The Noiseless code-length concept in subspace estimation for low SNR hyperspectral signals

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. In practice, there is no a priori knowledge of the noise statistics. In this paper, we propose the hyperspectral noiseless code-length (HYNCO) method that exploits the high correlation property of hyperspectral data in adjacent bands. HYNCO uses a multiple regression based method to estimate the second order statistics of the noise signal. Further, a combination of the noiseless code-length concept and the multiple regression method is introduced to estimate the rank of the hyperspectral data. Rank conjecture is obtained by locating the subset that minimizes the reconstruction error defined by the method. The algorithm was applied to both synthetically simulated data and to a real hyperspectral image. Comparing the results with existing methods indicates that this method would strongly improve the accuracy of subspace estimation in extremely noisy applications.