压缩感知图像重构及去噪算法的研究

发布时间：2018-03-10 19:52

本文选题：压缩感知　切入点：离散剪切波变换　出处：《燕山大学》2016年博士论文　论文类型：学位论文

【摘要】：压缩感知理论是建立在矩阵分析、概率统计、泛函与拓扑分析等基础学科之上的一种新的信号采样与处理理论,它基于信号的先验稀疏特性,在采样信号的同时实现了数据的压缩。采样频率可远低于奈奎斯特采样率,真正实现了高效的“信息直接获取”。其主要包含三方面基本内容:信号的稀疏表示、测量矩阵的构造及重构算法的设计。压缩感知理论突破了传统的信号获取与处理方式,具有广泛的应用前景。论文针对二维图像信号展开一系列研究,取得的研究成果和主要创新点包括以下四个方面:针对图像信号研究了一种带自修复功能的新型压缩感知图像重构算法。该算法综合分析了实际中的图像一般都存在的退化降质因素和问题,首先建立图像的退化降质数学模型,通过改进图像压缩感知系统中的测量矩阵和图像稀疏表示的方法,建立了一种新的重建图像算法模型。由于改进的测量矩阵的逆过程中包含升采样和去模糊操作,使得重构图像时具有图像自修复功能。仿真实验结果也证明了所建立的重构算法的有效性。研究了一种基于各向异性图像多尺度几何变换的压缩感知去噪算法。针对现有压缩感知算法在重建图像过程中利用TV滤波器剔除噪声时,无法兼顾降低噪声和保留细节的问题,借鉴离散剪切滤波器设计的原理,构造出了一种新型的紧框架下的各向异性的图像多尺度几何变换来实现对图像达到最优的稀疏表示,并在重构过程中采用改进的SALSA算法作为图像重建的算法。仿真实验结果表明,算法能够从少量受到噪声污染的观测值中重构图像,在有效消除噪声的同时也能保留更多的图像边缘和细节信息,相比于现有压缩感知去噪算法,算法在主客观成像效果上,均有明显的改进。针对多聚焦图像的噪声去除问题,研究了基于压缩感知的多聚焦图像去噪算法。在多聚焦图像去噪处理过程中,通过压缩感知实现对图像高频分量包含的有效信息进行重构,利用残差进行反加,避免在不知道噪声方差的情况下导致去噪过程中滤掉了过多的图像有用信息,从而提高去噪效果。针对相干成像过程中产生的散斑噪声,研究了同态滤波与中值滤波相融合的散斑噪声污染图像恢复算法。该算法充分考虑了两种经典去噪算法各自的优点,融合后的算法实现了两算法的优势互补,能有效去除散斑噪声,提高图像质量,仿真和实验结果证明其性能明显优于单一同态滤波或中值滤波算法。
[Abstract]:Compression sensing theory is a new signal sampling and processing theory based on matrix analysis, probability statistics, functional and topological analysis, which is based on the prior sparse characteristics of signals. The sampling frequency can be far lower than the Nyquist sampling rate, and the efficient "direct information acquisition" is realized. It mainly includes three basic contents: sparse representation of the signal. The construction of measurement matrix and the design of reconstruction algorithm. Compression sensing theory breaks through the traditional signal acquisition and processing methods and has a wide application prospect. The research results and main innovations include the following four aspects: a novel image reconstruction algorithm with self-repairing function is proposed. Degradation and degradation factors and problems, Firstly, the degradation and degradation mathematical model of image is established, and the method of measuring matrix and sparse representation of image in image compression perception system is improved. In this paper, a new image reconstruction algorithm model is established. Because the inverse process of the improved measurement matrix includes ascending sampling and de-blurring operations, The simulation results also prove the effectiveness of the proposed reconstruction algorithm. A compression perceptual denoising algorithm based on multi-scale geometric transformation of anisotropic images is studied. When using TV filter to remove noise in the process of image reconstruction, the existing compression sensing algorithm can eliminate the noise. The problem of reducing noise and preserving detail can not be taken into account. Based on the principle of discrete shear filter design, a new anisotropic image multi-scale geometric transform under compact frame is constructed to achieve the optimal sparse representation of the image. In the process of reconstruction, the improved SALSA algorithm is used as the image reconstruction algorithm. The simulation results show that the algorithm can reconstruct the image from a small number of observations contaminated by noise. In addition to effectively eliminating noise, more image edges and details can be retained. Compared with the existing compression perceptual denoising algorithms, the algorithm has obvious improvement in subjective and objective imaging effects, aiming at the problem of noise removal in multi-focus images. The multi-focus image denoising algorithm based on compression perception is studied. In the process of multi-focus image de-noising, the effective information contained in the high-frequency component of the image is reconstructed by compression perception, and the residual error is used to reverse add. To avoid filtering out too much useful information in the process of denoising without knowing the variance of noise, so as to improve the effect of de-noising. A speckle noise image restoration algorithm combining homomorphic filtering and median filtering is studied. The advantages of the two classical denoising algorithms are fully considered, and the advantages of the two algorithms are complementary. It can effectively remove speckle noise and improve image quality. Simulation and experimental results show that its performance is obviously superior to that of single homomorphic filter or median filter algorithm.
【学位授予单位】：燕山大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41

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