Adaptive noise variance estimation and intrinsic order selection for low SNR hyperspectral signals

Abstract

In hyperspectral applications, signal vectors belong to a much lower dimensional subspace than the observed data. The true dimensionality of hyperspectral data is difficult to determine in practice. In the presence of powerful noise, estimation of the number of spectrally distinct signal sources that characterize the hyperspectral data is a challenge. Existing methods mostly assume some prior knowledge of the noise and signal structure. In practice, there is no a priori knowledge of the noise or signal statistics. Eigenvalue decomposition based methods, as the most commonly used methods, assume that the contribution of noise to the signal is extractable. In a noisy hyperspectral application this assumption is questionable. In this paper, we propose the Adaptive Noise Variance Estimation and Intrinsic Order Selection method that exploits the concept of residual autocorrelation power to adaptively estimate the noise variance and then simultaneously denoise and estimate the rank of the hyperspectral data. Rank conjecture is obtained by locating an optimum subset that best represents the noiseless signal. The algorithm was applied to both synthetically simulated data and to a real hyperspectral image. Comparing the results with those of existing methods indicates that this method will substantially improve the accuracy of the rank estimation in extremely noisy hyperspectral applications.