Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography
Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography
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DOI：
10.1109/83.660997
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发表时间：
1998-02-01
影响因子：
10.6
通讯作者：
Bresler, Y
中科院分区：
文献类型：
--
作者：
Delaney, AH;Bresler, Y
我们介绍了最近提出的确定性松弛算法的线性反问题的边缘保持正则化的推广。这种最近提出的算法将原始（可能非凸）优化问题转化为一系列二次优化问题，并且已经证明在某些条件下收敛，当被最小化的原始成本泛函是严格凸的时，我们证明了我们更一般的算法是全局收敛的（即，收敛到一个局部最小值）。我们将该算法应用于有限角度数据的层析重建，将问题转化为正则化最小二乘优化问题。结果表明，通过使用边缘保持正则化，可以提供出色的有限角度断层重建。两个边缘保持正则化器-一个凸的，其他非凸的-在大量的模拟中使用，以证明该算法在各种有限的角度场景下的有效性，并探讨如何因素，如选择的误差范数，角度采样率和噪声量，影响重建质量和算法性能，这些模拟结果表明，对于这种应用程序，非凸正则化器产生一致的上级的结果。
We introduce a generalization of a recently proposed deterministic relaxation algorithm for edge-preserving regularization in linear inverse problems. This recently proposed algorithm transforms the original (possibly nonconvex) optimization problem into a sequence of quadratic optimization problems, and has been shown to converge under certain conditions when the original cost functional being minimized is strictly convex, We prove that our more general algorithm is globally convergent (i.e., converges to a local minimum from any initialization) under less restrictive conditions, even when the original cost functional is nonconvex, We apply this algorithm to tomographic reconstruction from limited-angle data by formulating the problem as one of regularized least-squares optimization, The results demonstrate that the constraint of piecewise smoothness, applied through the use of edge-preserving regularization, can provide excellent limited-angle tomographic reconstructions. Two edge-preserving regularizers-one convex, the other nonconvex-are used in numerous simulations to demonstrate the effectiveness of the algorithm under various limited-angle scenarios, and to explore how factors, such as choice of error norm, angular sampling rate and amount of noise, affect reconstruction quality and algorithm performance, These simulation results show that for this application, the nonconvex regularizer produces consistently superior results.