A modified reconstruction algorithm for compressed sensing with least square residual

L1-norm based solver has been successfully used for sparse signal reconstruction in compressed sensing. In the paper, we propose a modified method to boost the decoding performance with least-square residual for L1 algorithms. A further performance improvement is obtained by applying iteratively reweighted L1 minimization for sparsity pattern detection. Numerical experiments show that both the proposed methods lead to a better sparsity-measurement tradeoff than their benchmark algorithms.

[1]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.

[2]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[3]  Yonina C. Eldar,et al.  Structured Compressed Sensing: From Theory to Applications , 2011, IEEE Transactions on Signal Processing.

[4]  Namrata Vaswani,et al.  LS-CS-Residual (LS-CS): Compressive Sensing on Least Squares Residual , 2009, IEEE Transactions on Signal Processing.

[5]  Stephen J. Wright,et al.  Sparse Reconstruction by Separable Approximation , 2008, IEEE Transactions on Signal Processing.

[6]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[7]  Cristiano Jacques Miosso,et al.  Compressive Sensing Reconstruction With Prior Information by Iteratively Reweighted Least-Squares , 2009, IEEE Transactions on Signal Processing.

[8]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[9]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[10]  Gordon Erlebacher,et al.  A New Reweighted Algorithm With Support Detection for Compressed Sensing , 2012, IEEE Signal Processing Letters.

[11]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[12]  Stephen J. Wright,et al.  Computational Methods for Sparse Solution of Linear Inverse Problems , 2010, Proceedings of the IEEE.