Discrete Signal Reconstruction by Sum of Absolute Values

Author

Nagahara, Masaaki

Author_Institution

Grad. Sch. of Inf., Kyoto Univ., Kyoto, Japan

Volume

22

Issue

10

fYear

2015

fDate

Oct. 2015

Firstpage

1575

Lastpage

1579

Abstract

In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the reconstruction is exponential as it is. To overcome this difficulty, we extend the idea of compressed sensing, and propose to solve the problem by minimizing the sum of weighted absolute values. We assume that the probability distribution defined on an alphabet is known, and formulate the reconstruction problem as linear programming. Examples are shown to illustrate that the proposed method is effective.

Keywords

compressed sensing; computational complexity; linear programming; signal reconstruction; statistical distributions; compressed sensing; computational complexity; discrete signal reconstruction; finite alphabet; incomplete linear measurement; linear programming; probability distribution; sum of absolute values; Compressed sensing; Computational complexity; Image reconstruction; Optimization; Probability distribution; Signal reconstruction; Vectors; Compressed sensing; digital signals; discrete signal reconstruction; sparse optimization; sum of absolute values;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2015.2414932

Filename

7064695