Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothed l0 Norm

The smoothed l0 norm algorithm is a reconstruction algorithm in compressive sensing based on approximate smoothed l0 norm. It introduces a sequence of smoothed functions to approximate the l0 norm and approaches the solution using the specific iteration process with the steepest method. In order to...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014, Vol.2014 (2014), p.1-9
Main Authors: Fang, Xiao-Feng, Zhang, Jiang-She, Li, Ying-Qi
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Heuristic
Hyperbolic functions
Mathematical analysis
Mathematical models
Mathematical problems
Norms
Optimization
Sequences
Signal quality
Signal reconstruction
Sparsity
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Summary:The smoothed l0 norm algorithm is a reconstruction algorithm in compressive sensing based on approximate smoothed l0 norm. It introduces a sequence of smoothed functions to approximate the l0 norm and approaches the solution using the specific iteration process with the steepest method. In order to choose an appropriate sequence of smoothed function and solve the optimization problem effectively, we employ approximate hyperbolic tangent multiparameter function as the approximation to the big “steep nature” in l0 norm. Simultaneously, we propose an algorithm based on minimizing a reweighted approximate l0 norm in the null space of the measurement matrix. The unconstrained optimization involved is performed by using a modified quasi-Newton algorithm. The numerical simulation results show that the proposed algorithms yield improved signal reconstruction quality and performance.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/416542