An inner–outer iterative method for edge preservation in image restoration and reconstruction
An inner–outer iterative method for edge preservation in image restoration and reconstruction
复制标题
DOI：
10.1088/1361-6420/abb299
复制
发表时间：
2019-12
期刊：
影响因子：
2.1
通讯作者：
S. Gazzola;M. Kilmer;J. Nagy;O. Semerci;E. Miller
中科院分区：
文献类型：
--
作者：
S. Gazzola;M. Kilmer;J. Nagy;O. Semerci;E. Miller
提出了一种新的图像边缘增强的内外迭代算法。在每一次外部迭代中，我们制定了一个Tikhonov正则化问题，其中惩罚以两个范数表示，并涉及一个正则化算子，该算子旨在通过自适应过程，随着外部迭代的进展，提高边缘分辨率。一种有效的混合正则化方法被用来将Tikhonov正则化问题投影到增加维度的近似子空间（内部迭代）上，同时方便地选择正则化参数（通过将众所周知的技术，例如差异原理或L曲线准则应用于投影问题）。该过程导致用于边缘恢复的自动化算法，其不涉及用户的正则化参数调整，也不重复调用复杂的优化算法，因此从计算的角度来看特别有吸引力。新算法成功的关键是通过使用自适应对角加权矩阵来设计正则化算子，该自适应对角加权矩阵仅在需要时有效地执行平滑。我们证明了我们的方法在X射线CT图像重建和图像去模糊中的应用价值，并表明它可以在计算上比其他知名的边缘保护策略更具吸引力，同时提供更高或相等质量的解决方案。
We present a new inner–outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the two-norm and involves a regularization operator designed to improve edge resolution as the outer iterations progress, through an adaptive process. An efficient hybrid regularization method is used to project the Tikhonov-regularized problem onto approximation subspaces of increasing dimensions (inner iterations), while conveniently choosing the regularization parameter (by applying well-known techniques, such as the discrepancy principle or the L -curve criterion, to the projected problem). This procedure results in an automated algorithm for edge recovery that does not involve regularization parameter tuning by the user, nor repeated calls to sophisticated optimization algorithms, and is therefore particularly attractive from a computational point of view. A key to the success of the new algorithm is the design of the regularization operator through the use of an adaptive diagonal weighting matrix that effectively enforces smoothness only where needed. We demonstrate the value of our approach on applications in x-ray CT image reconstruction and in image deblurring, and show that it can be computationally much more attractive than other well-known strategies for edge preservation, while providing solutions of greater or equal quality.