Sparse Signal Recovery via Tail-FISTA

We propose tail fast iterative shrinkage-thresholding algorithm (tail-FISTA) to solve compressed sensing problem, and it considers fast iterative shrinkage-thresholding algorithm (FISTA) method to solve tail- ℓ
1
minimization problem. By means of the profile method, the tail- ℓ
1
minimization problem is rewritten as a transformed ordinary ℓ
1
minimization problem, and its solution can be obtained by FISTA. FISTA is attractive due to the computational simplicity and well global rate of convergence rate O(1/n
²
). In simulation study, the performance of numerical examples is better than traditional compressed sensing algorithms. From the application of tail-FISTA, we can find that tail-FISTA is a potential compressed sensing algorithm.