Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) for Image Deblurring

This document discusses the implementation of Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) for solving image deblurring problems. The implementation includes several MATLAB m-files that demonstrate the core algorithm components and an instructional document written by Amir Beck. FISTA provides an efficient optimization framework for image restoration by combining proximal gradient methods with acceleration techniques. The algorithm works through iterative updates that combine gradient descent steps with shrinkage/thresholding operations to handle non-smooth regularization terms. Key implementation aspects include: - Main optimization loop with Nesterov acceleration for faster convergence - Proximal operator implementations for various regularization types - Gradient computation for different blur kernel models - Convergence criteria and stopping conditions By utilizing FISTA, we can effectively address image blurring issues, significantly improving image clarity and quality. The method iteratively approaches the optimal solution through accelerated gradient steps, effectively removing blur and noise from images. The instructional document by Amir Beck provides comprehensive guidance on proper implementation techniques and parameter selection, enabling users to effectively apply this method to their own image deblurring challenges.