"Sparse super resolution and its trigonometric approximation in microscopy"Hockmann, MathiasMotivated by applications in single molecule light microscopy (SMLM), this talk deals with the recovery of discrete or singular continuous measures on $[0,1)^d$ from their trigonometric moments. We set up simple estimates by trigonometric polynomials and prove pointwise and weak convergence as the number of known moments increases. On the theoretical side, we show that the optimal weak convergence rate measured in the Wasserstein-1-distance is inversely proportional to the degree of the polynomial and that this rate is achieved by our algorithm. As a practical experiment, we apply our method to large scale SMLM data. This is joint work with Paul Catala, Stefan Kunis and Markus Wageringel. |
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