Spectral Image Recovery Based On Low-rank Approximation

Spectral image with its ”spectrum and space in one” imaging characteristic plays an important role in many practical areas, such as remote sensing and defense security, etc. Due to the faulty hardware and limited imaging sensor performance, the obtained spectral image suffers from data loss and lack of resolution during the actual imaging process, which have seriously affected the subsequent processing and utilization of spectral images. In order to acquire clear and high-resolution spectral image, many researchers have studied how to recovery high-quality spectral image from low-quality one, and several spectral image restoration methods have been proposed in recent years. However, the available spectral image restoration methods are mainly based on gray image representation models expressed by traditional total variation, discrete cosine transform and other mathematical methods, which can not effectively utilize the correlation of the spectral image in space and spectrum, leading to a limited recovery accuracy.This thesis begins with analyzing the prior knowledge of spectral image, focuses on the crucial characteristic of the regularization term in spectral image recovery model, and studies how to establish efficient regular constraints combining prior knowledge of spectral image. The main work and contributions of the dissertation are outlined as follows:1. By digging deep into spectral image’s prior characteristics, this thesis points out that the correlation of spectral image in 2-D space and 1-D spectrum finally results in non-local similarity of the whole 3-D data. Moreover, after statistical analysis, it finds out that the matrix consisting of spectral image’s non-local similar 3-D blocks has potential low-rank property.2. For the problem that traditional spectral image recovery methods can not take full advantages of the correlation of spectral image in 2-D space and 1-D spectrum and their recovery results are low-quality, the thesis proposes a spectral image recovery method via Schatten-p norm based low-rank approximation. The main idea of our method isoutlined as follows, firstly, search non-local similar 3-D blocks in Euclidean distance criterion under the framework of 3-D block-partitioning; secondly, establish the efficient regular constraint according to the low-rank property of similar 3-D blocks; afterwards, obtain the spectral image recovery model by using Schatten-p norm as nonconvex approximation of the rank of a matrix; finally, solve the spectral image and low-rank matrices iteratively by alternating optimization method. The experimental results of inpainting and compressive sensing reconstruction for spectral image demonstrate that the proposed method can effectively overcome the shortcoming of traditional spectral image recovery methods in both PSNR values and visual quality assessments. Moreover, the spectral images restored by our methods get higher PSNR values and have higher accuracy in structures such as edges and textures.