Novel approaches for spectral unmixing of hyperspectral data

Abstract

This thesis addresses the problem of spectral unmixing of remotely sensed hyperspectral data. The spectral unmixing has the objective of quantifying the reectance properties of di_erent materials on the earth. Complete spectral unmixing includes estimating the number of constituent materials in the data, extracting their spectral signatures called endmembers, and estimating their contributing ground cover fractions called abundances from each location of the acquired scene. The need of spectral unmixing has been fostered with the development of powerful hyperspectral sensors in the field of remote sensing. These hyperspectral imagers acquire a set of co-registered images of a scene with hundreds of narrow and contiguous bands covering the visible, the near-infrared, and the mid-infrared wavelengths of the electromagnetic spectrum. Due to limited spatial (ground) resolution supported by the high altitude sensors, the materials are often spatially mixed. One can unmix them using algorithmic approaches without the need for spatial resolution enhancement. This thesis contributes new methodologies for decomposing the hyperspectral data into its constituent entities and also provides a unified framework for the complete spectral unmixing of the data. This kind of analysis yields myriad of data products in remote sensing, defense and military, agricultural development, urban planning, and in many other areas. We begin by estimating the abundances considering cluttered endmembers that could happen in practice. Under linear mixing model, we consider an unmixing problem wherein given the extracted endmembers, the task is to estimate the abundances. This problem is solved using Tikhonov regularization within a total-least squares (TLS) framework that takes care of noise in both the data and endmembers. We discuss the role of regularization in the spectral unmixing, show the analysis of the regularized solution and compare it with a TLS-based direct inversion. The approach is experimentally tested on a synthetically generated hyperspectral data with di_erent noise levels in both data and ground truth endmembers as well as validated on the real hyperspectral data. The performance comparison using different quantitative measures is done with the existing approaches based on the TLS framework. We next consider the use of Huber-Markov random _eld (HMRF) prior on the abundances in order to improve their solution. Given the endmembers, we model the correlatedness among the abundances as the HMRF in the contiguous spectral space of the data. A maximum a posteriori (MAP) approach is used to solve for abundances using the fact that the abundances are dependent on the scene-contents and they represent mixing proportions of the endmembers over the scene area. The HMRF parameter is estimated from the data itself. For this we use an initial estimate of abundances that are estimated based on the matched-filter theory and thus derive a data-dependent or data-driven HMRF (dHMRF) prior. We present the theoretical analysis that shows the effectiveness of the proposed approach when compared to the state-of-art approaches. The proposed method has the following advantages: 1) The estimated abundances are resistant to noise since they are based on an initial estimate that has high signal-to-noise ratio (SNR). 2) The variance in the abundance maps is well preserved since the threshold in the dHMRF is derived from the data itself. The method is first evaluated on the simulated data for increasing noise levels and the sensitivity analysis is carried out for various parameters. The performance is also evaluated on a real hyperspectral imagery. The proposed approach outperforms the state-of-art methods when compared using different quantitative measures. Accurate estimate of endmembers is important when we attempt to solve the complete spectral unmixing. Towards this end, we next propose a novel approach for endmember extraction which gives band-wise estimate of the endmembers in order to enhance the accuracy of the estimation. This approach explores the spatial, spectral as well as temporal characteristics of the data for endmember extraction. An overdetermined system of linear equations is set-up using the knowledge of abundances and the multi-temporal data, and a constrained least-squares solution is sought to recover the endmembers. The approach is experimentally tested on a set of simulated data synthesized using real hyperspectral signatures. The method not only improves the accuracy of endmember extraction but also results in reduced computational complexity. Finally we provide a unified framework for the complete spectral unmixing in which we make use of the endmembers extracted using our band-wise endmember extraction algorithm. Inspired from the concept of bootstrapping in the field of linear electronics and by using the multitemporal data, we propose a novel approach for simultaneously identifying the number of endmembers, their signatures and carry out the unmixing without the need of additional information as used by other researchers. Here, the data reconstruction error (DRE) is utilized as a positive feedback to vary the number of endmembers. The process of iterative bootstraping (IB) is continued until the DRE between the available and reconstructed reectance is minimum, leading to an optimum solution in the leastsquares sense. The entire IB process is further described using geometric illustration. The proposed approach works as a self-regulatory mechanism for the complete spectral unmixing. It can also serve as a basis to find the temporal changes in a hyperspectral scene based on variations in the estimated abundances over a period of time. The efficacy of the method is tested on the multitemporal data constructed using the U.S. Geological Survey (USGS) spectral library signatures. The comparison of the results is shown with the standard hyperspectral unmixing process chains for the increasing noise levels in the data. The sensitivity analysis is carried out to verify the number of spectrally distinct signatures present in the scene, and finally a cross-check is done to further validate the unmixing.