An Improved Fast Iterative Shrinkage Thresholding Algorithm for Image Deblurring

An improved fast iterative shrinkage thresholding algorithm (IFISTA) for image deblurring is proposed. The IFISTA algorithm uses a positive definite weighting matrix in the gradient function of the minimization problem of the known fast iterative shrinkage thresholding (FISTA) image restoration algorithm. A convergence analysis of the IFISTA algorithm shows that due to the weighting matrix, the IFISTA algorithm has an improved convergence rate and improved restoration capability of the unknown image over that of the FISTA algorithm. The weighting matrix is predetermined and fixed, and hence, like the FISTA algorithm, the IFISTA algorithm requires only one matrix vector product operation in each iteration. As a result, the computational burden per iteration of the IFISTA algorithm remains the same as in the FISTA algorithm. Numerical examples are presented that demonstrate the improved performance of the IFISTA algorithm over that of the FISTA and iterative shrinkage thresholding (ISTA) algorithms in terms of the convergence speed and the peak signal-to-noise ratio.