely Many Non-Local Noisy Measurements by Exponential Fitting}, url = {http://arxiv.org/abs/2404.09503}, urldate = {2024-04-16}, bdsk-url-1 = {http://arxiv.org/abs/2404.09503}}`

- R. Katz, G. Giordano, and D. Batenkov, “Data-driven Delay Estimation in Reaction-Diffusion Systems via Exponential Fitting,” Preprint.

[Bibtex]`@article{katz2024a, author = {Katz, Rami and Giordano, Giulia and Batenkov, Dmitry}, date = {2024}, date-modified = {2024-04-24 11:27:35 -0400}, journal = {preprint}, pubstate = {preprint}, title = {Data-Driven {{Delay Estimation}} in {{Reaction-Diffusion Systems}} via {{Exponential Fitting}}}, url = {https://giuliagiordano.dii.unitn.it/docs/Katz2024.pdf}, bdsk-url-1 = {https://giuliagiordano.dii.unitn.it/docs/Katz2024.pdf}}`

- R. Katz, N. Diab, and D. Batenkov, “On the accuracy of Prony’s method for recovery of exponential sums with closely spaced exponents,” Arxiv.2302.05883.

[Bibtex]`@article{katz2024b, author = {Katz, Rami and Diab, Nuha and Batenkov, Dmitry}, date = {2024-04-16}, date-modified = {2024-04-24 11:26:49 -0400}, doi = {10.48550/arXiv.2302.05883}, eprint = {2302.05883}, eprintclass = {cs, math}, eprinttype = {arxiv}, journal = {arXiv.2302.05883}, pubstate = {preprint}, title = {On the Accuracy of {{Prony}}'s Method for Recovery of Exponential Sums with Closely Spaced Exponents}, bdsk-url-1 = {https://doi.org/10.48550/arXiv.2302.05883}}`

### Publications

- D. Batenkov and N. Diab, “Super-resolution of generalized spikes and spectra of confluent Vandermonde matrices,” Applied and Computational Harmonic Analysis, vol. 65, 2023.

[Bibtex]`@article{batenkov2022a, author = {Batenkov, Dmitry and Diab, Nuha}, date-added = {2023-04-09 15:26:45 +0300}, date-modified = {2023-04-09 15:26:54 +0300}, doi = {10.1016/j.acha.2023.03.002}, issn = {1063-5203}, journal = {{Applied and Computational Harmonic Analysis}}, keywords = {Confluent Vandermonde matrix,Decimation,Dirac distributions,ESPRIT,Min-max error,Partial Fourier matrix,Smallest singular value,Sparse recovery,Super-resolution}, month = jul, title = {Super-Resolution of Generalized Spikes and Spectra of Confluent {{Vandermonde}} Matrices}, urldate = {2023-03-20}, volume = {65}, year = {2023}, bdsk-url-1 = {https://doi.org/10.1016/j.acha.2023.03.002}}`

- R. Katz, N. Diab, and D. Batenkov, “Decimated Prony’s Method for Stable Super-Resolution,” IEEE Signal Processing Letters, vol. 30, p. 1467–1471, 2023.

[Bibtex]`@article{katz2022, title = {Decimated {{Prony}}'s {{Method}} for {{Stable Super-Resolution}}}, author = {Katz, Rami and Diab, Nuha and Batenkov, Dmitry}, year = {2023}, journal = {{IEEE Signal Processing Letters}}, volume = {30}, pages = {1467--1471}, issn = {1558-2361}, doi = {10.1109/LSP.2023.3324553}, urldate = {2023-10-25}, abstract = {We study recovery of amplitudes and nodes of a finite impulse train from noisy frequency samples. This problem is known as super-resolution under sparsity constraints and has numerous applications. An especially challenging scenario occurs when the separation between Dirac pulses is smaller than the Nyquist-Shannon-Rayleigh limit. Despite large volumes of research and well-established worst-case recovery bounds, there is currently no known computationally efficient method which achieves these bounds in practice. In this work we combine the well-known Prony's method for exponential fitting with a recently established decimation technique for analyzing the super-resolution problem in the above mentioned regime. We show that our approach attains optimal asymptotic stability in the presence of noise, and has lower computational complexity than the current state of the art methods.}, eventtitle = {{{IEEE Signal Processing Letters}}}, }`

- A. Kahana, S. Papadimitropoulos, E. Turkel, and D. Batenkov, “A physically informed deep-learning approach for locating sources in a waveguide,” The Journal of the Acoustical Society of America, vol. 154, iss. 4, p. 2553–2563, 2023.

[Bibtex]`@article{kahana2022, title = {A Physically Informed Deep-Learning Approach for Locating Sources in a Waveguide}, author = {Kahana, Adar and Papadimitropoulos, Symeon and Turkel, Eli and Batenkov, Dmitry}, date = {2023-10-24}, year = {2023}, journal = {{The Journal of the Acoustical Society of America}}, shortjournal = {The Journal of the Acoustical Society of America}, volume = {154}, number = {4}, pages = {2553--2563}, issn = {0001-4966}, doi = {10.1121/10.0021889}, urldate = {2023-10-24}, abstract = {Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the emitted wavelength. In this work we propose a method based on physically informed neural-networks for solving the source refocusing problem, constructing a novel loss term which promotes super-resolving capabilities of the network and is based on the physics of wave propagation. We demonstrate the approach in the setup of imaging an a priori unknown number of point sources in a two-dimensional rectangular waveguide from measurements of wavefield recordings along a vertical cross section. The results show the ability of the method to approximate the locations of sources with high accuracy, even when placed close to each other.}, }`

- D. Batenkov, G. Goldman, and Y. Yomdin, “Super-resolution of near-colliding point sources,” Information and Inference: A Journal of the IMA, vol. 10, iss. 2, p. 515–572, 2021.

