Complex Approximate Message Passing Algorithm for Two-Dimensional Compressed Sensing

Akira HIRABAYASHI  Jumpei SUGIMOTO  Kazushi MIMURA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.12   pp.2391-2397
Publication Date: 2013/12/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Image Processing
Keyword: 
compressed sensing,  two-dimensional signal,  approximate message passing,  

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Summary: 
The main target of compressed sensing is recovery of one-dimensional signals, because signals more than two-dimension can also be treated as one-dimensional ones by raster scan, which makes the sensing matrix huge. This is unavoidable for general sensing processes. In separable cases like discrete Fourier transform (DFT) or standard wavelet transforms, however, the corresponding sensing process can be formulated using two matrices which are multiplied from both sides of the target two-dimensional signals. We propose an approximate message passing (AMP) algorithm for the separable sensing process. Typically, we suppose DFT for the sensing process, in which the measurements are complex numbers. Therefore, the formulation includes cases in which both target signal and measurements are complex. We show the effectiveness of the proposed algorithm by computer simulations.