Abstract
In this article, a wavelet-based energy minimization framework is developed for joint estimation of endmembers and abundances without assuming pure pixels while considering noisy scenario. Spectrally dense and overlapped hyperspectral data are represented using biorthogonal wavelet bases that yield a compact linear mixing model in the wavelet domain. It acts as the data term and helps to reduce solution space of the unmixed components. Three prior terms are incorporated to better handle the ill-posedness, i.e., the logarithm of determinant volume regularizer enforces minimum endmember simplex, smoothness (spatial) prior to individual abundance maps, and spectral constraint through learning dictionary of abundances. Alternating nonnegative least-squares is employed to optimize the regularized and constrained nonnegative matrix factorization functional in the wavelet domain. We conduct theoretical analysis, discuss convergence and algorithmic details. Experiments are conducted on synthetic and three real benchmark hyperspectral data AVIRIS Cuprite, HYDICE Urban, and AVIRIS Jasper Ridge. The efficacy of the proposed algorithm is evaluated by comparing results with state of the art.
Highlights
AND LITERATURE REVIEWSpectral unmixing determines number of spectrally distinct materials signatures, extracts their signature values called endmembers, and estimates corresponding fractional contributions called abundances from a remotely acquired hyperspectral scene [1]
We found that hyperspectral data is better compressible in wavelet space (Fig. 2 and Table I), and we formulate the problem in the sparse wavelet domain that effectively reduces the solution space of the unmixed components by the proposed compact linear mixing model (LMM) (Eq (2))
This paper has proposed a novel blind spectral unmixing approach in the wavelet domain without assuming pure pixel and under noisy data setting
Summary
AND LITERATURE REVIEWSpectral unmixing determines number of spectrally distinct materials signatures, extracts their signature values called endmembers, and estimates corresponding fractional contributions called abundances from a remotely acquired hyperspectral scene [1]. Structured matrix factorization models such as nonnegative matrix factorization (NMF) has physically meaningful interpretation in solving the inverse ill-posed problem of joint estimation of endmembers and abundances. Several simplexbased spectral unmixing algorithms have been proposed under volume minimization or maximization based matrix factorization [5], [6], [7], [8]. It is recently demonstrated that if the data is represented in the sparse space, one could improve the quality of factorization [10]. To this end, the wavelet transform with its inherent compressibility, multiresolution and discriminating capability towards signal analysis can be sought. A curvelet domain-based NMF for the unmixing is recently proposed in [12]
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