基于四元數(shù)的彩色圖像去噪算法研究
發(fā)布時(shí)間：2019-07-02 19:32
【摘要】：傳統(tǒng)的彩色圖像處理方法通常將彩色圖像看成三幅獨(dú)立的灰度圖像,對三個(gè)通道分別處理,沒有考慮各通道之間的關(guān)聯(lián)性,難以獲得較好的處理效果。因此,為彩色圖像找到一種更好的表示方法,將其三個(gè)色彩通道看做一個(gè)整體,保留各通道之間的相關(guān)性具有重要的理論意義和應(yīng)用價(jià)值。四元數(shù)作為最先被發(fā)現(xiàn)的超復(fù)數(shù)代數(shù),為三維彩色圖像信號的重構(gòu)提供了實(shí)用的數(shù)學(xué)工具�；谒脑獢�(shù)的方法模仿人類對視覺環(huán)境的感知,以一種并行的方式處理多通道信息。作為一種新的彩色圖像表示工具,四元數(shù)在彩色圖像復(fù)原的諸多方面取得了令人滿意的效果。本文針對彩色圖像處理問題,提出一種基于四元數(shù)加權(quán)核范數(shù)最小模型和求解算法。論文的主要研究工作和創(chuàng)新點(diǎn)總結(jié)如下:第一,本文對現(xiàn)有的圖像去噪算法以及基于四元數(shù)的彩色圖像處理方法做了系統(tǒng)概述,詳述了四元數(shù)的基本運(yùn)算、彩色圖像的四元數(shù)表示法,深入研究了核范數(shù)最小(Nuclear Norm Minimization,NNM)和加權(quán)核范數(shù)最小(Weighted Nuclear Norm Minimization,WNNM)兩種算法以及四元數(shù)矩陣的奇異值分解方法。第二,論文的創(chuàng)新點(diǎn)在于將WNNM模型推廣到四元數(shù)域,提出一種新穎的基于四元數(shù)加權(quán)核范數(shù)最小(Quaternion Weighted Nuclear Norm Minimization,QWNNM)模型。根據(jù)奇異值大小在表示圖像時(shí)重要程度的不同,對較大的奇異值分配較小的權(quán)重以被較小收縮,采用一種迭代重加權(quán)的算法對四元數(shù)矩陣做低秩重構(gòu),并給出了該問題具有全局最優(yōu)解的證明。第三,論文以彩色圖像的四元數(shù)表示法為基礎(chǔ),引入自然圖像子塊之間的非局部自相似性,建立彩色圖像子塊QWNNM去噪模型,討論了在低噪聲水平、高噪聲水平以及未知噪聲三種情況下的去噪效果。特別地,本文實(shí)現(xiàn)了原WNNM算法在彩色圖像去噪中的應(yīng)用,并且為了保持對比實(shí)驗(yàn)的公平性,對于WNNM算法,本文增加了高噪聲水平時(shí)對原噪聲圖像做高斯低通濾波預(yù)處理的對比實(shí)驗(yàn)。大量的彩色圖像去噪實(shí)驗(yàn)表明,與經(jīng)典的K-SVD算法以及WNNM算法相比,用本文提出的方法處理后的圖像,其主觀視覺效果和客觀評價(jià)指標(biāo)都有顯著的提高。在四元數(shù)空間里,矢量重構(gòu)時(shí)可以完整保存彩色圖像的內(nèi)在結(jié)構(gòu)。QWNNM方法也可用于彩色圖像修復(fù)、去模糊、去馬賽克等圖像處理問題中。這種多維低秩矩陣重構(gòu)的思想也可以擴(kuò)展到彩色圖像分類、機(jī)器學(xué)習(xí)和模式識別等領(lǐng)域,有著廣泛的應(yīng)用和發(fā)展前景。
[Abstract]:The traditional color image processing method usually regards the color image as three independent gray images. The three channels are processed separately without considering the correlation between the channels, so it is difficult to obtain a better processing effect. Therefore, it is of great theoretical significance and application value to find a better representation method for color image, and to regard its three color channels as a whole, and it is of great theoretical significance and application value to retain the correlation between the channels. As the first discovered supercomplex algebra, quaternion provides a practical mathematical tool for the reconstruction of 3D color image signal. The quaternion method imitates human perception of visual environment and processes multi-channel information in a parallel way. As a new color image representation tool, quaternions have achieved satisfactory results in many aspects of color image restoration. In this paper, a minimum model and algorithm based on quaternion weighted kernel norm are proposed to solve the problem of color image processing. The main research work and innovations of this paper are summarized as follows: first, the existing image denoising algorithms and color image processing methods based on quaternion are systematically summarized, the basic operation of quaternion, the quaternion representation of color image are described in detail, and the minimum kernel norm (Nuclear Norm Minimization,NNM and weighted kernel norm minimum (Weighted Nuclear Norm Minimization, are deeply studied. WNNM) two algorithms and the singular value decomposition method of quaternion matrix. Secondly, the innovation of this paper is to extend the WNNM model to quaternion domain, and to propose a novel minimum (Quaternion Weighted Nuclear Norm Minimization,QWNNM model based on quaternion weighted kernel norm. According to the difference of the importance of the singular value in the representation of the image, a small weight is assigned to the larger singular value to be reduced. An iterative reweighting algorithm is used to reconstruct the quaternion matrix with low rank, and the proof that the problem has the global optimal solution is given. Thirdly, based on the quaternion representation of color image, the non-local self-similarity between natural image sub-blocks is introduced, and the QWNNM denoising model of color image sub-block is established, and the denoising effect in the case of low noise level, high noise level and unknown noise is discussed. In particular, this paper implements the application of the original WNNM algorithm in color image denoising, and in order to maintain the fairness of the contrast experiment, for WNNM algorithm, this paper adds a comparison experiment of Gaussian low-pass filtering preprocessing for the original noise image at high noise level. A large number of color image denoising experiments show that compared with the classical K-SVD algorithm and WNNM algorithm, the subjective visual effect and objective evaluation index of the image processed by the method proposed in this paper are significantly improved. In quaternion space, the internal structure of color image can be completely preserved in vector reconstruction. QWNNM method can also be used in color image restoration, deblurring, mosaic and other image processing problems. This idea of multi-dimensional low rank matrix reconstruction can also be extended to color image classification, machine learning and pattern recognition, and has a wide range of applications and development prospects.