[Bibtex]`@article{batenkov2019a, author = {Batenkov, Dmitry and Goldman, Gil and Yomdin, Yosef}, doi = {10.1093/imaiai/iaaa005}, journal = {{Information and Inference: A Journal of the IMA}}, language = {en}, month = jun, number = {2}, pages = {515--572}, publisher = {{Oxford Academic}}, title = {Super-Resolution of near-Colliding Point Sources}, volume = {10}, year = {2021}, bdsk-url-1 = {https://doi.org/10.1093/imaiai/iaaa005}}`

- D. Batenkov, B. Diederichs, G. Goldman, and Y. Yomdin, “The spectral properties of Vandermonde matrices with clustered nodes,” Linear Algebra and its Applications, vol. 609, p. 37–72, 2021.

[Bibtex]`@article{batenkov2019c, author = {Batenkov, Dmitry and Diederichs, Benedikt and Goldman, Gil and Yomdin, Yosef}, doi = {10.1016/j.laa.2020.08.034}, issn = {0024-3795}, journal = {{Linear Algebra and its Applications}}, keywords = {Condition number,Nonuniform Fourier matrices,Singular values,Sub-Rayleigh resolution,Subspace angles,Super-resolution,Vandermonde matrices with nodes on the unit circle}, language = {en}, month = jan, pages = {37--72}, title = {The Spectral Properties of {{Vandermonde}} Matrices with Clustered Nodes}, volume = {609}, year = {2021}, bdsk-url-1 = {https://doi.org/10.1016/j.laa.2020.08.034}}`

- D. Batenkov and G. Goldman, “Single-exponential bounds for the smallest singular value of Vandermonde matrices in the sub-Rayleigh regime,” Applied and Computational Harmonic Analysis, vol. 55, p. 426–439, 2021.

[Bibtex]`@article{batenkov2021b, title = {Single-Exponential Bounds for the Smallest Singular Value of {{Vandermonde}} Matrices in the Sub-{{Rayleigh}} Regime}, author = {Batenkov, Dmitry and Goldman, Gil}, date = {2021-11-01}, year = {2021}, journal = {{Applied and Computational Harmonic Analysis}}, shortjournal = {Applied and Computational Harmonic Analysis}, volume = {55}, pages = {426--439}, issn = {1063-5203}, doi = {10.1016/j.acha.2021.07.003}, urldate = {2021-08-05}, abstract = {Following recent interest by the community, the scaling of the minimal singular value of a Vandermonde matrix with nodes forming clusters on the length scale of Rayleigh distance on the complex unit circle is studied. Using approximation theoretic properties of exponential sums, we show that the decay is only single exponential in the size of the largest cluster, and the bound holds for arbitrary small minimal separation distance. We also obtain a generalization of well-known bounds on the smallest eigenvalue of the generalized prolate matrix in the multi-cluster geometry. Finally, the results are extended to the entire spectrum.}, keywords = {Condition number,Nonuniform Fourier matrices,Singular values,Sub-Rayleigh resolution,Super-resolution,Vandermonde matrices with nodes on the unit circle}, file = {/Users/dima/Zotero/storage/5ZDZTXWV/Batenkov_Goldman_2021_Single-exponential bounds for the smallest singular value of Vandermonde.pdf;/Users/dima/Zotero/storage/GN6YNN3Y/S1063520321000609.html} }`

- D. Batenkov, L. Demanet, G. Goldman, and Y. Yomdin, “Conditioning of Partial Nonuniform Fourier Matrices with Clustered Nodes,” SIAM Journal on Matrix Analysis and Applications, vol. 44, iss. 1, p. 199–220, 2020.

[Bibtex]`@article{batenkov2018v2, author = {Batenkov, Dmitry and Demanet, Laurent and Goldman, Gil and Yomdin, Yosef}, doi = {10/ggjwzb}, issn = {0895-4798}, journal = {{SIAM Journal on Matrix Analysis and Applications}}, month = jan, number = {1}, pages = {199--220}, title = {Conditioning of {{Partial Nonuniform Fourier Matrices}} with {{Clustered Nodes}}}, volume = {44}, year = {2020}, bdsk-url-1 = {https://doi.org/10/ggjwzb}}`

- D. Batenkov, A. Bhandari, and T. Blu, “Rethinking Super-resolution: the Bandwidth Selection Problem,” in ICASSP 2019 – 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, pp. 5087-5091.

[Bibtex]`@inproceedings{batenkov2019b, title = {Rethinking {{Super}}-Resolution: The {{Bandwidth Selection Problem}}}, shorttitle = {Rethinking {{Super}}-Resolution}, booktitle = {{{ICASSP}} 2019 - 2019 {{IEEE International Conference}} on {{Acoustics}}, {{Speech}} and {{Signal Processing}} ({{ICASSP}})}, doi = {10.1109/ICASSP.2019.8683322}, author = {Batenkov, D. and Bhandari, A. and Blu, T.}, month = may, year = {2019}, keywords = {super-resolution,spectral estimation,Sampling theory,sparse deconvolution,bandwidth,sparsity}, pages = {5087-5091} }`

- D. Batenkov, L. Demanet, and H. N. Mhaskar, “Stable soft extrapolation of entire functions,” Inverse Problems, vol. 35, iss. 1, p. 15011, 2019.

