基于稀疏表示的图像重构-计算数学专业论文.docx

摘要 图像获取是人类通过传感器将外界信号转换、采集进入计算机的一个过程。 随着图像在各方面应用的发展，对图像分辨率以及更快速成像等方面有更高的需 求，使得要研究一种对图像获取的新方法。而压缩感知作为一个新兴概念，为图 像获取提供了一种新思路，通过符合感知条件的投影测量获取信息，并能从投影 得到的少量测量值中通过重构方法，重构出应用所需要的图像。 图像处理中，对于理想的图像，选择合适的小波基，对其进行小波变换后， 得到的小波系数是稀疏的。通过少量的值实现可稀疏图像的重构。重构算法是其 中关键的一部分，它对于压缩后的信号的精确重构以及采样过程中的准确验证均 有着重要的意义。本文首先介绍了一些经典的重构算法，然后介绍了一种基于稀 疏的重构算法并进行改进, 提出了一种新的变参数算法，进而将改进的重构算法 用于基于小波变换的图像去噪中。和通常的小波阈值方法不同，我们将小波变换 得到的系数进行压缩感知得到小波系数的测量值，然后利用新的变参数算法对该 测量值进行稀疏重构，得到去噪后的小波系数。 本文是基于稀疏表示与压缩感知的思想，对于含噪图像在应用压缩感知时不 仅能够很好的重构图像还可以去噪，重构的质量无论在视觉效果上还是客观数据 上均优于现有同类算法，是一种重构效果很好的算法。 关键词：图像处理；压缩感知；稀疏表示；重构算法。 Abstract Image acquisition is a process that humans convert the signal with sensors and collect it into computers. With the rapid development of the image application, since image resolution and faster imaging become more and more important, it is necessary to design a new method to study an image acquisition. Compressed sensing as an emerging concept for image acquisition, it provides a new way to get information through the projection of the perception of the conditions measurement, the image can be reconstructed through the small number of the measured values obtained by the projection. In the image processing, after choosing the suit wavelet bases for ideal images and wavelet transforming, we can get the wavelet coefficients which is sparse. The sparse image can be reconstructed by a small amount of the value. The reconstruction algorithm is an important part of the image reconstruction, which play an important role in the precise reconstruction of the compressed signal and accurate verification of the sampling process. This paper firstly proposed some classical reconstruction algorithms. Then, a reconstruction algorithm based on sparse regularization term is proposed, put forward a new variable parameter algorithm and improved, and also be used in image denoising. The reconstruction quality of the proposed algorithm is superior to existing algorithms in terms of the visual effects and objective data. Key