gpeyre/2013-focm-sparsespikes

V. Duval, G. Peyré. Exact Support Recovery for Sparse Spikes Deconvolution. Foundations of Computational Mathematics, 15(5), pp. 1315–1355, 2015.

This toolbox implements the code to generate the figure of the article:

V. Duval, G. Peyré. Exact Support Recovery for Sparse Spikes Deconvolution. Foundations of Computational Mathematics, 15(5), pp. 1315–1355, 2015.

Copyright (c) 2013 Gabriel Peyré

====================== Description

It implements the resolution of the sparse spike deconvolution over measure following the method introduced by Candès and Fernandez-Granda. It also implements the computation of various dual pre-certificates. When these pre-certificate assume values in [-1,1], they are valid certificate and garantees the identifiability of an atomic measure, and also possibly some robustness to noise.

====================== Installation

It requires the CVX toolbox to be installed to work properly.

====================== List of scripts

test_path.m: test the resolution of the Lasso over measure using the SDP lifting. test_certificates.m: first main contribution of the paper, display the various pre-certificates. test_discrete.m: second main contribution of the paper, comparison of the discrete and continuous problems. test_proximal.m : test the resolution of the dual problem using DR proximal splitting.

====================== List of functions

compute_certificate.m: compute various pre-certificates kernel.m: [should not be used, depreciated] compute various kernels load_diracs.m: loads various input measures for tests. perform_lasso.m: solve the finite dimensional L^1 discrete regularization (and its dual) perform_sdp_dual.m: solve the dual problem of the blasso (Lasso over measures) perform_sdp_superresolution.m: solve the primal problem by root finding after solving the primal one. plot_certificates.m: helper function for the display of the pre-certificates. load_helpers.m: load a few helper function for Fourier transform and measurements.

toolbox/ contains useful functions.

Copyright (c) 2013 Gabriel Peyre