Noise Estimation for Hyperspectral Imagery using Spectral Unmixing and Synthesis

Most hyperspectral image (HSI) processing algorithms assume a signal to noise ratio model in their formulation which makes them dependent on accurate noise estimation. Many techniques have been proposed to estimate the noise. A very comprehensive comparative study on the subject is done by Gao et al. [1]. In a nut-shell, most techniques are based on the idea of calculating standard deviation from assumed-to-be homogenous regions in the image. Some of these algorithms work on a regular grid parameterized with a window size w, while others make use of image segmentation in order to obtain homogenous regions. This study focuses not only to the statistics of the noise but to the estimation of the noise itself. A noise estimation technique motivated from a recent HSI de-noising approach [2] is proposed in this study. The de-noising algorithm is based on estimation of the end-members and their fractional abundances using non-negative least squares method. The end-members are extracted using the well-known simplex volume optimization technique called N-FINDR after manual selection of number of end-members and the image is reconstructed using the estimated end-members and abundances. Actually, image de-noising and noise estimation are two sides of the same coin: Once we de-noise an image, we can estimate the noise by calculating the difference of the de-noised image and the original noisy image. In this study, the noise is estimated as described above. To assess the accuracy of this method, the methodology in [1] is followed, i.e., synthetic images are created by mixing end-member spectra and noise. Since best performing method for noise estimation was spectral and spatial de-correlation (SSDC) originally proposed in [3], the proposed method is compared to SSDC. The results of the experiments conducted with synthetic HSIs suggest that the proposed noise estimation strategy outperforms the existing techniques in terms of mean and standard deviation of absolute error of the estimated noise. Finally, it is shown that the proposed technique demonstrated a robust behavior to the change of its single parameter, namely the number of end-members