Past Minisymposium Stability of Moment Problems and Super-Resolution Imaging
Algebraic techniques have proven useful in different imaging tasks such as spike reconstruction (single molecule microscopy), phase retrieval (X-ray crystallography), and contour reconstruction (natural images). The available data typically consists of (trigonometric) moments of low to moderate order and one asks for the reconstruction of fine details modeled by zero- or positive-dimensional algebraic varieties. Often, such reconstruction problems have a generically unique solution when the number of data is larger than the degrees of freedom in the model.
Beyond that, the minisymposium concentrates on simple a-priori conditions to guarantee that the reconstruction problem is well or only mildly ill conditioned. For the reconstruction of points on the complex torus, popular results ask the order of the moments to be larger than the inverse minimal distance of the points. Moreover, simple and efficient eigenvalue based methods achieve this stability numerically in specific settings. Recently, the situation of clustered points, points with multiplicities, and positive-dimensional algebraic varieties have been studied by similar methods and shall be discussed within the minisymposium.
Dmitry Batenkov (MIT Boston). Introductory talk: stability of moment problems and super-resolution imaging Dominik Nagel (University Osnabrueck). The condition number of Vandermonde matrices with clustered nodes Gil Goldman (Weizmann Institute). Clustered Super-Resolution Yosef Yomdin (Weizmann Institute). Geometry of Error Amplification in Spike-train Fourier Reconstruction Ayush Bhandari (Imperial College London). Non-ideal Super-resolution and Variations on a Theme Tomas Sauer (University Passau). Generalized convolutions and Hankel operatorsMarkus Wageringel (University Osnabrueck). Reconstruction of generalized exponential sumsRobert Beinert (University Graz). Phase retrieval of sparse continuous-time signals by Prony's methodAlisha Zachariah (UW Madison). Sparse FFT, (RADAR) Channel Estimation and the Heisenberg Group Annie Cuyt (University Antwerpen), Wen-shin Lee (University of Stirling). Multidimensional Superresolution in Sonar and Radar ImagingMathews Jacob (University of Iowa). Recovery of surfaces and inference on surfaces: theory & applications to image recoveryMartin Vetterli, Pan Hanjie (EPFL). Looking beyond Pixels: Continuous-domain Sparse Recovery with an Application to Radioastronomy
Past Workshop on Mathematical Signal and Image Analysis