Variational lp-lq Model for Hyperspectral Image Restoration Under Mixed Noise

Abstract:

In this work, we study the weighted l2-norm for approximating the solution of general lp-lq-norm problem for recovering hyperspectral images (HSI) corrupted by a mixture of Gaussian-impulse noise. As a special case of p,q in {1,2}, we design an optimization framework to accommodate the combined effect of different noise sources. An initial impulse noise pre-detection phase decouples the raw noisy HSI data into impulse and Gaussian corrupted pixels. Gaussian corrupted pixels are handled by data-fidelity term in l2-norm while impulse corrupted pixels possess more Laplacian like behaviour; modelled using l1-norm. Solutions of problems involving ||.||_1 in data fidelity and regularization terms complicates the optimization process but are less sensitive to outlier pixels. On the other hand, the least square solutions ||.||_2 for the data misfit are computationally efficient but generates solutions which are quite sensitive to outlier pixels; which is the characteristic of impulse corrupted pixels. Therefore, in this paper, we decouple the set of pixels into two distinct parts; handled using separate data fidelity terms. Total variation (TV) is used on the Casorati representation of input data to exploit similarity along both spatial spectral dimensions. The resulting optimization problem is reformulated as iteratively reweighted least square for the general lp-lq-norm problem for p= {1,2} for data fidelity terms and q=1 for the TV regularization term. Experiments conducted over synthetically corrupted HSI data and images obtained from real HSI sensors confirm the suitability of the proposed weighted norm optimization framework (WNOF) over a wide range of degradation scenarios. 

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