NDLI: Sparse signal recovery via minimax-concave penalty and ℓ1-norm loss function

Content Provider	IET Digital Library
Author	Sun, Yuli Chen, Hao Tao, Jinxu
Abstract	In sparse signal recovery, to overcome the ℓ 1 -norm sparse regularisation's disadvantages tendency of uniformly penalise the signal amplitude and underestimate the high-amplitude components, a new algorithm based on a non-convex minimax-concave penalty is proposed, which can approximate the ℓ 0 -norm more accurately. Moreover, the authors employ the ℓ 1 -norm loss function instead of the ℓ 2 -norm for the residual error, as the ℓ 1 -loss is less sensitive to the outliers in the measurements. To rise to the challenges introduced by the non-convex non-smooth problem, they first employ a smoothed strategy to approximate the ℓ 1 -norm loss function, and then use the difference-of-convex algorithm framework to solve the non-convex problem. They also show that any cluster point of the sequence generated by the proposed algorithm converges to a stationary point. The simulation result demonstrates the authors’ conclusions and indicates that the algorithm proposed in this study can obviously improve the reconstruction quality.
Starting Page	1091
Ending Page	1098
Page Count	8
ISSN	17519675
Volume Number	12
e-ISSN	17519683
Issue Number	Issue 9, Dec (2018)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/12/9
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2018.5130
Journal	IET Signal Processing
Publisher Date	2018-07-17
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Approximation Theory Cluster Point Concave Programming Difference-of-convex Algorithm Framework High-amplitude Component Interpolation And Function Approximation Minimax Technique Nonconvex Minimax-concave Penalty Nonconvex Nonsmooth Problem Nonconvex Problem Numerical Analysis Optimisation Technique Reconstruction Quality Signal Amplitude Signal Processing And Detection Signal Processing Theory Signal Reconstruction Sparse Signal Recovery ℓ1-norm Loss Function ℓ1-norm Sparse Regularisation
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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