Sparse recovery techniques for hyperspectral imaging

Abstract

Human vision is a powerful imaging system that can capture and interpret light energy coming from different sources although it is limited to visible light. There are various applications such as face recognition, medical imaging, agriculture, geology, surveillance, etc. that benefits by imaging several bands of the electromagnetic spectrum outside the visible range. The hyperspectral imaging techniques are capable of capturing hundreds of bands of the electromagnetic spectrum and thus, can be considered as the generalization of color imaging. The focus of this dissertation is on modeling hyperspectral imaging problems as linear inverse problems and solving them by exploiting inherent data properties. These imaging problems often form an underdetermined system of the linear equations having infinitely many solutions; therefore, additional constraints based on prior knowledge about data can help in determining the solution uniquely. This work aims at developing multispectral image acquisition and reconstruction techniques such that minimal changes are required in the hardware of compact digital cameras. A uniform multispectral filter array design has been proposed that satisfy both spatial consistency and spectral uniformity requirements. Based on proposed filter array pattern, an efficient demosaicing algorithm has been proposed to reconstruct the full multispectral image from severely under-sampled raw image such that reconstructed image has good visual quality. This work also focuses on hyperspectral denoising problem. Anovel spatio-spectral total-variation model has been proposed that gives a sparser representation of the sorted discrete gradient coefficients as compared to the band by band hyperspectral total-variation model. A general additive noise model was considered that accounts for not only Gaussian noise but also the sparse noise that includes impulse noise and line strips. The resulting optimization problem was solved using augmented- Lagrangian like the split-Bregman algorithm. Another problem discussed in this work is the hyperspectral unmixing problem that is related to blind source separation problem in signal processing. A joint-sparse model along with total variation in the general noise model framework has been considered in formulating the problem as a linear sparse unmixing problem. Since a particular endmember may be present at several locations, therefore, abundance maps shows joint sparsity. Proposed joint-sparsity and total variation based unmixing algorithm have been compared with several related unmixing algorithms to empirically demonstrate its performance using visual quality as well as signal to noise ratio. Further, A deep dictionary learning based approach has been proposed for hyperspectral image classification problem. The learning proceeds in a greedy fashion, therefore for each level we only need to learn a single layer of the dictionary. A comparative study with deep belief network and stacked autoencoder based techniques suggests that in the practical scenario, when the training data is limited, the proposed method outperforms these more established tools.