IEICE TRANSACTIONS on Fundamentals
Complex Approximate Message Passing Algorithm for Two-Dimensional Compressed Sensing
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.12 pp.2391-2397
- Publication Date
- 2013/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E96.A.2391
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Image Processing
Authors
Akira HIRABAYASHI
Ritsumeikan University
Jumpei SUGIMOTO
Yamaguchi University
Kazushi MIMURA
Hiroshima City University
Keyword
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Akira HIRABAYASHI, Jumpei SUGIMOTO, Kazushi MIMURA, "Complex Approximate Message Passing Algorithm for Two-Dimensional Compressed Sensing" in IEICE TRANSACTIONS on Fundamentals,
vol. E96-A, no. 12, pp. 2391-2397, December 2013, doi: 10.1587/transfun.E96.A.2391.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.2391/_p
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@ARTICLE{e96-a_12_2391,
author={Akira HIRABAYASHI, Jumpei SUGIMOTO, Kazushi MIMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Complex Approximate Message Passing Algorithm for Two-Dimensional Compressed Sensing},
year={2013},
volume={E96-A},
number={12},
pages={2391-2397},
abstract={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.},
keywords={},
doi={10.1587/transfun.E96.A.2391},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Complex Approximate Message Passing Algorithm for Two-Dimensional Compressed Sensing
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2391
EP - 2397
AU - Akira HIRABAYASHI
AU - Jumpei SUGIMOTO
AU - Kazushi MIMURA
PY - 2013
DO - 10.1587/transfun.E96.A.2391
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2013
AB - 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.
ER -
English
