Abstract
Inspired by the fast iterative shrinkage-thresholding algorithm (FISTA), a tail-FISTA method based on the tail-ℓ1 minimization is proposed and analyzed for sparse signal recoveries. Solutions using the profile and the direct methods are both derived. It is also shown that the tail-FISTA method has the convergence rate of O(1/n2) for a given support index T. The tail-FISTA is therefore a much more efficient technique solving the tail-ℓ1 minimization problem than the usual basis pursuit solutions. The superior performance is also demonstrated through extensive numerical simulations in comparison with state-of-the-art algorithms. As an example, for A∈R64×128, traditional algorithms may recovery signals up to sparsity s≤15, while the tail-FISTA can recovery signals with sparsity s≤25. An image restoration/deblurring application is also studied among other techniques to demonstrate the effectiveness of the tail-FISTA technique.
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