Accelerating Overrelaxed and Monotone Fast Iterative Shrinkage-Thresholding Algorithms With Line Search for Sparse Reconstructions

Recently, specially crafted unidimensional optimization has been successfully used as line search to accelerate the overrelaxed and monotone fast iterative shrinkage-threshold algorithm (OMFISTA) for computed tomography. In this paper, we extend the use of fast line search to the monotone fast iterative shrinkage-threshold algorithm (MFISTA) and some of its variants. Line search can accelerate the FISTA family considering typical synthesis priors, such as the ℓ
₁
-norm of wavelet coefficients, as well as analysis priors, such as anisotropic total variation. This paper describes these new MFISTA and OMFISTA with line search, and also shows through numerical results that line search improves their performance for tomographic high-resolution image reconstruction.