Stable Image Reconstruction Algorithm Based on Resilient Total Variation Minimization

In image reconstruction, traditional total variation (TV) regularization often incurs staircase artifacts and compromises image contrast. In this work, we refine the total variation framework by incorporating a non-convex penalty function alongside a backward diffusion mechanism; on this basis, we propose a resilient total variation (RTV)–based image reconstruction model. First, to mitigate staircase artifacts, the proposed approach enhances the robustness of TV regularization by incorporating the transformed l_1 non-convex penalty functions, which improve the model’s adherence to the Restricted Isometry Property (RIP). Second, to mitigate contrast loss in the reconstructed image and suppress noise, a backward diffusion mechanism is incorporated into the model to ensure smoothness in homogeneous regions. Subsequently, based on the RIP conditions, we derive theoretical guarantees for the stable reconstruction of the RTV image reconstruction model. The developed model is solved using a combination scheme of DC (difference of convex functions) programming and the alternating direction multiplier method, yielding an efficient resilient total variation-based reconstruction algorithm. Extensive experiments on standard, natural, and medical images validate the method’s efficacy. The results demonstrate that the proposed approach achieves superior reconstruction quality in comparison to the state-of-the-art methods, particularly in under-sampled and noisy scenarios, highlighting its effectiveness, efficiency, and practical utility.