图像视频的压缩采样与稀疏重建的协同优化方法的研究

Visual sensors usually sample image/video signals far beyond their effective dimensions, which thus brings great burden to their storage and transmission. Fortunately the compressive sensing (CS) theory brings a whole new avenue to approximately obtain their effective dimension samplings of image/video signals. According to the CS theory, it is required to collaboratively design the measurement and sparse representation of image/video signals under the circumstance of strong incoherency. However,the design of measurement and sparse representation is implemented independently according the optimization principle of each own in traditional CS.Image/video signals are multi-dimensional sparse signals with high dynamic range property. Researches on multi-dimensional group structural sparsity demonstrate that, the approximation ability of effective dimensions by CS methods can be dramatically improved by restoring the sparse component with small amplitude of the signals and preserving their multi-dimensional structures. In this project, by introducing the multi-dimensional group sparsity, the following issues will be researched: 1. Aiming at the distribution property of image/video signals on different dimensions, based on the two classes of sparsifying basis of transform based and learning based, the group structural property of image/video signals and high efficient multi-dimensional group structural sparse representation will be investigated. 2. Collaborative optimization models including sparse recovery collaborated measurement and measurement collaborated sparse representation will be constructed, which achieves effective dimension sampling of image/video signals in the framework of CS.

视觉传感器通常以远超出有效维度对图像视频信号采样，从而导致了存储和传输的巨大压力，压缩感知理论为近似实现图像视频信号的有效维度采样提供一种崭新的思路。压缩感知理论要求在较强非一致关系下协同设计图像视频信号的观测和稀疏表示两个过程，而传统的观测与稀疏表示的设计是以各自的优化准则独立进行的。 图像视频信号是具有高动态范围特性的多维稀疏信号，研究图像视频信号的多维分组结构稀疏表示, 有效恢复信号中的低幅值稀疏成分和保持信号的多维结构，显著提升压缩感知方法对有效维度采样的逼近能力。本课题以多维分组结构稀疏的引入为契机，拟开展如下问题的研究: 1、针对图像视频信号在不同维度上的分布特性，基于变换和基于学习的两类稀疏基，探索图像视频信号的分组结构特性，研究高效多维分组结构稀疏表示。2、构建与稀疏重建协同的观测和与观测协同的稀疏表示二种协同优化模型，以实现信号在压缩感知框架下的有效维度采样.

压缩感知理论为实现图像视频信号的高效采样提供一种崭新的思路。在传统压缩感知系统中，观测与稀疏矩阵是彼此独立设计的，本课题提出协同设计观测和稀疏表示的压缩感知方法。该方法的优势主要体现在：提出了多种高效的稀疏表示模型，从结构、分组、多维度等方面提高图像的稀疏表示能力。在观测与稀疏表示协同的框架下，提出了优化的结构化观测和优化的结构稀疏字典设计方法，大幅度地提高了图像信号的采样性能。我们的工作包括如下三个方面：.1.在基于变换的稀疏表示方面，利用小波高低频分布特性和零树结构特性,提出了两类小波域的稀疏表示方法；结合小波域结构稀疏和图像的非局部相关性，提出了小波域的复合稀疏表示模型，此外提出了数据驱动的多尺度变换模型。.2．在基于学习的稀疏表示方面，提出了基于张量的多维稀疏表示模型及多维稀疏字典的训练算法,与一维稀疏模型相比，大幅度地减少了计算和存在代价，该模型是一维模型的推广。利用图像的非局部相关性，提出了二维分组稀疏表示模型。.3.在压缩感知系统优化方面, 以传统的压缩感知光场成像系统为研究平台，分析光场相机的掩膜观测矩阵的关系，挖掘光场数据的空间-角度相关性，提出了与结构化观测协同的结构化稀疏重建模型和与稀疏重建协同的结构化观测模型。搭建了一种基于压缩感知的光场相机原形系统，改善了传统的压缩感知光场相机的性能。..