2020/07/06 by Stéphane Chrétien, Andrew Thompson, Chrétien, Stéphane +3
Computer Science · Engineering · Mathematics · #Advanced Image Processing Techniques #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2007.02708
openalex publication_date 2020/07/06 · openalex created_date 2023/07/07 · openalex updated_date 2026/07/28
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 shown that exact recovery is possible by\nminimising the total variation norm of the measure, and a practical way of\nachieve this is by solving the dual problem. In this paper, we study the\nstability of solutions with respect to the solutions dual problem, both in the\ncase of exact measurements and in the case of measurements with additive noise.\nIn particular, we establish a relationship between perturbations in the dual\nvariable and perturbations in the primal variable around the optimiser and a\nsimilar relationship between perturbations in the dual variable around the\noptimiser and the magnitude of the additive noise in the measurements. Our\nanalysis is based on a quantitative version of the implicit function theorem.\n