2019/04/03 by Stéphane Chrétien, Andrew Thompson, Chretien, Stephane +3
Mathematics · Engineering · #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1904.01926
We study the problem of super-resolution, where we recover the locations and\nweights of non-negative point sources from a few samples of their convolution\nwith a Gaussian kernel. It has been recently shown that exact recovery is\npossible by minimising the total variation norm of the measure. An alternative\npractical approach is to solve its dual. In this paper, we study the stability\nof solutions with respect to the solutions to the dual problem. In particular,\nwe establish a relationship between perturbations in the dual variable and the\nprimal variables around the optimiser. This is achieved by applying a\nquantitative version of the implicit function theorem in a non-trivial way.\n