Abstract
<abstract> <p>The greedy block Kaczmarz (GBK) method has been successfully applied in areas such as data mining, image reconstruction, and large-scale image restoration. However, the computation of pseudo-inverses in each iterative step of the GBK method not only complicates the computation and slows down the convergence rate, but it is also ill-suited for distributed implementation. The leverage score sampling free pseudo-inverse GBK algorithm proposed in this paper demonstrated significant potential in the field of image reconstruction. By ingeniously transforming the problem framework, the algorithm not only enhanced the efficiency of processing systems of linear equations with multiple solution vectors but also optimized specifically for applications in image reconstruction. A methodology that combined theoretical and experimental approaches has validated the robustness and practicality of the algorithm, providing valuable insights for technical advancements in related disciplines.</p> </abstract>
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