Hyperspectral Image Denoising via Subspace Low-rank Representation and Spatial‐spectral Total Variation

Hyperspectral images (HSIs) acquired actually often contain various types of noise, such as Gaussian noise, impulse noise, and dead lines. On the basis of land covers, the spectral vectors in HSI can be separated into different classifications, which means the spectral space can be regarded as a union of several low-rank (LR) subspaces rather than a single LR subspace. Recently, LR constraint has been widely applied for denoising HSI. However, those LR-based methods do not constrain the intrinsic structure of spectral space. And these methods cannot make better use of the spatial or spectral features in an HSI cube. In this article, a framework named subspace low-rank representation combined with spatial‐spectral total variation regularization (SLRR-SSTV) is proposed for HSI denoising, where the SLRR is introduced to more precisely satisfy the low-rank property of spectral space, and the SSTV regularization is involved for the spatial and spectral smoothness enhancement. An inexact augmented Lagrange multiplier method by alternative iteration is employed for the SLRR-SSTV model solution. Both simulated and real HSI experiment results demonstrate that the proposed method can achieve a state-of-the-art performance in HSI denoising.

Robust Principal Component Analysis-Based Infrared Small Target Detection

A method based on Robust Principle Component Analysis (RPCA) technique is proposed to detect small targets in infrared images. Using the low rank characteristic of background and the sparse characteristic of target, the observed image is regarded as the sum of a low-rank background matrix and a sparse outlier matrix, and then the decomposition is solved by the RPCA. The infrared small target is extracted from the single-frame image or multi-frame sequence. In order to get more efficient algorithm, the iteration process in the augmented Lagrange multiplier method is improved. The simulation results show that the method can detect out the small target precisely and efficiently.

Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications

The problem of data recovery in multiway arrays (i.e., tensors) arises in many fields such as computer vision, image processing, and traffic data analysis. In this paper, we propose a scalable and fast algorithm for recovering a low-n-rank tensor with an unknown fraction of its entries being arbitrarily corrupted. In the new algorithm, the tensor recovery problem is formulated as a mixture convex multilinear Robust Principal Component Analysis (RPCA) optimization problem by minimizing a sum of the nuclear norm and theℓ1-norm. The problem is well structured in both the objective function and constraints. We apply augmented Lagrange multiplier method which can make use of the good structure for efficiently solving this problem. In the experiments, the algorithm is compared with the state-of-art algorithm both on synthetic data and real data including traffic data, image data, and video data.