High-Quality Recovery of Non-Sparse Signals from Compressed Sensing — Beyond <I>l</I><SUB>1</SUB> Norm Minimization —

Akira HIRABAYASHI; Norihito INAMURO; Aiko NISHIYAMA; Kazushi MIMURA

doi:10.1587/transfun.E98.A.1880

High-Quality Recovery of Non-Sparse Signals from Compressed Sensing — Beyond l₁ Norm Minimization —

Akira HIRABAYASHI, Norihito INAMURO, Aiko NISHIYAMA, Kazushi MIMURA

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We propose a novel algorithm for the recovery of non-sparse, but compressible signals from linear undersampled measurements. The algorithm proposed in this paper consists of two steps. The first step recovers the signal by the l₁-norm minimization. Then, the second step decomposes the l₁ reconstruction into major and minor components. By using the major components, measurements for the minor components of the target signal are estimated. The minor components are further estimated using the estimated measurements exploiting a maximum a posterior (MAP) estimation, which leads to a ridge regression with the regularization parameter determined using the error bound for the estimated measurements. After a slight modification to the major components, the final estimate is obtained by combining the two estimates. Computational cost of the proposed algorithm is mostly the same as the l₁-nom minimization. Simulation results for one-dimensional computer generated signals show that the proposed algorithm gives 11.8% better results on average than the l₁-norm minimization and the lasso estimator. Simulations using standard images also show that the proposed algorithm outperforms those conventional methods.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.9 pp.1880-1887

Publication Date: 2015/09/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E98.A.1880

Type of Manuscript: Special Section PAPER (Special Section on Signal Processing for Sensing and Diagnosis)

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Authors

Akira HIRABAYASHI
  Ritsumeikan University
Norihito INAMURO
  Ritsumeikan University
Aiko NISHIYAMA
  Ritsumeikan University
Kazushi MIMURA
  Hiroshima City University

Keyword

sparse signals, compressible signals, compressed sensing, l₁-norm minimization, lasso

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Akira HIRABAYASHI, Norihito INAMURO, Aiko NISHIYAMA, Kazushi MIMURA, "High-Quality Recovery of Non-Sparse Signals from Compressed Sensing — Beyond l1 Norm Minimization —" in IEICE TRANSACTIONS on Fundamentals, vol. E98-A, no. 9, pp. 1880-1887, September 2015, doi: 10.1587/transfun.E98.A.1880.
Abstract: We propose a novel algorithm for the recovery of non-sparse, but compressible signals from linear undersampled measurements. The algorithm proposed in this paper consists of two steps. The first step recovers the signal by the l₁-norm minimization. Then, the second step decomposes the l₁ reconstruction into major and minor components. By using the major components, measurements for the minor components of the target signal are estimated. The minor components are further estimated using the estimated measurements exploiting a maximum a posterior (MAP) estimation, which leads to a ridge regression with the regularization parameter determined using the error bound for the estimated measurements. After a slight modification to the major components, the final estimate is obtained by combining the two estimates. Computational cost of the proposed algorithm is mostly the same as the l₁-nom minimization. Simulation results for one-dimensional computer generated signals show that the proposed algorithm gives 11.8% better results on average than the l₁-norm minimization and the lasso estimator. Simulations using standard images also show that the proposed algorithm outperforms those conventional methods.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.1880/_p

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@ARTICLE{e98-a_9_1880,
author={Akira HIRABAYASHI, Norihito INAMURO, Aiko NISHIYAMA, Kazushi MIMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={High-Quality Recovery of Non-Sparse Signals from Compressed Sensing — Beyond l1 Norm Minimization —},
year={2015},
volume={E98-A},
number={9},
pages={1880-1887},
abstract={We propose a novel algorithm for the recovery of non-sparse, but compressible signals from linear undersampled measurements. The algorithm proposed in this paper consists of two steps. The first step recovers the signal by the l₁-norm minimization. Then, the second step decomposes the l₁ reconstruction into major and minor components. By using the major components, measurements for the minor components of the target signal are estimated. The minor components are further estimated using the estimated measurements exploiting a maximum a posterior (MAP) estimation, which leads to a ridge regression with the regularization parameter determined using the error bound for the estimated measurements. After a slight modification to the major components, the final estimate is obtained by combining the two estimates. Computational cost of the proposed algorithm is mostly the same as the l₁-nom minimization. Simulation results for one-dimensional computer generated signals show that the proposed algorithm gives 11.8% better results on average than the l₁-norm minimization and the lasso estimator. Simulations using standard images also show that the proposed algorithm outperforms those conventional methods.},
keywords={},
doi={10.1587/transfun.E98.A.1880},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - High-Quality Recovery of Non-Sparse Signals from Compressed Sensing — Beyond l1 Norm Minimization —
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1880
EP - 1887
AU - Akira HIRABAYASHI
AU - Norihito INAMURO
AU - Aiko NISHIYAMA
AU - Kazushi MIMURA
PY - 2015
DO - 10.1587/transfun.E98.A.1880
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2015
AB - We propose a novel algorithm for the recovery of non-sparse, but compressible signals from linear undersampled measurements. The algorithm proposed in this paper consists of two steps. The first step recovers the signal by the l₁-norm minimization. Then, the second step decomposes the l₁ reconstruction into major and minor components. By using the major components, measurements for the minor components of the target signal are estimated. The minor components are further estimated using the estimated measurements exploiting a maximum a posterior (MAP) estimation, which leads to a ridge regression with the regularization parameter determined using the error bound for the estimated measurements. After a slight modification to the major components, the final estimate is obtained by combining the two estimates. Computational cost of the proposed algorithm is mostly the same as the l₁-nom minimization. Simulation results for one-dimensional computer generated signals show that the proposed algorithm gives 11.8% better results on average than the l₁-norm minimization and the lasso estimator. Simulations using standard images also show that the proposed algorithm outperforms those conventional methods.
ER -