A Novel Approach for Abundance Estimation in Wavelet Domain

In this paper, we propose a novel algorithmic approach to estimate abundances given the endmembers of hyperspectral imagery. The problem is ill-posed mainly because of the highly correlated signatures and noise in the data. To this end, we observe that the hyperspectral measurements are compressible in the wavelet space that helps making the problem better-posed. We propose to represent the hyperspectral data using the biorthogonal wavelet packet bases, and obtain regularized fully constrained abundances. The problem is formulated in the energy minimization framework. The data term consists of the linear mixing model represented using the wavelet packet bases where the condition number of the resultant endmember matrix is lowest. This enhances the solution space of abundances. Since abundances of an endmember often smoothly vary within its abundance map, we impose the smoothness constraint spatially on individual maps and consider it as the prior term in our approach. This helps achieving numerically stable solution within the enhanced solution space for the abundances. The proposed algorithm is evaluated by experimenting on synthetic hyperspectral data at different noise levels, and on two benchmark real data AVIRIS Cuprite and HYDICE Urban. The results are qualitatively and quantitatively compared with state-of-the-art algorithms.