Sensor Signal and Information Processing II [Editorial]

This Special Issue compiles a set of innovative developments on the use of sensor signals and information processing. In particular, these contributions report original studies on a wide variety of sensor signals including wireless communication, machinery, ultrasound, imaging, and internet data, and information processing methodologies such as deep learning, machine learning, compressive sensing, and variational Bayesian. All these devices have one point in common: These algorithms have incorporated some form of computational intelligence as part of their core framework in problem solving. They have the capacity to generalize and discover knowledge for themselves, learning to learn new information whenever unseen data are captured

Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA). For long data sequences, if one tries to use a single lower dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201

Overcomplete Dictionary and Deep Learning Approaches to Image and Video Analysis

Extracting useful information while ignoring others (e.g. noise, occlusion, lighting) is an essential and challenging data analyzing step for many computer vision tasks such as facial recognition, scene reconstruction, event detection, image restoration, etc. Data analyzing of those tasks can be formulated as a form of matrix decomposition or factorization to separate useful and/or fill in missing information based on sparsity and/or low-rankness of the data. There has been an increasing number of non-convex approaches including conventional matrix norm optimizing and emerging deep learning models. However, it is hard to optimize the ideal l0-norm or learn the deep models directly and efficiently. Motivated from this challenging process, this thesis proposes two sets of approaches: conventional and deep learning based. For conventional approaches, this thesis proposes a novel online non-convex lp-norm based Robust PCA (OLP-RPCA) approach for matrix decomposition, where 0 < p < 1. OLP-RPCA is developed from the offline version LP-RPCA. A robust face recognition framework is also developed from Robust PCA and sparse coding approaches. More importantly, OLP-RPCA method can achieve real-time performance on large-scale data without parallelizing or implementing on a graphics processing unit. We mathematically and empirically show that our OLP-RPCA algorithm is linear in both the sample dimension and the number of samples. The proposed OLP-RPCA and LP-RPCA approaches are evaluated in various applications including Gaussian/non-Gaussian image denoising, face modeling, real-time background subtraction and video inpainting and compared against numerous state-of-the-art methods to demonstrate the robustness of the algorithms. In addition, this thesis proposes a novel Robust lp-norm Singular Value Decomposition (RP-SVD) method for analyzing two-way functional data. The proposed RP-SVD is formulated as an lp-norm based penalized loss minimization problem. The proposed RP-SVD method is evaluated in four applications, i.e. noise and outlier removal, estimation of missing values, structure from motion reconstruction and facial image reconstruction. For deep learning based approaches, this thesis explores the idea of matrix decomposition via Robust Deep Boltzmann Machines (RDBM), an alternative form of Robust Boltzmann Machines, which aiming at dealing with noise and occlusion for face-related applications, particularly. This thesis proposes an extension to texture modeling in the Deep Appearance Models (DAMs) by using RDBM to enhance its robustness against noise and occlusion. The extended model can cope with occlusion and extreme poses when modeling human faces in 2D image reconstruction. This thesis also introduces new fitting algorithms with occlusion awareness through the mask obtained from the RDBM reconstruction. The proposed approach is evaluated in various applications by using challenging face datasets, i.e. Labeled Face Parts in the Wild (LFPW), Helen, EURECOM and AR databases, to demonstrate its robustness and capabilities