基于稀疏表示与低秩逼近的高光谱图像重建.pdf

摘要
摘要
高光谱图像的窄波段成像特质使得其能够分辨更加精细的地物细节，从而在
海洋遥感、精细农业、地质探测、环境监测、军事等各领域均有广泛的应用。由
传统传感器获得的大量高光谱图像数据为其在星载设备上的传输和处理带来了诸
多困难。压缩感知理论从较少的数据中恢复出稀疏信号的思想为解决该问题带来
了新的思路。将压缩感知理论应用于光谱图像的获取，近年来提出了许多基于编
码感知的光谱图像获取方法，实现了数据采集与压缩的同步获取，并由此降低了
采样时间和观测数据量。图像重建是基于编码感知的光谱图像获取的一个关键问
题。本文提出了基于稀疏表示与低秩逼近的光谱图像重建方法，获得了较好的重
建效果。
文章首先对基于编码感知的高光谱图像获取方法进行了简要介绍。接着通过
稀疏与低秩矩阵分解（又称 Robust PCA）挖掘了光谱图像的稀疏和低秩特性，并
对光谱图像进行了稀疏与低秩表示。然后利用矩阵分解实现了对光谱图像的去噪，
验证了稀疏与低秩特性在光谱图像重建中的作用。最后，通过三维块匹配方法对
光谱图像的非局部相似块进行聚类，充分利用了光谱图像的空间相关性和谱间相
关性。以结构稀疏与低秩特性作为先验正则，提出了光谱图像在结构稀疏表示下
的低秩逼近模型，实现了基于稀疏表示与低秩逼近的光谱图像重建。实验结果表
明，较之于其他同类算法，文章提出的算法能获得更高质量的重建图像。
关键词： 光谱图像重建 压缩感知 稀疏表示 低秩逼近 谱间相关性
ABSTRACT
Abstract
Being capable of acquiring images in many contiguous and very narrow spectral
bands enables hyperspectral images to exploit fine spectral differences between various
materials of interest. Therefore, nowadays hyperectral images are widely used in a
variety of fields, including precision agriculture, marine remote sensing, geological
detection, environmental monitoring, military researches and so on. As the amount of
data acquired by conventional sensors creates significant handling problems on
satellites or aircrafts, compressed sensing (CS) can be thought of as a natural candidate
for acquisition of hyperspectral images because it allows to represent sparse signals
through a small number of linear projections. Applying CS theory to the acquisition of
hyperspectral images, many hyperspectral imagers based on coding sensing, which
realize data acquisition and compression simultaneously and then greatly decrease the
measurement time and storage volume, have been developed in recent years. Image
reconstruction has always been a key problem to hyperspectral image acquisition