[Bibtex]`@article{batenkov2019, author = {Batenkov, Dmitry and Demanet, Laurent and Mhaskar, Hrushikesh N}, doi = {10.1088/1361-6420/aaedde}, issn = {0266-5611, 1361-6420}, journal = {{Inverse Problems}}, language = {en}, month = jan, number = {1}, pages = {015011}, title = {Stable Soft Extrapolation of Entire Functions}, volume = {35}, year = {2019}, bdsk-url-1 = {https://doi.org/10.1088/1361-6420/aaedde}}`

- D. Batenkov, “Stability and super-resolution of generalized spike recovery,” Applied and Computational Harmonic Analysis, vol. 45, iss. 2, pp. 299-323, 2018.

[Bibtex]`@article{batenkov_stability_2016, author = {Batenkov, Dmitry}, doi = {10.1016/j.acha.2016.09.004}, issn = {1063-5203}, journal = {{Applied and Computational Harmonic Analysis}}, keywords = {Spike recovery, Prony system, Numerical conditioning, Super-resolution, Decimation}, month = sep, number = {2}, pages = {299-323}, title = {Stability and Super-Resolution of Generalized Spike Recovery}, volume = {45}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1016/j.acha.2016.09.004}}`

- D. Batenkov and L. Demanet, “Soft extrapolation of bandlimited functions,” in 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2017, pp. 1-5.

[Bibtex]`@inproceedings{batenkov_soft_2017, title = {Soft Extrapolation of Bandlimited Functions}, doi = {10.1109/CAMSAP.2017.8313182}, abstract = {Soft extrapolation refers to the problem of recovering a function from its samples multiplied by a fast-decaying window \textemdash{} in this note a narrow Gaussian. The question is akin to deconvolution, but leverages smoothness of the function in order to achieve stable recovery over an interval potentially larger than the essential support of the window. In case the function is bandlimited, we provide an error bound for extrapolation by a least-squares polynomial fit of a well-chosen degree: it is (morally) proportional to a fractional power of the perturbation level, which goes from 1 near the available samples, to 0 when the extrapolation distance reaches the characteristic smoothness length scale of the function. This bound is minimax in the sense that no algorithm can yield a meaningfully lower error over the same smoothness class. The result in this note can be put in the context of blind superresolution, where it corresponds to the limit of a single spike corrupted by a compactly-supported blur.}, booktitle = {2017 {{IEEE}} 7th {{International Workshop}} on {{Computational Advances}} in {{Multi}}-{{Sensor Adaptive Processing}} ({{CAMSAP}})}, author = {Batenkov, D. and Demanet, L.}, month = dec, year = {2017}, keywords = {Noise measurement,Noise level,Fourier transforms,Signal resolution,Extrapolation,Conferences,Microsoft Windows}, pages = {1-5}, file = {/Users/dima/Zotero/storage/SGPJURJF/Batenkov and Demanet - 2017 - Soft extrapolation of bandlimited functions.pdf;/Users/dima/Zotero/storage/XKHBQ9KL/metrics.html} }`

- D. Batenkov, Y. Romano, and M. Elad, “On the Global-Local Dichotomy in Sparsity Modeling,” in Compressed Sensing and its Applications, Birkhäuser, Cham, 2017, pp. 1-53.

[Bibtex]`@incollection{batenkov_global-local_2017, abstract = {The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches and processes these patches as if they were independent from each other. While producing state-of-the-art results, this methodology is suboptimal, as it does not attempt to model the entire global signal in any meaningful way\textemdash{}a nontrivial task by itself.In this paper we propose a way to bridge this theoretical gap by constructing a global model from the bottom-up. Given local sparsity assumptions in a dictionary, we show that the global signal representation must satisfy a constrained underdetermined system of linear equations, which forces the patches to agree on the overlaps. Furthermore, we show that the corresponding global pursuit can be solved via local operations. We investigate conditions for unique and stable recovery and provide numerical evidence corroborating the theory.}, author = {Batenkov, Dmitry and Romano, Yaniv and Elad, Michael}, booktitle = {Compressed {{Sensing}} and Its {{Applications}}}, doi = {10.1007/978-3-319-69802-1_1}, file = {/Users/dima/Zotero/storage/A7WVT5TR/Batenkov et al. - 2017 - On the Global-Local Dichotoy in Sparsity Modeling.pdf;/Users/dima/Zotero/storage/QVZYI8S7/10.html}, isbn = {978-3-319-69801-4 978-3-319-69802-1}, language = {en}, pages = {1-53}, publisher = {{Birkh{\"a}user, Cham}}, series = {Applied and Numerical Harmonic Analysis}, title = {On the {{Global}}-{{Local Dichotomy}} in {{Sparsity Modeling}}}, year = {2017}, bdsk-url-1 = {https://doi.org/10.1007/978-3-319-69802-1_1}}`

- D. Batenkov, “Accurate solution of near-colliding Prony systems via decimation and homotopy continuation,” Theoretical Computer Science, vol. 681, pp. 27-40, 2017.

[Bibtex]`@article{batenkov_accurate_2014, author = {Batenkov, Dmitry}, doi = {10.1016/j.tcs.2017.03.026}, issn = {0304-3975}, journal = {{Theoretical Computer Science}}, keywords = {Polynomial systems, decimation, Prony system, Homotopy continuation, ESPRIT}, month = jun, pages = {27-40}, series = {Symbolic Numeric Computation}, title = {Accurate Solution of Near-Colliding {{Prony}} Systems via Decimation and Homotopy Continuation}, volume = {681}, year = {2017}, bdsk-url-1 = {https://doi.org/10.1016/j.tcs.2017.03.026}}`

- D. Batenkov and Y. Yomdin, “Taylor domination, Turán lemma, and Poincaré-Perron sequences,” in Contemporary Mathematics, B. Mordukhovich, S. Reich, and A. Zaslavski, Eds., Providence, Rhode Island: American mathematical society, 2016, vol. 659, p. 1–15.

