A total variation denoising algorithm for hyperspectral data

Since noise can undermine the effectiveness of information extracted from hyperspectral imagery, noise reduction is a prerequisite for many classification-based applications of hyperspectral imagery. In this paper, an effective three dimensional total variation denoising algorithm for hyperspectral imagery is introduced. First, a three dimensional objective function of total variation denoising model is derived from the classical two dimensional TV algorithms. For the consideration of the fact that the noise of hyperspectral imagery shows different characteristics in spatial and spectral domain, the objective function is further improved by utilizing two terms (spatial term and spectral term) and separate regularization parameters respectively which can adjust the trade-off between the two terms. Then, the improved objective function is discretized by approximating gradients with local differences, optimized by a quadratic convex function and finally solved by a majorization-minimization based iteration algorithm. The performance of the new algorithm is experimented on a set of Hyperion imageries acquired in a desert-dominated area in 2007. Experimental results show that, properly choosing the values of parameters, the new approach removes the indention and restores the spectral absorption peaks more effectively while having a similar improvement of signal-to-noise-ratio as minimum noise fraction (MNF) method.