Hyperspectral mixed denoising via spectral difference-induced total variation and low-rank approximation

Exploration of multiple priors on observed signals has been demonstrated to be one of the effective ways for recovering underlying signals. In this paper, a new spectral difference-induced total variation and low-rank approximation (termed SDTVLA) method is proposed for hyperspectral mixed denoising. Spectral difference transform, which projects data into spectral difference space (SDS), has been proven to be powerful at changing the structures of noises (especially for sparse noise with a specific pattern, e.g., stripes or dead lines present at the same position in a series of bands) in an original hyperspectral image (HSI), thus allowing low-rank techniques to get rid of mixed noises more efficiently without treating them as low-rank features. In addition, because the neighboring pixels are highly correlated and the spectra of homogeneous objects in a hyperspectral scene are always in the same low-dimensional manifold, we are inspired to combine total variation and the nuclear norm to simultaneously exploit the local piecewise smoothness and global low rankness in SDS for mixed noise reduction of HSI. Finally, the alternating direction methods of multipliers (ADMM) is employed to effectively solve the SDTVLA model. Extensive experiments on three simulated and two real HSI datasets demonstrate that, in terms of quantitative metrics (i.e., the mean peak signal-to-noise ratio (MPSNR), the mean structural similarity index (MSSIM) and the mean spectral angle (MSA)), the proposed SDTVLA method is, on average, 1.5 dB higher MPSNR values than the competitive methods as well as performing better in terms of visual effect.