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 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 multi-task learning, a multi-task SNMF (MTSNMF) method is developed in which band-wise denoising is linked across the spectral domain by sharing a common coefficient matrix. The intrinsic image structures are treated differently but inter-dependently within the spatial and spectral domains, which allows the physical properties of image in both spatial and spectral domains to be reflected in the denoising model. In addition, we introduce variance stabilizing transformation (VST) to provide a denoising solution for HSI which has both signal-dependent and signal-independent noise components. The experimental results show that MTSNMF has superior performance on both synthetic and real-world data compared with several other denoising methods. Index Terms Hyperspectral imagery, noise reduction, multi-task learning, nonnegative matrix factorization, sparse coding. M. Ye and Y. Qian are with the Institute of Artificial Intelligence, College of Computer Science, Zhejiang University, Hangzhou 310027, P.R. China. Correspondence author: Y. Qian ([email protected]) J. Zhou is with School of Information and Communication Technology, Griffith University, Nathan, Australia. This work was supported by the National Basic Research Program of China (No. 2012CB316400), the National Natural Science Foundation of China (No. 61171151), and Australian Research Councils DECRA Projects funding scheme (project ID DE120102948)