基于非凸稀疏促进性先验的图像盲恢复问题研究

Blind image restoration is one of the important scientific problems and hot topics in the field of image processing. During the processing of recording, the observed images may be blurred due to camera shake, defocus or atmospheric turbulence. Blind image restoration aims to recover clear image and point spread function simultaneously, with the knowledge of observed blurred image and priors on estimated image and PSF. The problem is very ill-posed and difficult to solve. Our key problem is to establishing a reasonable mathematical model for blind image restoration problem and designing corresponding reliable and efficient algorithm. This project aims to study on the method of blind restoration based on the nonconvex sparsity-promoting prior. The main contents include: (1) to propose a novel blind restoration framework based on the nonconvex sparsity-promoting prior; specially set up the nonconvex sparsity constraint with different sparsity transformation for cartoon part and texture part from the perspective of image decomposition; (2) to design efficient algorithm for the proposed blind restoration model and analyze the convergence; (3) to study the proposed sparsity prior for blind image restoration under non-additive noise.

图像盲恢复问题是图像处理领域重要的科学问题与热点问题之一。在图像获取过程中，因相机抖动、失焦或者大气湍流等，造成图像模糊。盲恢复问题旨在依据观测降质图像，基于一定的先验信息，同时恢复出清晰图像和模糊算子。此类问题严重病态，求解十分困难。建立合理的图像盲恢复模型和稳定高效的求解算法是我们面临的关键问题。本课题拟研究基于非凸稀疏促进性正则化的图像盲恢复方法。具体包括：(1) 基于非凸稀疏促进性先验建立图像盲恢复模型；特别地，考虑了图像分解的方法，对于分解得到的卡通和纹理部分利用不同稀疏变换的非凸正则化方法；(2) 研究处理非凸非光滑正则函数的方法，设计盲恢复最小化问题的高效算法并分析收敛性；（3）稀疏先验在非加性噪声干扰下的图像盲恢复研究。

近年来，图像盲恢复问题受到了广泛的关注和研究，它也是图像处理领域重要的科学问题与热点问题之一，非凸稀疏促进性正则化方法是建立图像恢复模型的重要途径，项目组以“非凸先验建模----稀疏优化高性能算法”为研究主线，进行了系统性研究，也得到了不错的研究成果。项目组基于问题背景，提出了图像盲恢复、非盲恢复以及半盲恢复的数学模型及求解算法，也研究了超光谱图像的全色锐化问题。在项目资助期间，项目组共发表SCI期刊文章5篇，含IEEE汇刊(如IEEE TPAMI)国际权威学术期刊文章；以及1篇学术会议文章，即图像处理领域会议ICIP(IEEE International Conference on Image Processing)。在读硕士4名。

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