Name
Title | ||
|---|---|---|
A Convergence Analysis For Iterative Sparsification Projection With Soft-Thresholding |
Abstract | ||
|---|---|---|
The recently proposed iterative sparsification projection (ISP), a fast and robust sparse signal recovery algorithm framework, can be classified as smooth-ISP and nonsmooth-ISP. However, no convergence analysis has been established for the nonsmooth-ISP in the previous works. Motivated by this absence, the present paper provides a convergence analysis for ISP with soft-thresholding (ISP-soft) which is an instance of the nonsmooth-ISP. In our analysis, the composite operator of soft-thresholding and proximal projection is viewed as a fixed point mapping, whose nonexpansiveness plays a key role. Specifically, our convergence analysis for the sequence generated by ISP-soft can be summarized as follows: 1) For each inner loop, we prove that the sequence has a unique accumulation point which is a fixed point, and show that it is a Cauchy sequence; 2) for the last inner loop, we prove that the accumulation point of the sequence is a critical point of the objective function if the final value of the threshold satisfies a condition, and show that the corresponding objective values are monotonically nonincreasing. A numerical experiment is given to validate some of our results and intuitively present the convergence. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1007/s11760-021-01910-9 | SIGNAL IMAGE AND VIDEO PROCESSING |
Keywords | DocType | Volume |
Convergence, Iterative sparsification projection, Fixed point mapping | Journal | 15 |
Issue | ISSN | Citations |
8 | 1863-1703 | 0 |
PageRank | References | Authors |
0.34 | 0 | 1 |