Efficient Pixel-Wise SVD Required for Image Processing Using the Color Line Feature
Efficient Pixel-Wise SVD Required for Image Processing Using the Color Line Feature
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DOI：
10.1109/access.2021.3083895
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发表时间：
2021
期刊：
影响因子：
3.9
通讯作者：
K. Shirai;Yuya Ito;H. Miyao;M. Maruyama
中科院分区：
文献类型：
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作者：
K. Shirai;Yuya Ito;H. Miyao;M. Maruyama
在基于数学优化的彩色图像处理中，人们考虑了彩色图像的色线特征，并提出了许多方法，取得了较好的效果。色线是在局部图像区域中观察到的线性颜色分布（相关线），并且由从相邻像素值生成的数据矩阵的稀疏度在数值上表示。然而，计算需要大量的处理时间，因为每个数据矩阵通过逆计算或奇异值分解（SVD）处理，并对分解的奇异值进行一些操作。在本文中，为了解决这个问题，我们提出了一种方法，可以有效地计算每个数据矩阵的SVD。利用从相邻区域（每个以相邻像素为中心）获得的矩阵彼此相似的实验知识，我们有意地通过使用迭代方法（Arnoldi迭代）来设计SVD，并将在像素处收敛的奇异向量传播到下一个像素作为迭代的初始向量。这种传播可以大大减少收敛所需的迭代次数。此外，奇异值和向量以降序获得，这在减少小奇异值之后重构矩阵时是有利的，因此当奇异值变得低于阈值时，我们可以截断计算。为了证明其有效性，我们将所提出的方法应用于去噪方法，安排结构张量全变差（ASTV），并表明与朴素方法相比，处理时间缩短了95%，而不会失去数值精度。
In color image processing based on mathematical optimization, a color-line image feature has been considered and many methods that give good results have been proposed. A color-line is a linear color distribution (correlation line) observed in a local image region, and is numerically represented by the sparsity of a data matrix generated from the neighboring pixel values. However, the calculation requires a lot of processing time because each data matrix is processed by inverse calculation or singular value decomposition (SVD) with some operations on the decomposed singular values. In this paper, in order to address this problem, we propose a method that can effectively compute SVD for each data matrix. Using the experimental knowledge that matrices obtained from neighboring regions (each centered at an adjacent pixel) are similar to each other, we intentionally design the SVD by using an iterative method (Arnoldi iteration), and propagate the converged singular vectors at a pixel to the next pixel as the initial vectors of the iteration. This propagation can drastically reduce the number of iterations required for convergence. Additionally, the singular values and vectors are obtained in descending order, which is advantageous when a matrix is reconstructed after reducing small singular values, so we can truncate the calculation when a singular value becomes lower than a threshold value. To show the effectiveness, we apply the proposed method to a denoising method, arranged structure-tensor total variation (ASTV), and show that the processing time is shortened by 95% compared to the naive method without losing numerical accuracy.