[Bibtex]`@incollection{mordukhovich_taylor_2016, address = {Providence, Rhode Island}, author = {Batenkov, Dmitry and Yomdin, Yosef}, booktitle = {Contemporary {Mathematics}}, doi = {10.1090/conm/659/13162}, editor = {Mordukhovich, Boris and Reich, Simeon and Zaslavski, Alexander}, file = {Batenkov_Yomdin_Taylor Domination, Tur{\'a}n lemma, and Poincar{\'e}-Perron Sequences.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/Z7WU5V63/Batenkov_Yomdin_Taylor Domination, Tura?n lemma, and Poincare?-Perron Sequences.pdf:application/pdf}, isbn = {978-1-4704-1736-9 978-1-4704-2904-1}, language = {en}, owner = {dima}, pages = {1--15}, publisher = {American Mathematical Society}, timestamp = {2016.08.04}, title = {Taylor domination, {Tur{\'a}n} lemma, and {Poincar{\'e}}-{Perron} sequences}, url = {http://dx.doi.org/10.1090/conm/659/13162}, urldate = {2016-04-07}, volume = {659}, year = {2016}, bdsk-url-1 = {http://dx.doi.org/10.1090/conm/659/13162}}`

- D. Batenkov and G. Binyamini, “Uniform upper bounds for the cyclicity of the zero solution of the Abel differential equation,” Journal of Differential Equations, vol. 259, iss. 11, p. 5769–5781, 2015.

[Bibtex]`@article{batenkov_uniform_2015, author = {Batenkov, Dmitry and Binyamini, Gal}, doi = {10.1016/j.jde.2015.07.009}, file = {Batenkov_Binyamini_2015_Uniform upper bounds for the cyclicity of the zero solution of the Abel.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/9M8HT664/Batenkov_Binyamini_2015_Uniform upper bounds for the cyclicity of the zero solution of the Abel.pdf:application/pdf}, issn = {0022-0396}, journal = {{Journal of Differential Equations}}, mrnumber = {3397308}, number = {11}, owner = {dima}, pages = {5769--5781}, timestamp = {2016.08.04}, title = {Uniform upper bounds for the cyclicity of the zero solution of the {Abel} differential equation}, url = {http://www.ams.org/mathscinet-getitem?mr=3397308}, urldate = {2016-08-04}, volume = {259}, year = {2015}, bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=3397308}, bdsk-url-2 = {https://doi.org/10.1016/j.jde.2015.07.009}}`

- D. Batenkov and Y. Yomdin, “Local and Global Geometry of Prony Systems and Fourier Reconstruction of Piecewise-Smooth Functions,” in Operator-Related Function Theory and Time-Frequency Analysis, Springer, 2015, p. 57–76.

[Bibtex]`@incollection{batenkov_local_2015, author = {Batenkov, D. and Yomdin, Y.}, booktitle = {{Operator-Related Function Theory and Time-Frequency Analysis}}, date-modified = {2016-02-01 13:08:38 +0000}, doi = {10.1007/978-3-319-08557-9_2}, file = {Batenkov_Yomdin_2013_Local and global geometry of Prony systems and Fourier reconstruction of.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/56HEPPH7/Batenkov_Yomdin_2013_Local and global geometry of Prony systems and Fourier reconstruction of.pdf:application/pdf;Snapshot:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/WPVSWPC3/978-3-319-08557-9_2.html:text/html}, owner = {dima}, pages = {57--76}, publisher = {Springer}, timestamp = {2014.12.15}, title = {{Local and Global Geometry of Prony Systems and Fourier Reconstruction of Piecewise-Smooth Functions}}, url = {http://link.springer.com/chapter/10.1007/978-3-319-08557-9_2}, urldate = {2014-11-29}, year = {2015}, bdsk-url-1 = {http://link.springer.com/chapter/10.1007/978-3-319-08557-9_2}}`

- D. Batenkov, “Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier Data,” Mathematics of Computation, vol. 84, iss. 295, p. 2329–2350, 2015.

[Bibtex]`@article{batenkov_complete, author = {Batenkov, D.}, date-modified = {2016-02-01 13:07:11 +0000}, doi = {10.1090/S0025-5718-2015-02948-2}, file = {Batenkov_Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/R93HPHEK/Batenkov_Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier.pdf:application/pdf}, journal = {{Mathematics of Computation}}, keywords = {zrread}, number = {295}, owner = {dima}, pages = {2329--2350}, timestamp = {2014.08.20}, title = {{Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier Data}}, url = {http://www.ams.org/mcom/0000-000-00/S0025-5718-2015-02948-2/}, volume = {84}, year = {2015}, bdsk-url-1 = {http://www.ams.org/mcom/0000-000-00/S0025-5718-2015-02948-2/}, bdsk-url-2 = {http://dx.doi.org/10.1090/S0025-5718-2015-02948-2}}`

- D. Batenkov, O. Friedland, and Y. Yomdin, “Sampling, Metric Entropy and Dimensionality Reduction,” SIAM J.Math.Anal., vol. 47, iss. 1, p. 786–796, 2015.

