Sparse non-negative signal reconstruction using fraction function penalty

Many practical problems in the real world can be formulated as the non-negative $\ell _0$ℓ0-minimisation problems, which seek the sparsest non-negative signals to underdetermined linear equations. They have been widely applied in signal and image processing, machine learning, pattern recognition and...

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Veröffentlicht in:IET signal processing Jg. 13; H. 2; S. 125 - 132
Hauptverfasser: Cui, Angang, Peng, Jigen, Li, Haiyang, Wen, Meng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: The Institution of Engineering and Technology 01.04.2019
Schlagworte:
computational complexity
computer vision
fraction function penalty
image processing
iterative methods
learning (artificial intelligence)
machine learning
minimisation
nonconvex fraction function
nonnegative fraction function minimisation problem
nonnegative iterative thresholding
nonnegative signal recovery problems
NP‐hard
pattern recognition
Research Article
signal processing
signal reconstruction
sparse nonnegative signal reconstruction
underdetermined linear equations
image processing
iterative methods
NP-hard
nonnegative iterative thresholding
signal processing
nonnegative signal recovery problems
machine learning
fraction function penalty
nonnegative fraction function minimisation problem
computer vision
underdetermined linear equations
signal reconstruction
sparse nonnegative signal reconstruction
minimisation
learning (artificial intelligence)
nonconvex fraction function
computational complexity
pattern recognition
ISSN:1751-9675, 1751-9683, 1751-9683
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Beschreibung
Zusammenfassung:Many practical problems in the real world can be formulated as the non-negative $\ell _0$ℓ0-minimisation problems, which seek the sparsest non-negative signals to underdetermined linear equations. They have been widely applied in signal and image processing, machine learning, pattern recognition and computer vision. Unfortunately, this non-negative $\ell _0$ℓ0-minimisation problem is non-deterministic polynomial hard (NP-hard) because of the discrete and discontinuous nature of the $\ell _0$ℓ0-norm. Inspired by the good performances of the fraction function in the authors’ former work, in this paper, the authors replace the $\ell _0$ℓ0-norm with the non-convex fraction function and study the minimisation problem of the fraction function in recovering the sparse non-negative signal from an underdetermined linear equation. They discuss the equivalence between non-negative $\ell _0$ℓ0-minimisation problem and non-negative fraction function minimisation problem, and the equivalence between non-negative fraction function minimisation problem and regularised non-negative fraction function minimisation problem. It is proved that the optimal solution to the non-negative $\ell _0$ℓ0-minimisation problem could be approximately obtained by solving their regularised non-negative fraction function minimisation problem if some specific conditions are satisfied. Then, they propose a non-negative iterative thresholding algorithm to solve their regularised non-negative fraction function minimisation problem. At last, numerical experiments on some sparse non-negative signal recovery problems are reported.
ISSN:1751-9675
1751-9683
1751-9683
DOI:10.1049/iet-spr.2018.5056