SPB

This is a collection of MATLAB codes to reproduce all figures in the paper "The springback penalty for robust signal recovery" by Congpei An, Hao-Ning Wu, and Xiaoming Yuan, which is published with DOI j.acha.2022.07.002.

This collection consists of one demo and three folders. To reproduce the figures in the mentioned paper, one may need the MATLAB Parallel Computing Toolbox. If this toolbox is unavailable, one may need to replace all command "parfor" with "for".

Just run the demo to see how the springback-penalized model works!

functions

The folder entitled "functions" contains subroutines that implement sparse optimization models, including

• ADMM_L1.m for the unconstrained L1 model solved by ADMM
• DCA_L12.m for the unconstrained L1-L2 model solved by DCA+ADMM
• DCA_MCP.m for the unconstrained MCP model solved by DCA+ADMM
• DCA_SPB.m for the unconstrained springback model solved by DCA+ADMM
• DCA_SPBconstrained.m for the constrained springback model solved by DCA+ADMM
• DCA_SPBconstrainednoisy.m for the constrained springback model (with noisy measurements) solved by DCA+ADMM

Reproducing

The folder entitled "Reproducing" contains codes for reproducing all figures in the mentioned paper, including

• plotshrinkage.m: Fig. 1
• safeguardedalpha.m: Fig. 2
• groundtruth.m: Figs. 3 and 6
• noisefreetestonRIPmatrices.m: Fig. 4
• noisefreetestonoverDCT.m: Fig. 5
• noisytestonRIPandoverDCT.m: Fig .7
• numericalverification.m: Fig.8

Besides these scripts, there are eponymous MATLAB functions with the suffix "forPC". For executing for-loop iterations in parallel on MATLAB, the body of the parfor-loop should be independent and be implemented by a single subroutine. Thus, such a body is defined by those "forPC" functions, where "PC" stands for parallel computing.

Utilities

The zip file entitled "Utilities" contains codes written by other researchers, to whom the credit must go. Please unzip it and add it to path first. These codes are available online.

• DCATL1-master: Transformed L1-related codes

  Zhang, S., & Xin, J. (2018). Minimization of transformed L1 penalty: theory, difference of convex function algorithm, and robust application in compressed sensing. Mathematical Programming, 169(1), 307-336.

  Codes available at https://github.com/zsivine/DCATL1.

• IRucLq: IRLS-Lp-related codes

  Lai, M. J., Xu, Y., & Yin, W. (2013). Improved iteratively reweighted least squares for unconstrained smoothed \ell_q minimization. SIAM Journal on Numerical Analysis, 51(2), 927-957.

  Codes available at https://xu-yangyang.github.io/codes/IRucLq.zip

• sparsify_0_5: AIHT-related codes

  Blumensath, T., & Davies, M. E. (2009). Iterative hard thresholding for compressed sensing. Applied and computational harmonic analysis, 27(3), 265-274.

  Codes available at http://www.personal.soton.ac.uk/tb1m08/sparsify/sparsify_0_5.zip.

• POR: for projection onto the ball $|x|_2\leq\tau$

  The Proximity Operator Repository http://proximity-operator.net/