[Bibtex]`@article{batenkov_sampling_2013, author = {Batenkov, D. and Friedland, O. and Yomdin, Y.}, date-modified = {2016-02-01 14:24:36 +0000}, doi = {10.1137/130944436}, file = {arXiv.org Snapshot:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/PP4XKBI4/1308.html:text/html;Batenkov et al_2013_Sampling, Metric Entropy and Dimensionality Reduction.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/V7HBCR9S/Batenkov et al_2013_Sampling, Metric Entropy and Dimensionality Reduction.pdf:application/pdf}, journal = {{SIAM J.Math.Anal.}}, keywords = {{65T40}, {65D15}, Mathematics - Classical Analysis and {ODEs}}, number = {1}, owner = {dima}, pages = {786--796}, timestamp = {2014.02.26}, title = {{Sampling, Metric Entropy and Dimensionality Reduction}}, url = {http://epubs.siam.org/doi/abs/10.1137/130944436}, urldate = {2014-02-26}, volume = {47}, year = {2015}, bdsk-url-1 = {http://arxiv.org/abs/1308.2781}}`

- A. Akinshin, D. Batenkov, and Y. Yomdin, “Accuracy of spike-train Fourier reconstruction for colliding nodes,” in 2015 International Conference on Sampling Theory and Applications (SampTA), 2015, p. 617–621.

[Bibtex]`@InProceedings{akinshin_accuracy_2015, author = {Akinshin, Andrey and Batenkov, Dmitry and Yomdin, Yosef}, title = {{Accuracy of spike-train {Fourier} reconstruction for colliding nodes}}, booktitle = {2015 {International} {Conference} on {Sampling} {Theory} and {Applications} ({SampTA})}, year = {2015}, pages = {617--621}, month = may, abstract = {We consider signal reconstruction problem for signals $F$ of the form $ F(x)=\left(x\right)=\sum_{j=1}^{d}a_{j}\delta\left(x-x_{j}\right),$ from their Fourier transform ${\cal F}(F)(s)=\int_{-\infty}^\infty F(x)e^{-isx}dx.$ We assume ${\cal F}(F)(s)$ to be known for each $s\in [-N,N],$ with an absolute error not exceeding $\epsilon > 0$. We give an {\it absolute lower bound} (which is valid with any reconstruction method) for the ``worst case'' error of reconstruction of $F$ from ${\cal F}(F),$ in situations where the nodes $x_j$ are known to form an $l$ elements cluster of a size $h \ll 1$. Using ``decimation'' algorithm of [6,7] we provide an upper bound for the reconstruction error, essentially of the same form as the lower one. Roughly, our main result states that for $h$ of order $\frac{1}{N}\epsilon ^{\frac{1}{2l-1}}$ the worst case reconstruction error of the cluster nodes is of the same order $\frac{1}{N}\epsilon^{\frac{1}{2l-1}}$, and hence the inside configuration of the cluster nodes (in the worst case scenario) cannot be reconstructed at all. On the other hand, decimation algorithm reconstructs $F$ with the accuracy of order $\frac{1}{N}\epsilon^{\frac{1}{2l}}$.}, bdsk-url-1 = {http://dx.doi.org/10.1109/SAMPTA.2015.7148965}, date-modified = {2016-02-01 14:21:24 +0000}, doi = {10.1109/SAMPTA.2015.7148965}, file = {Akinshin et al_2015_Accuracy of spike-train Fourier reconstruction for colliding nodes.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/9EXEPW7X/Akinshin et al_2015_Accuracy of spike-train Fourier reconstruction for colliding nodes.pdf:application/pdf;IEEE Xplore Abstract Record:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/N9GSC2ZE/articleDetails.html:text/html}, keywords = {Accuracy, Fourier transforms, Geometry, image resolution, Jacobian matrices, Reconstruction algorithms, Signal resolution}, owner = {dima}, timestamp = {2015.07.29} }`

- D. Batenkov, “Prony Systems via Decimation and Homotopy Continuation,” in Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, New York, {NY}, {USA}, 2014, p. 59{–}60.

[Bibtex]`@InProceedings{bat2014snc, author = {Batenkov, Dmitry}, title = {{Prony Systems via Decimation and Homotopy Continuation}}, booktitle = {{Proceedings of the 2014 Symposium on Symbolic-Numeric Computation}}, year = {2014}, series = {{SNC} '14}, pages = {59{\textendash}60}, address = {New York, {NY}, {USA}}, publisher = {{ACM}}, abstract = {We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recently discovered "decimation" technique, we present an algorithm which applies homotopy continuation on a sequence of modified Hankel-type systems as above. In this way, we are able to solve for the nonlinear variables of the original system with high accuracy when the data is perturbed.}, bdsk-url-1 = {http://doi.acm.org/10.1145/2631948.2631961}, bdsk-url-2 = {http://dx.doi.org/10.1145/2631948.2631961}, doi = {10.1145/2631948.2631961}, file = {Batenkov_2014_Prony Systems via Decimation and Homotopy Continuation.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/JKCJ8WHH/Batenkov_2014_Prony Systems via Decimation and Homotopy Continuation.pdf:application/pdf}, isbn = {978-1-4503-2963-7}, keywords = {decimation, Prony systems}, owner = {dima}, timestamp = {2014.08.21}, url = {http://doi.acm.org/10.1145/2631948.2631961}, urldate = {2014-08-13} }`

- D. Batenkov and Y. Yomdin, “Geometry and Singularities of the Prony mapping,” Journal of Singularities, vol. 10, p. 1–25, 2014.

