Minimizing L 1 over L 2 norms on the gradient
Minimizing L 1 over L 2 norms on the gradient
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DOI：
10.1088/1361-6420/ac64fb
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发表时间：
2021-01
期刊：
影响因子：
2.1
通讯作者：
Chao Wang;M. Tao;Chen-Nee Chuah;J. Nagy;Y. Lou
中科院分区：
文献类型：
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作者：
Chao Wang;M. Tao;Chen-Nee Chuah;J. Nagy;Y. Lou
本文研究了梯度上的L1/L2最小化算法在成像中的应用。最近的一些工作表明，L1/L2是优于L1范数时，近似的L0范数，以促进稀疏性。因此，我们假设在梯度上应用L1/L2比经典的全变分（梯度上的L1范数）更好地增强图像梯度的稀疏性。数值上，我们设计了一个特殊的分裂格式，在一定条件下，我们证明了交替方向乘子法（ADMM）的连续收敛性和全局收敛性。实验上，我们证明了明显的改善L1/L2超过L1和其他非凸正则化的图像恢复从低频测量和两个医疗应用的磁共振成像和计算机断层扫描重建。最后，我们揭示了一些经验证据的优越性L1/L2超过L1时，恢复分段恒定信号从低频测量，以阐明未来的工作。
In this paper, we study the L 1/L 2 minimization on the gradient for imaging applications. Several recent works have demonstrated that L 1/L 2 is better than the L 1 norm when approximating the L 0 norm to promote sparsity. Consequently, we postulate that applying L 1/L 2 on the gradient is better than the classic total variation (the L 1 norm on the gradient) to enforce the sparsity of the image gradient. Numerically, we design a specific splitting scheme, under which we can prove subsequential and global convergence for the alternating direction method of multipliers (ADMM) under certain conditions. Experimentally, we demonstrate visible improvements of L 1/L 2 over L 1 and other nonconvex regularizations for image recovery from low-frequency measurements and two medical applications of magnetic resonance imaging and computed tomography reconstruction. Finally, we reveal some empirical evidence on the superiority of L 1/L 2 over L 1 when recovering piecewise constant signals from low-frequency measurements to shed light on future works.