Enhanced FISTA for Non-Blind Image Deblurring

The image deblurring problem is an active area of research in image processing. The Fast Iterative Shrinkage Thresholding Algorithm (FISTA) has garnered significant attention for solving deblurring problems with $l_{1}$– based sparsity constraints. This paper proposes a new $l_{1}$– based algorithm called Enhanced FISTA (EFISTA) that incorporates accelerated gradient descent and an appropriate proximal operation. We have studied the impact of accelerated gradient descent in noisy conditions, which helps us identify the importance of a well-designed proximal operation to mitigate noise interference. The experimental results show that EFISTA exhibits superior execution speed while maintaining reconstruction performance comparable to its predecessors. This highlights the robustness and efficiency of EFISTA in addressing image deblurring challenges, particularly at high noise levels.