[Bibtex]`@article{batenkov_geometry_2014, author = {Batenkov, Dmitry and Yomdin, Yosef}, date-modified = {2016-02-01 13:33:10 +0000}, doi = {10.5427/jsing.2014.10a}, file = {Batenkov_Yomdin_2014_Geometry and Singularities of the Prony mapping.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/UTEDMNA2/Batenkov_Yomdin_2014_Geometry and Singularities of the Prony mapping.pdf:application/pdf;Journal of Singularities | Volume 10:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/QRBWTHZD/article1.html:text/html}, issn = {19492006}, journal = {{Journal of Singularities}}, owner = {dima}, pages = {1--25}, timestamp = {2014.12.25}, title = {{Geometry and Singularities of the Prony mapping}}, url = {http://www.journalofsing.org/volume10/article1.html}, urldate = {2014-12-25}, volume = {10}, year = {2014}, bdsk-url-1 = {http://www.journalofsing.org/volume10/article1.html}, bdsk-url-2 = {http://dx.doi.org/10.5427/jsing.2014.10a}}`

- D. Batenkov, N. Sarig, and Y. Yomdin, “Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals,” Sampling Theory in Signal and Image Processing, vol. 13, iss. 2, p. 151–173, 2014.

[Bibtex]`@article{batenkov_accuracy_2014, author = {Batenkov, Dmitry and Sarig, Niv and Yomdin, Yosef}, date-modified = {2016-02-01 14:16:06 +0000}, file = {arXiv.org Snapshot:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/TV4PJS45/1311.html:text/html;Batenkov et al_2013_Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/U94DQS48/Batenkov et al_2013_Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals.pdf:application/pdf}, journal = {{Sampling Theory in Signal and Image Processing}}, keywords = {94A20, 65T40, Mathematics - Classical Analysis and {ODEs}}, number = {2}, owner = {dima}, pages = {151--173}, timestamp = {2015.01.06}, title = {{Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals}}, url = {http://stsip.org/pdf/vol13/vol13no2pp151-173.pdf}, urldate = {2014-02-26}, volume = {13}, year = {2014}, bdsk-url-1 = {http://stsip.org/pdf/vol13/vol13no2pp151-173.pdf}}`

- Y. Yomdin, D. Batenkov, and N. Sarig, “Decoupling of Fourier Reconstruction System for Shifts of Several Signals,” in 10th international conference on Sampling Theory and Applications (SampTA 2013), Bremen, Germany, 2013, pp. 580-583.

[Bibtex]`@InProceedings{sampta13niv, author = {Yosef Yomdin and Dmitry Batenkov and Niv Sarig}, title = {{Decoupling of Fourier Reconstruction System for Shifts of Several Signals}}, booktitle = {{10th international conference on Sampling Theory and Applications (SampTA 2013)}}, year = {2013}, pages = {580-583}, address = {Bremen, Germany}, month = jul, abstract = {We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals $f\_1,\ldots,f\_k$ from the Fourier samples. For each $r=1,\ldots,k$ we choose sampling set $S\_r$ to be a subset of the common set of zeroes of the Fourier transforms ${\cal F}(f\_\l), \ \l \ne r$, on which ${\cal F}(f\_r)\ne 0$. We show that in this way the reconstruction system is reduced to $k$ separate systems, each including only one of the signals $f\_r$. Each of the resulting systems is of a ``generalized Prony'' form. We discuss the problem of unique solvability of such systems, and provide some examples.}, days = {1}, keywords = {Shifts of signals; Fourier samples; Prony system, decoupling, non-uniform sampling}, owner = {dima}, timestamp = {2016.08.04} }`

- D. Batenkov, V. Golubyatnikov, and Y. Yomdin, “Reconstruction of Planar Domains from Partial Integral Measurements,” Contemporary Mathematics, vol. 591, pp. 51-66, 2013.

[Bibtex]`@article{planar_domains, author = {Batenkov, D. and Golubyatnikov, V. and Yomdin, Y.}, date-modified = {2016-02-01 14:23:37 +0000}, doi = {10.1090/conm/591/11826}, journal = {{Contemporary Mathematics}}, owner = {dmitryb}, pages = {51-66}, timestamp = {2012.03.11}, title = {{Reconstruction of Planar Domains from Partial Integral Measurements}}, volume = {591}, year = {2013}, bdsk-url-1 = {https://doi.org/10.1090/conm/591/11826}}`

- D. Batenkov and Y. Yomdin, “On the accuracy of solving confluent Prony systems,” SIAM J. Appl. Math., vol. 73, iss. 1, p. 134–154, 2013.

[Bibtex]`@article{batenkov2011accuracy, author = {Batenkov, D. and Yomdin, Y.}, date-modified = {2016-02-01 13:09:44 +0000}, doi = {10.1137/110836584}, journal = {{SIAM J. Appl. Math.}}, number = {1}, owner = {dima}, pages = {134--154}, timestamp = {2012.10.24}, title = {{On the accuracy of solving confluent Prony systems}}, volume = {73}, year = {2013}, bdsk-url-1 = {https://doi.org/10.1137/110836584}}`

- D. Batenkov and Y. Yomdin, “Algebraic signal sampling, Gibbs phenomenon and Prony-type systems,” in 10th international conference on Sampling Theory and Applications (SampTA 2013), Bremen, Germany, 2013, pp. 137-140.

[Bibtex]`@InProceedings{sampta13_bat, author = {Dmitry Batenkov and Yosef Yomdin}, title = {{Algebraic signal sampling, Gibbs phenomenon and Prony-type systems}}, booktitle = {{10th international conference on Sampling Theory and Applications (SampTA 2013)}}, year = {2013}, pages = {137-140}, address = {Bremen, Germany}, month = jul, abstract = {Systems of Prony type appear in various reconstruction problems such as finite rate of innovation, superresolution and Fourier inversion of piecewise smooth functions. By keeping the number of equations small and fixed, we demonstrate that such {"}decimation{"} can lead to practical improvements in the reconstruction accuracy. As an application, we provide a solution to the so-called Eckhoff's conjecture, which asked for reconstructing jump positions and magnitudes of a piecewise-smooth function from its Fourier coefficients with maximal possible asymptotic accuracy -- thus eliminating the Gibbs phenomenon.}, days = {1}, keywords = {Algebraic sampling; Gibbs phenomenon; superresolution; Prony system}, owner = {dima}, timestamp = {2016.08.04} }`

- D. Batenkov and Y. Yomdin, “Taylor Domination, Difference Equations, and Bautin Ideals,” in Difference Equations, Discrete Dynamical Systems and Applications, L. A. i Soler, J. M. Cushing, S. Elaydi, and A. A. Pinto, Eds., Springer Berlin Heidelberg, 2012, pp. 303-319.

