图像视频信号的压缩采样与稀疏重建

要视觉传感器通常不知道它们“看到”的现象之下的物理过程，以远远超出图像视频信号有效维度的Shannon／Nyquist采样率获取图像视频数据，从而导致了对图像视频信号的存储、传输等数字处理的巨大压力．压缩感知（compressivesensing，CS）理论表明：在某个线性变换域下稀疏的信号，可以利用少量的观测数据精确地重建，或在噪声情况下鲁棒地重建．压缩感知是实现图像视频信号有效维度采样的理论基础，为图像视频信号的采样、处理和识别等领域带来了前所未有的突破．本文对图像视频信号领域压缩感知面临的基本问题：压缩采样、稀疏重建模型及其优化求解算法的研究进展进行了综述．在采样方面，分析了图像视频信号随机观测矩阵和有结构观测矩阵的性能；在稀疏重建模型方面，从图像视频信号的稀疏先验性出发、介绍了分析型的重建模型和合成型重建模型的构建方法；在优化求解方面，针对重建模型，介绍了约束优化问题和无约束优化问题两类求解算法．以此为基础，分析了在图像视频领域压缩感知的理论与应用的进一步发展所面临的问题和挑战，展望了未来的发展方向．

Compressive sampling and sparse reconstruction of images/videos

Vision sensors usually do not account for the physical process of imaging and they acquire im- age/video samples at the Nyquist rate. The Nyquist rate is significantly higher than the effective dimensions of an image/video, and consequently compression is essential for the image/video prior to storage or transmission. The emerging Compressive Sensing （CS） theory states that a signal can be perfectly reconstructed, or can be robustly approximated in the presence of noise, using a few random measurements, provided that it is sparse in some linear transform domain. CS is the theoretical foundation for capturing a signal with effective information dimensions, and thus represents an unprecedented breakthrough in many fields such as sampling, processing, and recognition of image/video. We review the fundamental problems of CS for image/video including compressive sampling, sparse reconstruction models, and algorithms for the models. For compressive sampling, the construc- tion of random and structural measurement matrices are considered separately and the performance of these two kinds of matrices is evaluated. For sparse reconstruction, models are classified as analysis-based or synthesis- based reconstruction models by the sparse representation prior, features of which are presented. The optimization models can be considered as constrained and unconstrained optinfization problems. Some feasible algorithms for these two kinds of optimization problems are explained in detail and the performance of the algorithms is given. In addition, several challenges of compressive sensing technology are presented and future work is discussed.