NONLINEAR TOTAL VARIATION BASED NOISE REMOVAL ALGORITHMS
NONLINEAR TOTAL VARIATION BASED NOISE REMOVAL ALGORITHMS
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DOI：
10.1016/0167-2789(92)90242-f
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发表时间：
1992-11-01
期刊：
影响因子：
4
通讯作者：
FATEMI, E
中科院分区：
文献类型：
--
作者：
RUDIN, LI;OSHER, S;FATEMI, E
提出了一种约束优化型的图像去噪数值算法。图像的总变化最小化受到涉及噪声的统计的约束。使用拉格朗日乘数施加约束。采用梯度投影法求解。这相当于在由约束条件确定的流形上求解一个依赖于时间的偏微分方程。当t -->无穷大时，解收敛到一个稳定状态，即去噪图像。数值算法简单，速度较快。结果似乎是国家的最先进的非常嘈杂的图像。该方法是非侵入性的，在图像中产生锐利的边缘。该技术可以被解释为第一步，以等于水平集的曲率除以图像的梯度的大小的速度移动图像的每个水平集垂直于其自身，以及第二步，将图像投影回约束集。
A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t --> infinity the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set.