[Bibtex]`@incollection{batenkov_taylor_2014, author = {Batenkov, Dmitry and Yomdin, Yosef}, booktitle = {Difference {{Equations}}, {{Discrete Dynamical Systems}} and {{Applications}}}, copyright = {\textcopyright{}2016 Springer-Verlag Berlin Heidelberg}, doi = {10.1007/978-3-662-52927-0_21}, editor = {i Soler, Llu\'is Alsed\`a and Cushing, Jim M. and Elaydi, Saber and Pinto, Alberto A.}, isbn = {978-3-662-52926-3 978-3-662-52927-0}, keywords = {Difference and Functional Equations, Discrete Mathematics, Complex Systems, Statistical Physics and Dynamical Systems, Recurrence relations, Bautin ideals, Domination of initial Taylor coefficients}, language = {en}, month = jul, number = {180}, pages = {303-319}, publisher = {{Springer Berlin Heidelberg}}, series = {Springer Proceedings in Mathematics \& Statistics}, title = {Taylor {{Domination}}, {{Difference Equations}}, and {{Bautin Ideals}}}, year = {2012}, bdsk-url-1 = {https://doi.org/10.1007/978-3-662-52927-0_21}}`

- D. Batenkov and Y. Yomdin, “Algebraic Fourier reconstruction of piecewise smooth functions,” Mathematics of Computation, vol. 81, p. 277–318, 2012.

[Bibtex]`@article{batyom_alg_fourier, adsnote = {Provided by the SAO/NASA Astrophysics Data System}, adsurl = {http://adsabs.harvard.edu/abs/2010arXiv1005.1884B}, archiveprefix = {arXiv}, author = {Batenkov, D. and Yomdin, Y.}, date-modified = {2016-02-01 13:05:00 +0000}, doi = {10.1090/S0025-5718-2011-02539-1}, eprint = {1005.1884}, journal = {{Mathematics of Computation}}, keywords = {Mathematics - Classical Analysis and ODEs, 65T40 (Primary), 65D15 (Secondary)}, owner = {Dima}, pages = {277--318}, timestamp = {2010.12.10}, title = {{Algebraic Fourier reconstruction of piecewise smooth functions}}, url = {http://dx.doi.org/10.1090/S0025-5718-2011-02539-1}, volume = {81}, year = {2012}, bdsk-url-1 = {http://dx.doi.org/10.1090/S0025-5718-2011-02539-1}}`

- D. Batenkov, G. Dinkin, and Y. Yomdin, “Automatic animation of high resolution images,” in 2012 IEEE 27th Convention of Electrical Electronics Engineers in Israel (IEEEI), 2012, p. 1–5.

[Bibtex]`@InProceedings{batenkov_automatic_2012, author = {Batenkov, D. and Dinkin, G. and Yomdin, Y.}, title = {{Automatic animation of high resolution images}}, booktitle = {2012 {IEEE} 27th {Convention} of {Electrical} {Electronics} {Engineers} in {Israel} ({IEEEI})}, year = {2012}, pages = {1--5}, month = nov, abstract = {In the report, we present a novel photo-animation method and an animation tool for transformation of a photo into an animated video clip. In opposite to the existing tools, our technology provides both automatic and intuitive interactive photo-animation of high-resolution images. Our method and technology comprise the following main components: 1. Vectorization of the image, i.e. its representation by the sets of primitive structures (geometric models) in different scales. 2. 3D-2D global scale kinematic models for various image objects, especially, for the patterns of human bodies. These models allow an adaptation to definite parameters of the patterns and provide a high visual quality of motions' reproduction, including relatively large 3D rotations. 3. Tools and methods for translation of true 3D motion (like various scenarios of human 3D motion appearing in the Carnegie Mellon University database) into 2.5D animation. 4. Tools and methods for real-time automatic fitting of the models to image objects. In the course of fitting, specific anatomic parameters of the pattern are detected and preserved. The suggested method starts with face detection and model fitting, and then extends up to a full body pose capturing and model fitting. Our approach strongly relies on information provided by a vectorized image data, like the geometry of the edges and ridges and their color profiles, and on the transformations of 3D and 2D models. 5. High level scenarios and their automatic adaptation to the actual position of the characters in the photo. The presented technology is illustrated by several examples. Links to more running examples and to our on-line Photoanimation tool are provided.}, doi = {10.1109/EEEI.2012.6376903}, file = {Batenkov et al_2012_Automatic animation of high-resolution images.pdf:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/VE3ETQGV/Batenkov et al_2012_Automatic animation of high-resolution images.pdf:application/pdf;IEEE Xplore Abstract Record:/Users/dima/Library/Application Support/Zotero/Profiles/pvpguanx.default/zotero/storage/DSUFX5GJ/login.html:text/html}, keywords = {2.5D animation, 3D-2D global scale kinematic models, 3D motion, 3D rotations, animated video clip, Animation, automatic photo-animation, Carnegie Mellon University database, color profiles, Computational modeling, computer animation, face detection, face recognition, Fitting, full body pose capturing, geometric modeling, geometric models, Geometry, high resolution images, high visual quality, human bodies, Humans, image colour analysis, image objects, image processing, image resolution, image vectorization, intuitive interactive photo-animation, Minimization, model fitting, motions reproduction, photoanimation, primitive structures, realtime automatic fitting, Skeleton, Solid modeling}, owner = {dima}, timestamp = {2016.08.04} }`

- D. Batenkov and G. Binyamini, “Moment Vanishing of Piecewise Solutions of Linear ODEs,” in Difference Equations, Discrete Dynamical Systems and Applications, L. A. i Soler, J. M. Cushing, S. Elaydi, and A. A. Pinto, Eds., Springer Berlin Heidelberg, 2012, pp. 15-28.

