Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements

Background subtraction has been a fundamental and widely studied task in video analysis, with a wide range of applications in video surveillance, teleconferencing and 3D modeling. Recently, motivated by compressive imaging, background subtraction from compressive measurements (BSCM) is becoming an active research task in video surveillance. In this paper, we propose a novel tensor-based robust PCA (TenRPCA) approach for BSCM by decomposing video frames into backgrounds with spatial-temporal correlations and foregrounds with spatio-temporal continuity in a tensor framework. In this approach, we use 3D total variation (TV) to enhance the spatio-temporal continuity of foregrounds, and Tucker decomposition to model the spatio-temporal correlations of video background. Based on this idea, we design a basic tensor RPCA model over the video frames, dubbed as the holistic TenRPCA model (H-TenRPCA). To characterize the correlations among the groups of similar 3D patches of video background, we further design a patch-group-based tensor RPCA model (PG-TenRPCA) by joint tensor Tucker decompositions of 3D patch groups for modeling the video background. Efficient algorithms using alternating direction method of multipliers (ADMM) are developed to solve the proposed models. Extensive experiments on simulated and real-world videos demonstrate the superiority of the proposed approaches over the existing state-of-the-art approaches.Comment: To appear in IEEE TI

Joint Nonlocal, Spectral, and Similarity Low-Rank Priors for Hyperspectral-Multispectral Image Fusion

The fusion of a low-spatial-and-high-spectral resolution hyperspectral image (HSI) with a high-spatial-and-low-spectral resolution multispectral image (MSI) allows synthesizing a high-resolution image (HRI), supporting remote sensing applications, such as disaster management, material identification, and precision agriculture. Unlike existing variational methods using low-rank regularizations separately, we present an HSI-MSI fusion method promoting various low-rank regularizations jointly. Our method refines the HRI spatial and spectral correlations from the individual HSI and MSI data through the proper plug-and-play (PnP) of a nonlocal patch-based denoiser in the alternating direction method of multipliers (ADMM). Notably, we consider the nonlocal self-similarity, the spectral low-rank, and introduce a rank-one similarity prior. Furthermore, we demonstrate via an extensive empirical study that the rank-one similarity prior is an inherent characteristic of the HRI. Simulations over standard benchmark datasets show the effectiveness of the proposed HSI-MSI fusion outperforming state-of-the-art methods, particularly in recovering low-contrast areas.acceptedVersionPeer reviewe

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Group-based Sparse Representation for Image Restoration

Traditional patch-based sparse representation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational complexity in dictionary learning. Second, each patch is considered independently in dictionary learning and sparse coding, which ignores the relationship among patches, resulting in inaccurate sparse coding coefficients. In this paper, instead of using patch as the basic unit of sparse representation, we exploit the concept of group as the basic unit of sparse representation, which is composed of nonlocal patches with similar structures, and establish a novel sparse representation modeling of natural images, called group-based sparse representation (GSR). The proposed GSR is able to sparsely represent natural images in the domain of group, which enforces the intrinsic local sparsity and nonlocal self-similarity of images simultaneously in a unified framework. Moreover, an effective self-adaptive dictionary learning method for each group with low complexity is designed, rather than dictionary learning from natural images. To make GSR tractable and robust, a split Bregman based technique is developed to solve the proposed GSR-driven minimization problem for image restoration efficiently. Extensive experiments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed GSR modeling outperforms many current state-of-the-art schemes in both PSNR and visual perception.Comment: 34 pages, 6 tables, 19 figures, to be published in IEEE Transactions on Image Processing; Project, Code and High resolution PDF version can be found: http://idm.pku.edu.cn/staff/zhangjian/. arXiv admin note: text overlap with arXiv:1404.756