Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems Export

@article{citeulike:2821748, abstract = {Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ) error term combined with a sparseness-inducing regularization term. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution, and compressed sensing are a few well-known examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems. We test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method. Computational experiments show that these GP approaches perform well in a wide range of applications, often being significantly faster (in terms of computation time) than competing methods. Although the performance of GP methods tends to degrade as the regularization term is de-emphasized, we show how they can be embedded in a continuation scheme to recover their efficient practical performance.}, author = {Figueiredo, M. A. T. and Nowak, R. D. and Wright, S. J.}, booktitle = {Selected Topics in Signal Processing, IEEE Journal of}, citeulike-article-id = {2821748}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/JSTSP.2007.910281}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4407762}, doi = {10.1109/JSTSP.2007.910281}, journal = {Selected Topics in Signal Processing, IEEE Journal of}, keywords = {compressed-sensing}, number = {4}, pages = {586--597}, posted-at = {2009-04-03 18:27:23}, priority = {2}, title = {Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems}, url = {http://dx.doi.org/10.1109/JSTSP.2007.910281}, volume = {1}, year = {2007} }

TY - JOUR ID - citeulike:2821748 L3 - citeulike-article-id:2821748 N2 - Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ) error term combined with a sparseness-inducing regularization term. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution, and compressed sensing are a few well-known examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems. We test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method. Computational experiments show that these GP approaches perform well in a wide range of applications, often being significantly faster (in terms of computation time) than competing methods. Although the performance of GP methods tends to degrade as the regularization term is de-emphasized, we show how they can be embedded in a continuation scheme to recover their efficient practical performance. IS - 4 JF - Selected Topics in Signal Processing, IEEE Journal of EP - 597 TI - Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems VL - 1 T2 - Selected Topics in Signal Processing, IEEE Journal of SP - 586 KW - compressed-sensing AU - Figueiredo, MAT AU - Nowak, RD AU - Wright, SJ PY - 2007/// UR - http://dx.doi.org/10.1109/JSTSP.2007.910281 ER -