[Bibtex]`@incollection{batenkov2013moment, author = {Batenkov, Dmitry and Binyamini, Gal}, booktitle = {Difference {{Equations}}, {{Discrete Dynamical Systems}} and {{Applications}}}, copyright = {\textcopyright{}2016 Springer-Verlag Berlin Heidelberg}, doi = {10.1007/978-3-662-52927-0_2}, editor = {i Soler, Llu\'is Alsed\`a and Cushing, Jim M. and Elaydi, Saber and Pinto, Alberto A.}, isbn = {978-3-662-52926-3 978-3-662-52927-0}, keywords = {Difference and Functional Equations, Discrete Mathematics, Complex Systems, Statistical Physics and Dynamical Systems, Recurrence relations, Moment vanishing, Holonomic ODEs, Generalised exponential sums}, language = {en}, month = jul, number = {180}, pages = {15-28}, publisher = {{Springer Berlin Heidelberg}}, series = {Springer Proceedings in Mathematics \& Statistics}, title = {Moment {{Vanishing}} of {{Piecewise Solutions}} of {{Linear ODEs}}}, year = {2012}, bdsk-url-1 = {https://doi.org/10.1007/978-3-662-52927-0_2}}`

- D. Batenkov, N. Sarig, and Y. Yomdin, “An “algebraic” reconstruction of piecewise-smooth functions from integral measurements,” Functional Differential Equations, vol. 19, iss. 1-2, p. 13–30, 2012.

[Bibtex]`@article{batenkov_fde, author = {Batenkov, D. and Sarig, N. and Yomdin, Y.}, date-modified = {2016-02-01 13:05:29 +0000}, journal = {{Functional Differential Equations}}, number = {1-2}, owner = {dmitryb}, pages = {13--30}, timestamp = {2012.03.11}, title = {{An ``algebraic" reconstruction of piecewise-smooth functions from integral measurements}}, volume = {19}, year = {2012}}`

- D. Batenkov, “Open BEAGLE: a generic framework for evolutionary computations,” Genetic Programming and Evolvable Machines, pp. 1-3, 2011.

[Bibtex]`@article{genetic_beagle, affiliation = {Weizmann Institute of Science, Rehovot, Israel}, author = {Batenkov, Dmitry}, date-modified = {2016-02-01 13:18:33 +0000}, doi = {10.1007/s10710-011-9135-4}, issn = {1389-2576}, journal = {{Genetic Programming and Evolvable Machines}}, keyword = {Computer Science}, note = {10.1007/s10710-011-9135-4}, owner = {dima}, pages = {1-3}, publisher = {Springer Netherlands}, timestamp = {2011.04.01}, title = {{Open BEAGLE: a generic framework for evolutionary computations}}, url = {http://dx.doi.org/10.1007/s10710-011-9135-4}, year = {2011}, bdsk-url-1 = {http://dx.doi.org/10.1007/s10710-011-9135-4}}`

- D. Batenkov, “Moment inversion problem for piecewise D-finite functions,” Inverse Problems, vol. 25, iss. 10, p. 105001, 2009.

[Bibtex]`@article{bat2008, author = {D. Batenkov}, date-modified = {2016-02-01 13:09:02 +0000}, doi = {10.1088/0266-5611/25/10/105001}, journal = {{Inverse Problems}}, month = {October}, number = {10}, owner = {Dima}, pages = {105001}, timestamp = {2010.12.10}, title = {{Moment inversion problem for piecewise D-finite functions}}, url = {http://iopscience.iop.org/0266-5611/25/10/105001/}, volume = {25}, year = {2009}, bdsk-url-1 = {http://iopscience.iop.org/0266-5611/25/10/105001/}, bdsk-url-2 = {http://dx.doi.org/10.1088/0266-5611/25/10/105001}}`

- D. Batenkov, N. Sarig, and Y. Yomdin, “An “algebraic” reconstruction of piecewise-smooth functions from integral measurements,” in Proc. of Sampling Theory and Applications (SAMPTA), 2009.

[Bibtex]`@InProceedings{batenkov2009arp, author = {D. Batenkov and N. Sarig and Y. Yomdin}, title = {{An ``algebraic'' reconstruction of piecewise-smooth functions from integral measurements}}, booktitle = {{Proc. of Sampling Theory and Applications (SAMPTA)}}, year = {2009}, abstract = {This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier coef cients, Radon transform, etc.). Our results concern reconstruction (from the moments) of signals in two special classes: linear combinations of shifts of a given function, and ``piecewise $D$-finite functions'' which satisfy on each continuity interval a linear differential equation with polynomial coefficients.}, comment = {Arxiv preprint arXiv:0901.4659}, date-modified = {2016-02-01 14:41:26 +0000}, owner = {dima}, timestamp = {2013.04.15}, url = {https://hal.archives-ouvertes.fr/hal-00452200} }`