國立東華大學應用數學系

專    題    演    講

主講人：許瑞麟

                       成功大學數學系

講  題：On RIC bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using l q Quasi Norms

時  間：103 年 05月 16 日 (星期五)  15: 20-16:50

地  點：理工一館 A324 會議室

大   綱

This talk follows the recent discussion on the sparse solution recovery with quasi-norms lq , q ∈ (0, 1) when the sensing matrix possesses a Restricted Isom- etry Constant δ2k (RIC). Our key tool is an improvement on a version of “the converse of a generalized Cauchy-Schwarz inequality” extended to the setting of quasi-norm. We show that, if δ2k ≤ 1/2, any minimizer of the lq minimization, at least for those lq ∈ (0, 0.9181], is the sparse solution of the corresponding un- derdetermined linear system. Moreover, if δ2k ≤ 0.4931, the sparse solution can be recovered by any lq , q ∈ (0, 1] minimization. The values 0.9181 and 0.4931 improve those reported previously in the literature.

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