Mohsin Yasir Q, Ongie Gregory, Jacob Mathews
IEEE Trans Med Imaging. 2015 Dec;34(12):2417-28. doi: 10.1109/TMI.2015.2398466. Epub 2015 Jan 30.
We introduce a fast iterative shrinkage algorithm for patch-smoothness regularization of inverse problems in medical imaging. This approach is enabled by the reformulation of current non-local regularization schemes as an alternating algorithm to minimize a global criterion. The proposed algorithm alternates between evaluating the denoised inter-patch differences by shrinkage and computing an image that is consistent with the denoised inter-patch differences and measured data. We derive analytical shrinkage rules for several penalties that are relevant in non-local regularization. The redundancy in patch comparisons used to evaluate the shrinkage steps are exploited using convolution operations. The resulting algorithm is observed to be considerably faster than current alternating non-local algorithms. The proposed scheme is applicable to a large class of inverse problems including deblurring, denoising, and Fourier inversion. The comparisons of the proposed scheme with state-of-the-art regularization schemes in the context of recovering images from undersampled Fourier measurements demonstrate a considerable reduction in alias artifacts and preservation of edges.
我们介绍了一种用于医学成像中逆问题的补丁平滑正则化的快速迭代收缩算法。这种方法是通过将当前的非局部正则化方案重新表述为一种交替算法来最小化全局准则来实现的。所提出的算法在通过收缩评估去噪后的补丁间差异与计算与去噪后的补丁间差异和测量数据一致的图像之间交替进行。我们推导了几种在非局部正则化中相关惩罚的解析收缩规则。用于评估收缩步骤的补丁比较中的冗余通过卷积运算来利用。结果表明，所得算法比当前的交替非局部算法快得多。所提出的方案适用于一大类逆问题，包括去模糊、去噪和傅里叶反演。在从欠采样傅里叶测量中恢复图像的背景下，将所提出的方案与最先进的正则化方案进行比较，结果表明混叠伪影显著减少且边缘得以保留。
