Krylov Subspace Based FISTA‐Type Methods for Linear Discrete Ill‐Posed Problems

Several iterative soft-thresholding algorithms, such as FISTA, have been proposed in the literature for solving regularized linear discrete inverse problems that arise in various applications in science and engineering. These algorithms are easy to implement, but their rates of convergence may be slow. This paper describes novel approaches to reduce the computations required for each iteration by using Krylov subspace techniques. Specifically, we propose to impose sparsity on the coefficients in the representation of the computed solution in terms of a Krylov subspace basis. Several numerical examples from image deblurring and computerized tomography are used to illustrate the efficiency and accuracy of the proposed methods.