Weighted Minimization For Sparse Signal Recovery Under Multiple Prior Support Information

Compressive sensing?CS? can acquire sparse signals effectively through a small num-ber of nonadaptive linear measurements,which provides a new sampling method.It breaks through the limitations of the traditional Shannon sampling theorem.In this paper,we mainly study the recovery performance of weighted ?_p-minimization for signal recovery and weighted ?₁-minimization for phaseless compressed sensing when multiple prior support in-formation is available.The first chapter introduces the research background and some preliminaries of com-pressed sensing,and introduces the main results and the symbols used in this work.In Chapter 2,we study the performance of reconstructing sparse signals from com-pressed sampling measurement by using weighted ?_p-minimization when the prior informa-tion is obtained in the form of support estimation,weighted ?_p-minimization of recovery conditions and related recovery guarantees.This setting can be used when there are multi-ple estimates for signal support and these estimates have varying degrees of accuracy.Our analysis extends the existing work,assuming that only a constant weight is used.At the same time,the advantage of using non-uniform weight in reconstruction is analyzed.In Chapter 3,we study the weighted ?₁-minimization restoration condition for recon-struction of real signal from phaseless compressed sensing data when some supporting in-formation is available.A strong restricted isometry?SRIP?condition is proposed to ensure stable restoration.