Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Digital Signal Processing
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
IEEE Transactions on Image Processing
SIAM Journal on Scientific Computing
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
Sparse representations and sphere decoding for array signal processing
Digital Signal Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
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In compressed sensing, sparse signal reconstruction is a required stage. To find sparse solutions of reconstruction problems, many methods have been proposed. It is time-consuming for some methods when the regularization parameter takes a small value. This paper proposes a decomposition algorithm for sparse signal reconstruction, which is almost insensitive to the regularization parameter. In each iteration, a subproblem or a small quadratic programming problem is solved in our decomposition algorithm. If the extended solution in the current iteration satisfies optimality conditions, an optimal solution to the reconstruction problem is found. On the contrary, a new working set must be selected for constructing the next subproblem. The convergence of the decomposition algorithm is also shown in this paper. Experimental results show that the decomposition method is able to achieve a fast convergence when the regularization parameter takes small values.