11-magic : Recovery of sparse signals via convex programming

For maximum computational efficiency, the solvers for each of the seven problems are implemented separately. They all have the same basic structure, however, with the computational bottleneck being the calculation of the Newton step (this is discussed in detail below). The code can be used in either “small scale” mode, where the system is constructed explicitly and solved exactly, or in “large scale” mode, where an iterative matrix-free algorithm such as conjugate gradients (CG) is used to approximately solve the system.

[1]  M. Saunders,et al.  Solution of Sparse Indefinite Systems of Linear Equations , 1975 .

[2]  J. Shewchuk An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

[3]  Stephen J. Wright Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[4]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[5]  Gene H. Golub,et al.  A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration , 1999, SIAM J. Sci. Comput..

[6]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[7]  James Renegar,et al.  A mathematical view of interior-point methods in convex optimization , 2001, MPS-SIAM series on optimization.

[8]  Donald Goldfarb,et al.  Second-order cone programming , 2003, Math. Program..

[9]  G. Stadler,et al.  AN INFEASIBLE PRIMAL-DUAL ALGORITHM FOR TV-BASED INF-CONVOLUTION-TYPE IMAGE RESTORATION , 2004 .

[10]  Wotao Yin,et al.  Second-order Cone Programming Methods for Total Variation-Based Image Restoration , 2005, SIAM J. Sci. Comput..

[11]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[12]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[13]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

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

[15]  Emmanuel J. Candès,et al.  Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions , 2004, Found. Comput. Math..

[16]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[17]  Terence Tao,et al.  The Dantzig selector: Statistical estimation when P is much larger than n , 2005, math/0506081.