Optimal transport problem has gained much attention in image processing field, such as computer vision, image interpolation and medical image registration. In this paper, we incorporate optimal transport into linear inverse problems as a regularization technique. We establish a new variational model based on Benamou-Brenier energy to regularize the evolution path from a template to latent image dynamically. The initial state of the continuity equation can be regarded as a template, which can provide priors for the reconstructed images. Also, we analyze the existence of solutions of such variational problem in Radon measure space. Moreover, the first-order primal-dual algorithm is constructed for solving this general imaging problem in a special grid strategy. Finally, numerical experiments for undersampled MRI reconstruction are presented which show that our proposed model can recover images well with high quality and structure preservation.

翻译：最佳传输问题在图像处理领域,如计算机视觉、图像内插和医学图像登记等,引起了人们的极大关注。在本文中,我们将最佳传输作为一种正规化技术,纳入线性反问题中。我们建立了以Benamu-Brenier能源为基础的新的变异模型,以便对从模板到潜在图像的进化路径进行动态规范。连续性方程式的初始状态可以被视为一个模板,可为重建后的图像提供前缀。此外,我们还分析了Radon测量空间中存在这种变异问题的解决办法。此外,为了在特殊的网格战略中解决这一一般成像问题,还建立了第一级初等双轨算法。最后,介绍了对未经过取样的MRI重建进行的数字实验,这些实验表明,我们提议的模型可以恢复高品质和结构保护的图像。</s>