In this paper, we present two novel algorithms for denoising hyperspectral data. Each algorithm exploits correlation between bands by enforcing simultaneous sparsity on their wavelet representations. This is done in a non-linear manner using wavelet decompositions and sparse approximation techniques. The first algorithm denoises an entire cube of data. Our experiments show that it outperforms wavelet-based global soft thresholding techniques in both a mean-square error (MSE) and a qualitative visual sense. The second algorithm denoises a set of noisy, user designated bands ("junk bands") by exploiting correlated information from higher quality bands within the same cube. We prove the utility of our junk band denoising algorithm by denoising ten bands of actual AVIRIS data by a significant amount. Preprocessing data cubes with these algorithms is likely to increase the performance of classifiers that make use of hyperspectral data, especially if the denoised and/or recovered bands contain spectral features useful for discriminating between classes.
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