面向高光谱图像的自适应压缩采样与低秩稀疏重构

Hyperspectral imaging is a natural field for the implementation of compressive sensing because typical captured hyperspectral data cubes involve large amount of data which is also often very redundant. The construction of sensing Matrix and the design of reconstruction algorithm are two key issues of hyperspectral Compressive Imaging. A remarkable feature of the compressive sensing is that the sensing is completely non-adaptive, but that not means no effort whatsoever should be made to understand the signal acquired. In the project, the degree of redundancy of hyperspectral image block is estimated only based on small amount of compressive measurements. Then, the rest adaptive sampling rate is assigned to each block according to the compressibility estimated. When the size of adaptive sensing matrix is determined, the corresponding adaptive sensing matrix is constructed as a structured sensing matrix by combining the deterministic sensing matrix and the random sensing matrix. The former assigns the sensing vectors to the location where the information most likely lies and acquires the common structure contained in the image blocks, and the latter is to sense the difference and the individual structure of images possessed as an essential and unique characteristic. To reconstruct the hyperspectral image, the low-rank sparse decomposition of the matrix is introduce to the high order tensor decomposition and image reconstruction based on the tensor approximation is propose. This project will establish the foundation for the further development of theory and practice of the compressive sampling in the field of Hyperspectral compressive imaging.

波段数目多、光谱分辨率高、波段宽度窄等特点导致高光谱图像包含丰富冗余，研究面向高光谱图像压缩采样方法具有深远的科学意义和明显的应用前景。而现有分块压缩采样忽略图像块之间的差异，容易造成非可压缩图像块资源不足而可压缩块资源过剩，从而导致重构精度差等问题。本项目主要研究高光谱图像的自适应结构化压缩采样和低秩稀疏张量重构.在采样方面,设计基于部分压缩采样的信息冗余度的估计方法,提出采样率自适应分配策略,使得可压缩块获得相对较少的资源,而非可压缩块得到充足的采样,为精确重构奠定基础.在采样矩阵构造方面，在确定采样和随机采样间进行折衷, 设计了基于内容的结构化采样矩阵,提高了采样的效率.在压缩重构方面,将矩阵的低秩稀疏分解推广到高阶张量的低秩稀疏逼近，充分利用高光谱图像中所包含的非局部冗余和结构冗余，提出基于低秩稀疏先验的张量重构方法. 通过该项目的研究，为自适应压缩感知的理论和应用奠定一定基础。

采样矩阵构造和压缩感知重构是压缩采样成像的关键问题。针对某特定类型的信号，信息的分布并不是完全均匀随机的，也就是说，信号信息的分布既具有确定性，又具有随机性，设计了结构化采样矩阵，提高采样效率。在重构算法方面,将矩阵的低秩稀疏分解、非局部全变分和基于压缩采样的像元聚类引入压缩重构，充分利用高光谱图像中所包含的非局部冗余和结构冗余，提出基于低秩稀疏分解的高光谱图像重构,基于NLTV的高光谱压缩重构方法,基于聚类和低秩稀疏分解的高光谱图像重构,基于聚类NLTV和低秩稀疏分解的高光谱图像重构, 以及基于低秩稀疏矩阵分解的压缩采样ISAR成像方法。通过该项目的研究，为自适应压缩感知的理论和应用奠定一定基础。