面向图像混合噪声去除的非局部稀疏学习方法研究

Recent years, sparse representation has been widely used to remove noise from images. Conventional sparse representation models are designed under the assumption that the fitting residual error follows the Gaussian distribution. However, the fitting residual error of mixed noise corrupted image no longer follows the Gaussian distribution, which brings in new challenges for the sparse representation based image denoising methods..In this project, we plan to develop high-performance nonlocal sparse learning techniques for the restoration of mixed noise corrupted images. Specifically, the research includes three main parts as follows: 1) Considering of the noise distributions and the image structure information, jointly design a series of nonlocal sparse representation based image denoising methods such that the noise can be completely removed, while the image structure information can still be well preserved. 2) Develop optimization algorithms to adaptively update the weights in the weighted sparse models, which can dramatically drop the model error. Therefore, the robustness and practicability of the model can be improved. 3) The previous established methods will be further generalized into the quaternion space for efficiently removing the mixed noise in color images. On one hand, the research achievements will provide new perspectives to make the conventional sparse learning techniques robust to mixed noise. On the other hand, the developed tools and platforms will benefit a rich variety of applications when dealing with the enhancement of image data.

近年来，稀疏表示理论被广泛应用于图像噪声去除中。传统的稀疏表示模型建立在数据拟合残差服从高斯分布的基础上，然而被混合噪声干扰的图像数据拟合残差不再服从高斯分布，这给基于稀疏表示理论的图像去噪方法带来了新的挑战。.本课题研究图像中混合噪声高效去除的非局部稀疏学习方法。主要研究内容包括以下三个部分：首先，协同考虑噪声分布特点和图像结构信息，提出一套考虑到非局部自相似性先验的加权稀疏表示图像去噪方法，实现在去除混合噪声的同时保持好图像结构信息；其次，设计加权稀疏模型中权值系数的自适应优化方法，降低模型优化误差，提高模型的鲁棒性和实用性；最后，将上述方法推广到四元数域中，有效去除三维彩色图像中的混合噪声。本项目的创新成果，将为稀疏表示方法对混合噪声的鲁棒化提供新思路，同时对构建图像质量增强平台具有重要的理论意义和应用价值。

稀疏表示理论一直以来是图像处理领域的研究热点，尤其在图像去噪复原应用中取得了较大成功。然而传统的稀疏表示模型建立在数据拟合残差服从高斯分布的基础上，对具有复杂分布的混合噪声数据往往会失效，因此，如何构建满足复杂噪声分布特征的新型高鲁棒稀疏表征模型，已成为图像稀疏表示领域亟待解决的瓶颈难题。本项目对噪声稀疏建模与稀疏流形学习理论进行了系统的研究，提出了加权稀疏流形学习理论，突破了含噪声源低分辨率图像协同去噪和超分复原的瓶颈；设计了一种自适应的权值更新方法，提升了加权稀疏模型的鲁棒性和泛化性；构建了四元素高维稀疏学习框架，解决了彩色噪声图像复原的难题。项目的研究成果为极低质量噪声图像复原提供了技术支撑，使得稀疏表示和图像复原获得了进一步的发展研究。受项目资助发表科技论文9篇，其中SCI论文5篇、IEEE会刊论文3篇，相关成果发表在IEEE TCYB、IEEE TCSVT、IEEE TSMC: system、Information Sciences、自动化学报等国内外顶级期刊上。

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