图像压缩感知的重构算法研究

发布时间：2018-03-13 00:13

本文选题：压缩感知　切入点：图像重构　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：压缩感知理论是一种新颖的采样理论,和传统的采样理论比较,其优势主要有两个。一个是信号的压缩和采样是同时进行的,另一个是在信号采样率较低的情况下重构原始信号。作为压缩感知理论的核心内容之一,重构算法的好坏影响着压缩感知理论在实际应用的情况。近些年信号的重构问题被应用于图像复原、语言处理、地质勘探等方面,如何设计出高质量的压缩感知重构算法来精确重构出原始信号,是相关领域研究人员的研究重点。在这背景下,本文以图像压缩感知重构算法为研究对象,寻求高质量的压缩感知重构算法。本文主要研究以下三个方面的内容:(1)对压缩采样匹配追踪(CoSaMP)算法进行了改进。在匹配追踪类算法中CoSaMP算法对信号的重构效果比较好,考虑该算法中的内积运算不能最大限度地体现出残差向量和观测矩阵中原子的关联度,然而相关系数可以更好地表示向量间的关联程度。为此本文提出了一种优化的CoSaMP图像压缩感知重构算法,并在一维模拟信号和图像信号上进行实验,通过实验证明该算法的重构精度更高。(2)对基于GPU并行加速的图像压缩感知重构算法进行了研究。非局部低秩正则化的压缩感知(NLR-CS)算法对图像有较好的重构效果,但NLR-CS算法存在运行时间较长的缺点,因此可引入目前流行的GPU并行加速技术,提出一种基于GPU的并行NLR-CS算法。在熟悉NLR-CS算法流程的基础上,对串行执行方式进行热点分析,找出算法的性能瓶颈,同时分析算法的可并行性。再结合并行图像处理技术,根据GPU的硬件特性,采用CUDA编程模型对NLR-CS算法进行并行化设计和实现,最后通过实验证明该算法能够在不影响图像重构质量的情况下取得良好的加速效果。(3)对当前较好的图像压缩感知(NLR-CS)算法进行了改进。该算法利用低秩正则化对图像进行重构,但该算法仅利用图像的非局部相似性特征,未考虑图像的局部结构特征,重构出的图像不能较好地保留图像的纹理信息。为此本文提出一种基于低秩和全变差正则化的图像压缩感知重构算法,算法结合了图像的非局部相似性、局部梯度稀疏信息以及传统的压缩感知理论,构造出新的重构模型。最后采用交替方向乘子法实现图像的重构,在图像信号进行实验,通过实验证明该算法重构的图像效果更好。
[Abstract]:Compression sensing theory is a new sampling theory. Compared with the traditional sampling theory, it has two main advantages. One is that the compression and sampling of signals are carried out simultaneously. The other is to reconstruct the original signal when the sampling rate is low. In recent years, the problem of signal reconstruction has been applied to image restoration, language processing, geological exploration and so on. How to design a high quality compression perception reconstruction algorithm to accurately reconstruct the original signal is the research focus of the researchers in related fields. Under this background, this paper takes the image compression perception reconstruction algorithm as the research object. In this paper, we mainly study the following three aspects: we improve the compression sampling matching tracking CoSMP algorithm. In the matching tracking algorithm, the CoSaMP algorithm has a good effect on signal reconstruction. Considering the inner product operation in this algorithm, the correlation degree between the residual vector and the atoms in the observation matrix can not be maximized. However, the correlation coefficient can better represent the correlation between vectors. In this paper, an optimized CoSaMP image compression perceptual reconstruction algorithm is proposed, and experiments are carried out on one-dimensional analog signals and image signals. It is proved by experiments that the algorithm has higher reconstruction accuracy. (2) the image compression perceptual reconstruction algorithm based on GPU parallel acceleration is studied. The non-local low rank regularized compression sensing algorithm has good effect on image reconstruction. But the NLR-CS algorithm has the disadvantage of long running time, so we can introduce the popular GPU parallel acceleration technology, and propose a parallel NLR-CS algorithm based on GPU. Based on the familiar with the NLR-CS algorithm flow, the serial execution mode is analyzed. Find out the performance bottleneck of the algorithm, at the same time analyze the parallelism of the algorithm, then combine the parallel image processing technology, according to the hardware characteristic of GPU, adopt the CUDA programming model to design and implement the NLR-CS algorithm parallelism. Finally, experiments show that the algorithm can achieve a good acceleration effect without affecting the quality of image reconstruction. It improves the current better image compression perception (NLR-CS) algorithm. The algorithm uses low-rank regularization to reconstruct the image. However, the algorithm only uses the non-local similarity feature of the image, and does not consider the local structure feature of the image. The reconstructed image can not preserve the texture information of the image. In this paper, an image compression perceptual reconstruction algorithm based on low rank and total variation regularization is proposed, which combines the non-local similarity of the image. Based on the local gradient sparse information and the traditional theory of compression perception, a new reconstruction model is constructed. Finally, the alternating direction multiplier method is used to reconstruct the image, and the experiment is carried out on the image signal. Experiments show that the algorithm has better image effect.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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