Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration

In this paper, we present a spatial spectral hyperspectral image (HSI) mixed-noise removal method named total variation (TV)-regularized low-rank matrix factorization (LRTV). In general, HSIs are not only assumed to lie in a low-rank subspace from the spectral perspective but also assumed to be piecewise smooth in the spatial dimension. The proposed method integrates the nuclear norm, TV regularization, and L
₁
-norm together in a unified framework. The nuclear norm is used to exploit the spectral low-rank property, and the TV regularization is adopted to explore the spatial piecewise smooth structure of the HSI. At the same time, the sparse noise, which includes stripes, impulse noise, and dead pixels, is detected by the L
₁
-norm regularization. To tradeoff the nuclear norm and TV regularization and to further remove the Gaussian noise of the HSI, we also restrict the rank of the clean image to be no larger than the number of endmembers. A number of experiments were conducted in both simulated and real data conditions to illustrate the performance of the proposed LRTV method for HSI restoration.