NDLI: Sparse non-negative signal reconstruction using fraction function penalty

Content Provider	IET Digital Library
Author	Cui, Angang Peng, Jigen Li, Haiyang Wen, Meng
Abstract	Many practical problems in the real world can be formulated as the non-negative ℓ 0 -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 ℓ 0 -minimisation problem is non-deterministic polynomial hard (NP-hard) because of the discrete and discontinuous nature of the ℓ 0 -norm. Inspired by the good performances of the fraction function in the authors’ former work, in this paper, the authors replace the ℓ 0 -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 ℓ 0 -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 ℓ 0 -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.
Starting Page	125
Ending Page	132
Page Count	8
ISSN	17519675
Volume Number	13
e-ISSN	17519683
Issue Number	Issue 2, Apr (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/13/2
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2018.5056
Journal	IET Signal Processing
Publisher Date	2018-08-29
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Computational Complexity Computer Vision Fraction Function Penalty Image Processing Interpolation And Function Approximation Iterative Method Learning in AI Machine Learning Minimisation Nonconvex Fraction Function Nonnegative Fraction Function Minimisation Problem Nonnegative Iterative Thresholding Nonnegative Signal Recovery Problem NP-hard Numerical Analysis Optimisation Technique Pattern Recognition Signal Processing Signal Processing And Detection Signal Processing Theory Signal Reconstruction Sparse Nonnegative Signal Reconstruction Underdetermined Linear Equation
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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