【學(xué)位授予單位】：五邑大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP391.41
本文編號：2509170
[Abstract]:The traditional color image processing method usually regards the color image as three independent gray images. The three channels are processed separately without considering the correlation between the channels, so it is difficult to obtain a better processing effect. Therefore, it is of great theoretical significance and application value to find a better representation method for color image, and to regard its three color channels as a whole, and it is of great theoretical significance and application value to retain the correlation between the channels. As the first discovered supercomplex algebra, quaternion provides a practical mathematical tool for the reconstruction of 3D color image signal. The quaternion method imitates human perception of visual environment and processes multi-channel information in a parallel way. As a new color image representation tool, quaternions have achieved satisfactory results in many aspects of color image restoration. In this paper, a minimum model and algorithm based on quaternion weighted kernel norm are proposed to solve the problem of color image processing. The main research work and innovations of this paper are summarized as follows: first, the existing image denoising algorithms and color image processing methods based on quaternion are systematically summarized, the basic operation of quaternion, the quaternion representation of color image are described in detail, and the minimum kernel norm (Nuclear Norm Minimization,NNM and weighted kernel norm minimum (Weighted Nuclear Norm Minimization, are deeply studied. WNNM) two algorithms and the singular value decomposition method of quaternion matrix. Secondly, the innovation of this paper is to extend the WNNM model to quaternion domain, and to propose a novel minimum (Quaternion Weighted Nuclear Norm Minimization,QWNNM model based on quaternion weighted kernel norm. According to the difference of the importance of the singular value in the representation of the image, a small weight is assigned to the larger singular value to be reduced. An iterative reweighting algorithm is used to reconstruct the quaternion matrix with low rank, and the proof that the problem has the global optimal solution is given. Thirdly, based on the quaternion representation of color image, the non-local self-similarity between natural image sub-blocks is introduced, and the QWNNM denoising model of color image sub-block is established, and the denoising effect in the case of low noise level, high noise level and unknown noise is discussed. In particular, this paper implements the application of the original WNNM algorithm in color image denoising, and in order to maintain the fairness of the contrast experiment, for WNNM algorithm, this paper adds a comparison experiment of Gaussian low-pass filtering preprocessing for the original noise image at high noise level. A large number of color image denoising experiments show that compared with the classical K-SVD algorithm and WNNM algorithm, the subjective visual effect and objective evaluation index of the image processed by the method proposed in this paper are significantly improved. In quaternion space, the internal structure of color image can be completely preserved in vector reconstruction. QWNNM method can also be used in color image restoration, deblurring, mosaic and other image processing problems. This idea of multi-dimensional low rank matrix reconstruction can also be extended to color image classification, machine learning and pattern recognition, and has a wide range of applications and development prospects.
【學(xué)位授予單位】：五邑大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP391.41
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