2017/07/03 by Brett Bernstein, Bernstein, Brett, Carlos Fernandez‐Granda +1
Engineering · #Sparse and Compressive Sensing Techniques #Photoacoustic and Ultrasonic Imaging #Microwave Imaging and Scattering Analysis
paper · pdf · doi:10.48550/arxiv.1707.00808
In this work we analyze a convex-programming method for estimating\nsuperpositions of point sources or spikes from nonuniform samples of their\nconvolution with a known kernel. We consider a one-dimensional model where the\nkernel is either a Gaussian function or a Ricker wavelet, inspired by\napplications in geophysics and imaging. Our analysis establishes that\nminimizing a continuous counterpart of the \ℓ1 norm achieves exact\nrecovery of the original spikes as long as (1) the signal support satisfies a\nminimum-separation condition and (2) there are at least two samples close to\nevery spike. In addition, we derive theoretical guarantees on the robustness of\nthe approach to both dense and sparse additive noise.\n