A computational algorithm for minimizing total variation in image restoration
A computational algorithm for minimizing total variation in image restoration
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DOI：
10.1109/83.503914
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发表时间：
1996-06-01
影响因子：
10.6
通讯作者：
Santosa, F
中科院分区：
文献类型：
--
作者：
Li, YY;Santosa, F
基于Rudin等人提出的最小全变差原理，提出了一种可靠、高效的模糊和噪声图像恢复算法。对于离散图像，该算法使一个分段线性L(1)函数(总变差的度量)最小化，该函数受单个2范数不等式约束(数据拟合的度量)约束。该算法首先利用(部分)共轭梯度法寻找不等式约束的可行点，这对应于一个去模糊过程，噪声和其他伪影通过随后的总变差最小化过程被去除。使用线性L(1)目标函数进行总变差测量导致了更简单的计算算法，最速下降和仿射比例牛顿法被考虑来解决这个约束分段线性L(1)最小化问题。当被视为图像恢复和增强过程时，所得到的算法的特征是它可以在噪声方差知识不可用或不可靠的情况下以自适应/交互的方式使用，数值算例验证了所提迭代图像恢复和增强过程的有效性。
A reliable and efficient computational algorithm for restoring blurred and noisy images is proposed, The restoration process is based on the minimal total variation principle introduced by Rudin et al, For discrete images, the proposed algorithm minimizes a piecewise linear l(1) function (a measure of total variation) subject to a single 2-norm inequality constraint (a measure of data fit). The algorithm starts by finding a feasible point for the inequality constraint using a (partial) conjugate gradient method, This corresponds to a deblurring process, Noise and other artifacts are removed by a subsequent total variation minimization process, The use of the linear l(1) objective function for the total variation measurement leads to a simplier computational algorithm, Both the steepest descent and an affine scaling Newton method are considered to solve this constrained piecewise linear l(1) minimization problem.The resulting algorithm, when viewed as an image restoration and enhancement process, has the feature that it can be used in an adaptive/interactive manner in situations when knowledge of the noise variance is either unavailable or unreliable, Numerical examples are presented to demonstrate the effectiveness of the proposed iterative image restoration and enhancement process.