Performance Evaluation of Finite Sparse Signals for Compressed Sensing Frameworks

Abstract

SUMMARY In this paper, we consider to develop a recovery algorithm of a sparse signal for a compressed sensing (CS) framework over finite fields. A basic framework of CS for discrete signals rather than continuous signals is established from the linear measurement step to the reconstruction. With predetermined priori distribution of a sparse signal, we reconstruct it by using a message passing algorithm, and evaluate the performance obtained from simulation. We compare our simulation results with the theoretic bounds obtained from probability analysis.

A compressive sensing–based adaptable secure data collection scheme for distributed wireless sensor networks

“…Incidentally, we just take it as a black box, and the detail construction can also utilize the corresponding method in previous studies. [16][17][18][19] Definition 7. Let RecSig(F, y) is a polynomial time algorithm, when inputs parameters (F, y), it outputs signals…”

“…. , x n T 2 Z n 2 be d-spare signal, v be the measurement times to x needed in CS algorithm, it satisfying n ) v (note that we just take CS as a black-box, so the specific relationship among v, d, and n is based on concrete CS algorithm, [16][17][18][19] We need an oracle O to solve LWE with respect to L(G T ) for any error vector in some P 1=2 (q Á B) where B k k = O(1). (The constructions of oracle O can be seen in section 4 in MP12.)…”

“…DM09 16 pointed out that a necessary condition for the successful recovery of all k-sparse signal is m.2k, if more tractable l 1 minimization is used, then the sparse source can still be recovered if m.Cn log (1=), where C is a constant. S18 17 introduced methods of selecting the measure matrix and reconstructing signals, respectively.…”

“…Considering convenience to descript, we give the definition of measure matrix selection algorithm as follow. By the way, we just take it as a black box, and detail construction can utilize the method in previous studies [16][17][18][19] according the specific circumstances. Definition 6.…”

“…. , x n T 2 Z n 2 be d-spare signal, v be the measurement times to x needed in CS algorithm, it satisfying n ) v (note that we just take CS as a black-box, so the specific relationship among v, d, and n is based on concrete CS algorithm, [16][17][18][19] We need a special collection in the ring R = Z q (x)=f (x) and an injective ring homomorphism h : R ! Z l 3 l q (see section 6.1 in MP12).…”