基于无偏风险估计准则的图像稀疏复原优化方法研究

在航天遥感、医学、公共安全和日常生活等众多领域，由于成像设备固有的物理局限性和实际拍摄环境的复杂性，图像在形成、传输和记录过程中会出现模糊、失真、有噪点等现象，严重影响图像场景的分析与理解、目标检测与识别。图像复原旨在消除或降低图像模糊或噪点，提高图像质量。近年来，基于图像全局或局部稀疏特性的正则化技术已成为求解该问题的代表性方法，然而，目前该类方法普遍缺乏先验稀疏假设和参数选择的鲁棒性，且迭代收敛速度慢。本项目针对高斯/泊松噪声的情况，提出以递归和非递归形式的无偏风险估计——均方误差的无偏估计——作为图像稀疏复原的优化准则，能够从理论上保证稀疏复原算法的鲁棒性和最小均方误差意义上的最优性；提出基于无偏风险估计准则的交替更新策略和线性参数化迭代方法，可显著提高算法效率和图像复原质量。

In many real applications, including remote sensing, biomedical imaging, and photography, the image would suffer from blurring, distortion and contaminated by noise, during the image formation, transmission and recording. The image degradation deteriorates image analysis and understanding, object detection and recognition. Image restoration aims at improving image quality, by denoising and deblurring. Recently, the sparsity-promoting regularization has been a standard technique for solving this problem. However, the method lacks robustness, and has slow convergence speed. For both Gaussian and Poisson noises, this project proposes SURE/PURE (Stein/Poisson unbiased risk estimates)---unbiased estimates of MSE (mean squared error)---as the criteria for optimization of image restoration, which theoretically guarantee the restoration optimality in terms of MSE. We incorporate the alternating update and LET (linear expansion of thresholds) strategies into the restoration process, to accelerate the computational speed, and significantly improve the image restoration quality.