Department of Applied Mathematics
My general research area is inverse problems and computational science. A major effort is invested in the problem of super-resolution, with applications to wave-based imaging at nanometer scale below the diffraction limit using prior knowledge, elimination of spurious artifacts, with provable guarantees. Theoretical aspects include deriving mathematical limits of resolution from noisy low-frequency data under different kinds of prior information, using tools from approximation theory, harmonic, nonlinear analysis, optimization and quantitative singularity theory. We also develop novel optimal computational methods, by identifying and localizing well-conditioned geometric features which can be stably recovered. Current collaborations with experts in bio-medical and super-resolution imaging, time-of-flight imaging.
- ISF 1793/20 (2020-2024), 225,000€: Super-resolution and computational inverse problems: hybrid modeling, performance bounds, and algorithms
- Research Cooperation Lower Saxony-Israel (2020-2023), 286,300€: Stability of Moment Problems and Super- Resolution Imaging
- Batenkov, D.; Goldman, G. Single-Exponential Bounds for the Smallest Singular Value of Vandermonde Matrices in the Sub-Rayleigh Regime. Applied and Computational Harmonic Analysis 2021, 55, 426–439. https://doi.org/10.1016/j.acha.2021.07.003.
- D. Batenkov, G. Goldman, and Y. Yomdin, "Super-resolution of near-colliding point sources," Information and Inference: A Journal of the IMA, p. iaaa005, May 2020, doi: 10.1093/imaiai/iaaa005.
- 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), May 2019, pp. 5087–5091. doi: 10.1109/ICASSP.2019.8683322.
- D. Batenkov, "Complete algebraic reconstruction of piecewise-smooth functions from Fourier data," Math. Comp., vol. 84, no. 295, pp. 2329–2350, 2015, doi: 10.1090/S0025-5718-2015-02948-2.