Hyperspectral Image Reconstruction Based On Compressive Sensing

Hyperspectral Images(HSI) are huge collection of images that have been acquired simultaneously from a scene in a few hundred narrow adjacent frequency bands by the spectrometer. An HSI data set is thus a cube with two spatial and one spectral dimensions. The price to pay for such high spatio-spectral resolution is to handle extremely large data size. Such enormous amount of information brings serious challenges. Conventional compression methods sample the data with the Nyquist rate, and then compress and transmit it. This sampling process with high redundancy before compressing causes a great waste of resources, leading to an increase of computational complexity, and not suitable for the airborne or spaceborne applications with low power and limited resources. As a novel signal acquisition theory, compressed sensing(CS) combines the conventional sampling with compressing process. It acquires the measurement data directly at the pace of rate far blow Nyquist, and in this way the sampling costs and storage resource are reduced. The idea of CS is that the reconstruction model should be established on the basis of a fully exploit of the properties and priories of original data, which ensure the optimization of solution. Therefore, an algorithm research should be conducted on the basis of having a fully understanding of properties of hyperspectral images for the reconstruction problem.Based on these questions above, this paper investigates the compressed sensing reconstruction of HSI, summarized as the following three aspects:Firstly, a research on how the low-rank and sparse decomposition model bring an improvement in compressing and reconstruction performance of HSI is provided. This paper analyzes that there exists a strong correlation in different bands of hyperspectral images, and then proposes a reconstruction model based on low-rank and sparse decomposition in the background of low-rank matrix recovery. This model characterizes the correlation between spectra by low-rank constraint, and the difference is represented by sparse component. By comparing the simulation results, an improvement on reconstruction SNR of this algorithm is verified.Secondly, the nonlocal property of hyperspectral image is researched and a reconstruction model on the basis of non-local total variation is proposed. Comparing the natural images, there exist abundant texture and more edges in HSI. Traditional TV reconstruction method can easily lead to an edge blur and unsatisfactory reconstruction on details. Building upon the consideration of nonlocal structural features of HSI, this paper provides a hyperspectral reconstruction algorithm based on non-local TV and low-rank sparse decomposition. The simulation results show that this algorithm can ensure a high reconstruction quality, meanwhile, obtaining a better restoration on details.Although there exists a high correlation in different bands in HSI, it will decrease along with the increase of distance away from different bands. Through an analysis of the characteristics of HSI, a high degree of similarity among the pixels which representative similar substance is discovered. On the whole, the matrix composed of similar voxels has a more low-rank property than inhomogeneous voxels, and is more suitable for low-rank and sparse reconstruction model. Therefore, on the basis of previous work, a cluster-based non-local as well as low-rank and sparse model is proposed. The simulation results show that this algorithm indeed play a significant lifting effect on the reconstruction of HSI.