Efficient image reconstruction via regularized variable s-step conjugate gradient method for Sylvester matrix equations

Abstract

In image and signal processing, one or more transformations are applied to the desired image (signal), and the original image (signal) should be reconstructed by reversing these transformations. One important equation for modeling image (signal) processing problems is the Sylvester matrix equation, which modifies the image by applying two transformations on both sides. In this paper, we introduce an algorithm for solving the Sylvester matrix equation based on the conjugate gradient algorithm. This algorithm employs the $s$-step technique to reduce communication overhead and aims to enhance its performance by adjusting the $s$ parameter during the iterations. Since the algorithm can become unstable with a sudden increase in $s$, this instability is addressed through the use of mapped regularization filters. Finally, the effectiveness and efficiency of the algorithm are evaluated using several numerical examples.