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    基于弹性全变分最小化的稳定图像重建算法

    Stable Image Reconstruction Algorithm Based on Resilient Total Variation Minimization

    • 摘要: 在图像重建领域,传统的全变分(total variation,TV)会导致重建图像出现阶梯效应和对比度损失. 针对此问题,利用非凸罚函数对TV进行改进并引入后向扩散处理机制,基于此,提出一种基于弹性全变分的图像重建模型. 首先,为了克服重建图像的阶梯效应,用变形l_1非凸罚函数对TV进行改进,以此加强模型对约束等距性质(restricted isometry property,RIP)的鲁棒性. 其次,为了降低重建图像的对比度损失并抑制噪声,通过在模型中引入后向扩散处理机制,以便保证图像均匀区域的平滑性. 然后,基于RIP条件推导了模型稳定重建的理论保证. 最后,联合DC(difference of convex functions)规划和交替方向乘子法对模型进行求解,基于此进一步提出一个基于弹性全变分的图像重建方法. 为了验证所提出方法的有效性、高效性和实用性,分别使用标准图像、自然图像和医学图像进行重建实验. 实验结果表明,与已有方法相比,所提出方法在欠采样场景和噪声环境中的重建质量均有不同程度的改善和提高.

       

      Abstract: 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.

       

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