A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Gradient Method with Retards and Generalizations
SIAM Journal on Numerical Analysis
Relaxed Steepest Descent and Cauchy-Barzilai-Borwein Method
Computational Optimization and Applications
A New Active Set Algorithm for Box Constrained Optimization
SIAM Journal on Optimization
Algorithm 890: Sparco: A Testing Framework for Sparse Reconstruction
ACM Transactions on Mathematical Software (TOMS)
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
IEEE Transactions on Image Processing
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
Bregman operator splitting with variable stepsize for total variation image reconstruction
Computational Optimization and Applications
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The convergence rate is analyzed for the sparse reconstruction by separable approximation (SpaRSA) algorithm for minimizing a sum $f(\mathbf{x})+\psi(\mathbf{x})$, where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that if $f$ is convex, then the error in the objective function at iteration $k$ is bounded by $a/k$ for some $a$ independent of $k$. Moreover, if the objective function is strongly convex, then the convergence is $R$-linear. An improved version of the algorithm based on a cyclic version of the BB iteration and an adaptive line search is given. The performance of the algorithm is investigated using applications in the areas of signal processing and image reconstruction.