Image Denoising Based on HOSVD With Iterative-Based Adaptive Hard Threshold Coefficient Shrinkage

Abstract

Natural images often have self-similarity, which can be used to remove noise. Therefore, many current denoising methods denoise by processing similar image block matrix. Aiming at the problem that these methods will destroy the two-dimensional structure of image blocks when they are expanded into one-dimensional column vectors, a new image denoising method based on high-order singular value decomposition is proposed. Several similar image blocks are stacked into three-dimensional arrays and treated as a third-order tensor; then, higher-order singular value decomposition can be performed. For the core tensor obtained by decomposition, an iterative algorithm with adaptive hard threshold coefficient shrinkage is proposed. The experimental results show that the proposed method outperforms the state-ofthe-art methods in peak-signal-to-noise ratio, structural similarity, and visual effects.INDEX TERMS Image denoising, tensor, high order singular value decomposition, adaptive hard thresholding, threshold coefficient shrinkage.

Quaternion higher-order singular value decomposition and its applications in color image processing

“…From the formula ( 27), we can see that the coefficients in Ṡj are actually to re-decompose the corresponding singular values so that the noise energy originally concentrated on the singular values is mainly transferred to the smaller coefficients in Ṡj while larger coefficients are less affected by noise [5]. Thus, to perform denoising, the smaller coefficients are truncated by adopting the following method of hard threshold shrinkage:…”

“…Dataset: We conduct the experiments on a popular multi-focus image dataset, Lytro [36], which is publicly available online 5 . The 20 pairs (with two images) of color multi-focus images of size 520 × 520 pixels are adopted from the dataset.…”

“…H Igher-order singular value decomposition (HOSVD) is a natural extension of the singular value decomposition (SVD) in higher dimensional space [1]. Benefiting from the outstanding ability of high-dimensional data representing and feature extracting, the HOSVD has been widely applied in many areas such as image fusion [2], face recognition [3], texture synthesis [4], image denoising [5], etc. On the other hand, quaternion, as an elegant color image representation tool, has attracted much attention in the field of color image processing, recently.…”

“…However, the fixed base of QWT and QCT usually cannot obtain accurate features of color images. Motivated by the fact that HOSVD, an efficient data-driven decomposition technique, can obtain a dynamic adaptive base [5], and it has the salient ability for feature extraction [29], we design a novel multi-focus color image fusion method based on the defined QHOSVD procedure. In consideration of the fact that image fusion mainly depends on local information of source images [29], the source images are firstly divided into image patches using the sliding window technique.…”

Historical Multi-Station SCADA Data Compression of Distribution Management System Based on Tensor Tucker Decomposition

“…In literature [13] and [14], their authors show that SVD and PCA methods have good performance in SCADA data compression of the power distribution system. To demonstrate the superiority of the TD compression method, the proposed method is compared with the two data compression methods of SVD and PCA in this section.…”