Tensor Multi-Subspace Representation for Remote Sensing Image Mixed Noise Removal

Remote sensing image (RSI) denoising is an important and fundamental task in RSI processing. Existing denoising methods usually assume that RSI lies in a single matrix or tensor subspace. However, due to the wavelength difference or/and temporal variability, the assumption of a single subspace may not be suitable for RSI. To address this, we propose a tensor multi-subspace representation (TenMSR) for RSI mixed noise removal. To be specific, in this work, we introduce TenMSR to finely characterize the intrinsic tensor multi-subspace structure of RSI. Compared with the single matrix/tensor subspace-based methods, the proposed method can not only precisely describe the wavelength difference or/and temporal variability of RSI but also produce a more compact image distribution in tensor multi-subspace. To mine and preserve the multi-subspace structure, we introduce a nonlinear transform-based 3-D tensor nuclear norm to characterize the tensor low rankness of the multi-subspace representation coefficient. An effective algorithm based on the proximal alternating minimization (PAM) framework is developed to solve the proposed model with theoretical convergence analysis. Extensive experiments show the effectiveness and superiority of the proposed method over existing state-of-the-art single matrix/tensor subspace RSI denoising methods.