基于稀疏理论和图Laplacian矩阵的图像去噪理论与方法研究

项目名称： 基于稀疏理论和图Laplacian矩阵的图像去噪理论与方法研究

项目编号： No.61501169

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 无线电电子学、电信技术

项目作者： 汤一彬

作者单位： 河海大学

项目金额： 19万元

中文摘要： 为进一步提高去噪图像质量，本项目以基于稀疏理论的图像去噪为基础，利用图Laplacian矩阵（简称图L阵）的相关理论，研究稀疏理论和图L阵相结合的去噪方法，构建稀疏去噪新方案。项目首先对含噪图L阵从数学角度进行分析，探索含噪矩阵中真实图像块间关系信息的估计方法，以实现图像块间关系在稀疏去噪中的充分利用。同时，基于图L阵正则项稀疏去噪模型，利用图像在各尺度、各层上对应的图L阵的不同特性，进行多尺度、多层的去噪框架设计，并实现相关参数的优化。此外，通过对图L阵特征向量的研究，提出基于该特征向量的稀疏去噪新模型，并实现稀疏求解、图L阵特征向量选取等问题的解决。本项目拟通过上述研究，在基于稀疏理论与图L阵的图像去噪方面，探索一条有效提高去噪性能的新途径，为后续基于图像的各种应用提供良好的基础。

中文关键词： 图像去噪；图像噪声；加性噪声；稀疏表示；图Laplacian

英文摘要： To improve the quality of denoised images, in this project, a new denoising scheme is taken into account with the advantage of two theories, i.e., sparse theory and graph Laplacian matrix. Here, some algorithms are presented to exploit the attributes of graph Laplacian matrix combined with image denoising via sparse theory. The general denoising framework is also built with both sparse theory and graph Laplacian matrix. In details, the noised graph Laplacian matrix is firstly analyzed mathematically to estimate the correlation information of clean image patches, which aims to enhance the denoising performance with sparse theory more efficiently. Meanwhile, several sparse models with the graph Laplacian regularized terms are designed via the multiscale and multilayer image analysis, which employ the different features of the graph Laplacian in each scale and layer, respectively. The corresponding denoising frameworks are sequently constructed with the introduction of the parameter optimization. Moreover, a novel sparse model is proposed based on the eigenvectors of the graph Laplacian matrix, in which several important problems, e.g., the sparse solution and the graph-based eigenvector selection, are well solved. In brief, this project contributes to the development of the image denoising scheme via sparse theory and graph Laplacian matrix. It attempts to explore a new way to further improve the denoising performance, which provides a better platform for various other image applications.

英文关键词： image denoising;image noise;additive noise;sparse representation;graph Laplacian