Spatial and spectral regularization in unmixing of remotely sensed data
Patel, Jignesh Rameshchandra
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The hyperspectral imaging opens the broad possibilities for remote sensing data analysis with it’s rich spectral information. However, this has a trade-off with limited spatial details due to the presence of several hardware constraints. Hence, due to the low spatial (ground) resolution, more than one material is generally mixed in a single pixel (location) of acquired scene data. The process of identifying and then quantifying the materials present in a scene, pixel-by-pixel, is called spectral unmixing. This has three steps, 1) estimating the number of endmembers (pure pixels), 2) extracting endmembers, i.e., spectral signatures of the constituted materials, and, 3) estimating abundances, i.e., fractional contribution of each endmember across all locations in a scene. With the passive remote sensing and to achieve mathematical tractability, endmembers are considered as non-negative while abundances are constrained to non-negative as well as sum-to-one at every location. To improve the performance, one should employ regularization that captures the prior information about data. Abundance maps are used to infer the proportions of endmembers with the given endmember signatures and reflectance value at each location. In this thesis, we begin with an algorithmic approach to estimate fractions (abundances) of materials (endmembers) in a pixel by considering linear mixture model (LMM) and where the endmembers are known. We propose the use of Inhomogeneous Gaussian Markov random field (IGMRF) as a prior on abundances that captures the smoothness as well as preserves the discontinuities among the abundance values. We obtain the IGMRF parameters using the initial estimate of abundances. Both the abundances and IGMRF parameters are refined by optimizing an energy function. A two-step iterative approach is proposed to obtain the final estimates of both the abundance maps and their prior parameters. In order to demonstrate the efficacy of the proposed approach, we conduct experiments on the synthetic hyperspectral images (HSIs) with different noise levels as well as on the real HSIs and compare our results with other state-of-the-art approaches. The IGMRF prior captures the smoothness and preserves discontinuities among abundance values locally. Besides, abundance maps exhibit redundancy which can be taken into account by another prior called sparsity-induced prior. We then build upon our first work and include sparsity-induced prior along with IGMRF prior. Here, we calculate IGMRF parameters at every pixel location, learn a dictionary and the sparse representation for abundances using the initial estimate in phase one; while the final abundance maps are estimated in the phase two. In order to learn the sparsity, we use the approach based on K- singular value decomposition (K-SVD). Both the IGMRF and sparseness parameters are initialized using an initial estimate of abundances and refined using the two-phase iterative approach. The experiments are conducted on the synthetic HSIs with different noise levels as well as on two real HSIs. The results are qualitatively and quantitatively compared with state-of-the-art approaches. Experimental results demonstrate the effectiveness of the proposed approach. We note that the abundance maps contain spatial information of the HSI. Hence, we seek to use abundance maps to enhance the spatial resolution of the HSI. We transfer the mapping from the low-resolution (LR) and high-resolution (HR) natural images learnt by a deep convolutional neural network (CNN) to get the initial estimates of the super-resolved abundance maps where the input corresponds to LR abundances maps. To get the better estimates of abundances and in turn improve the super-resolution (SR) of HSIs, we use a regularization framework in which both the LR and HR abundances are modelled as IGMRF that serves as the prior. Finally, the SR HSIs are obtained by using a linear mixing model that uses the SR abundances and the endmembers estimated using an appropriate technique. Experiments on synthetic as well as on real HSIs show that the proposed method performs better when compared to other existing SR approaches. One can see that the method do not require auxiliary image as used in many of the existing SR methods and, the spectral details are better preserved since the SR is carried out in abundance domain. Moreover, computational complexity is reduced since the SR is carried out on abundances which are a few in number when compared to the number of hyperspectral band images. Finally, we propose a novel approach for jointly estimating endmembers and abundances based on unsupervised learning using autoencoder with IGMRF as prior for regularization. The decoder part of proposed autoencoder has linear weights making it a LMM. The weights represent the endmember matrix that makes the hidden units of autoencoder as abundances. IGMRF is used to apply spatial regularization on abundances that also preserves the discontinuities. To incorporate the spectral regularization, we use IGMRF priors on endmembers. In addition, we also apply the spatial and spectral regularizations on the given HSI. IGMRF parameters at every pixel location are calculated using initial estimates of endmembers and abundances. We obtain both the endmembers and their abundances by optimizing the energy function that consists of a data term and IGMRF prior terms. Experiments are performed with different noise levels on the synthetic data and on two real data (Jasper ridge and Urban). The results of the proposed approach are better when compared to the existing state-of-the-art approaches.
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