This paper studies the hyperspectral image (HSI) denoising problem under the assumption that the signal is low in rank. In this paper, a mixture of Gaussian noise and sparse noise is considered. The sparse noise includes stripes, impulse noise, and dead pixels. The denoising task is formulated as a low-rank tensor recovery (LRTR) problem from Gaussian noise and sparse noise. Traditional low-rank tensor decomposition methods are generally NP-hard to compute. Besides, these tensor decomposition based methods are sensitive to sparse noise. In contrast, the proposed LRTR method can preserve the global structure of HSIs and simultaneously remove Gaussian noise and sparse noise.The proposed method is based on a new tensor singular value decomposition and tensor nuclear norm. The NP-hard tensor recovery task is well accomplished by polynomial time algorithms. The convergence of the algorithm and the parameter settings are also described in detail. Preliminary numerical experiments have demonstrated that the proposed method is effective for low-rank tensor recovery from Gaussian noise and sparse noise. Experimental results also show that the proposed LRTR method outperforms other denoising algorithms on real corrupted hyperspectral data.

Several bandwise total variation (TV) regularized low-rank (LR)-based models have been proposed to remove mixed noise in hyperspectral images (HSIs). These methods convert high-dimensional HSI data into 2-D data based on LR matrix factorization. This strategy introduces the loss of useful multiway structure information. Moreover, these bandwise TV-based methods exploit the spatial information in a separate manner. To cope with these problems, we propose a spatial-spectral TV regularized LR tensor factorization (SSTV-LRTF) method to remove mixed noise in HSIs. From one aspect, the hyperspectral data are assumed to lie in an LR tensor, which can exploit the inherent tensorial structure of hyperspectral data. The LRTF-based method can effectively separate the LR clean image from sparse noise. From another aspect, HSIs are assumed to be piecewisely smooth in the spatial domain. The TV regularization is effective in preserving the spatial piecewise smoothness and removing Gaussian noise. These facts inspire the integration of the LRTF with TV regularization. To address the limitations of bandwise TV, we use the SSTV regularization to simultaneously consider local spatial structure and spectral correlation of neighboring bands. Both simulated and real data experiments demonstrate that the proposed SSTV-LRTF method achieves superior performance for HSI mixed-noise removal, as compared to the state-of-the-art TV regularized and LR-based methods.

The extraction of a valuable set of features and the design of a discriminative classifier are crucial for target recognition in SAR image. Although various features and classifiers have been proposed over the years, target recognition under extended operating conditions (EOCs) is still a challenging problem, e.g., target with configuration variation, different capture orientations, and articulation. To address these problems, this paper presents a new strategy for target recognition. We first propose a low-dimensional representation model via incorporating multi-manifold regularization term into the low-rank matrix factorization framework. Two rules, pairwise similarity and local linearity, are employed for constructing multiple manifold regularization. By alternately optimizing the matrix factorization and manifold selection, the feature representation model can not only acquire the optimal low-rank approximation of original samples, but also capture the intrinsic manifold structure information. Then, to take full advantage of the local structure property of features and further improve the discriminative ability, local sparse representation is proposed for classification. Finally, extensive experiments on moving and stationary target acquisition and recognition (MSTAR) database demonstrate the effectiveness of the proposed strategy, including target recognition under EOCs, as well as the capability of small training size.

This study combines a smooth prior long autoregressive (SLAR) model and Riemannian geometry method to realise target detection in the presence of non‐stationary clutter. First, SLAR is used for parameterisation of the signal. Then, the signal is mapped to a parameter vector space which can be described as a complex Riemannian manifold. Each point of this manifold is identified by a vector of AR coefficients. The principle of detection is that if a location has an enough Riemannian distance from the Riemannian median estimated by its neighbouring locations, targets are supposed to appear at this location. Numeric experiments and real radar target detection within sea clutter are given to demonstrate the effectiveness of the proposed targets detection method.