Multitask Sparse Nonnegative Matrix Factorization for Joint Spectral–Spatial Hyperspectral Imagery Denoising

Hyperspectral imagery (HSI) denoising is a challenging problem because of the difficulty in preserving both spectral and spatial structures simultaneously. In recent years, sparse coding, among many methods dedicated to the problem, has attracted much attention and showed state-of-the-art performance. Due to the low-rank property of natural images, an assumption can be made that the latent clean signal is a linear combination of a minority of basis atoms in a dictionary, while the noise component is not. Based on this assumption, denoising can be explored as a sparse signal recovery task with the support of a dictionary. In this paper, we propose to solve the HSI denoising problem by sparse nonnegative matrix factorization (SNMF), which is an integrated model that combines parts-based dictionary learning and sparse coding. The noisy image is used as the training data to learn a dictionary, and sparse coding is used to recover the image based on this dictionary. Unlike most HSI denoising approaches, which treat each band image separately, we take the joint spectral-spatial structure of HSI into account. Inspired by multitask learning, a multitask SNMF (MTSNMF) method is developed, in which bandwise denoising is linked across the spectral domain by sharing a common coefficient matrix. The intrinsic image structures are treated differently but interdependently within the spatial and spectral domains, which allows the physical properties of the image in both spatial and spectral domains to be reflected in the denoising model. The experimental results show that MTSNMF has superior performance on both synthetic and real-world data compared with several other denoising methods.