Invited Talks to RSL-CV 2015
Incremental Robust Principal Component Analysis for Video Background Modeling: theory, applications and jitter invariant extension. (Speaker: Paul Rodriguez)
Abstract: While Robust Principal Component Analysis (RPCA), a.k.a. Principal Component Pursuit (PCP), is currently considered to be the state of the art method for video background modeling, it suffers from a number of limitations, including a high computational cost, a batch operating mode, and sensitivity to camera jitter. The original PCP problem considers the nuclear and l1 norms as penalties for the background (low-rank) and foreground or moving objects (sparse) with an equality constrain for the observed videos and low-rank and sparse components. In this talk we propose to change constrains to penalties, obtaining a variant where the restoration error (observed video minus low-rank and sparse component) and l1 norm are penalties while imposing the rank of the low-rank component as a constraint. Interestingly, this particular variant can be effectively solved in an incremental fashion, allowing real-time implementation for live-feed HD videos; moreover, considering T(.), an unknown rigid transformation, applied to the low-rank component, we can also cope with translational and rotational jitter, allowing almost real-time processing. Furthermore, in this talk we will also include a detail analysis of the proposed RPCA variant as well as incremental SVD, which is the key to solve the equivalent problem incrementally.
Biography: Paul Rodriguez received the BSc degree in electrical engineering from the « Pontificia Universidad Católica del Perú » (PUCP), Lima, Peru, in 1997, and the MSc and PhD degrees in electrical engineering from the University of New Mexico, USA, in 2003 and 2005 respectively. He spent two years (2005-2007) as a postdoctoral researcher at Los Alamos National Laboratory, and is currently a Full Professor with the Department of Electrical Engineering at PUCP. His research interests include AM-FM models, parallel algorithms, adaptive signal decompositions, and inverse problems in signal and image processing.
Low-rank plus sparse dynamic MRI: Accelerated data acquisition, robust background suppression and self-learning of inter-frame motion fields (Speaker: Ricardo Otazo)
Abstract: Dynamic MRI techniques acquire a series of images that encode information of clinical interest, such as contrast enhancement and signal relaxation. Fast imaging is required to enable simultaneous high spatial and temporal resolution, and appropriate volumetric coverage. Extensive spatiotemporal correlations in dynamic MRI enable the application of compressed sensing and low-rank matrix completion to accelerate data acquisition. The combination of both approaches is very attractive to increase imaging speed and can offer additional benefits such as automatic background suppression and motion compensation. This talk will present: a) the application of the low-rank plus sparse (L+S) matrix decomposition or robust principal component analysis (RPCA) to reconstruct undersampled dynamic MRI data with separation of background (L) and dynamic (S) components; and b) an extension of the L+S approach that is robust to organ motion (motion-guided L+S), which learns inter-frame motion fields within the image reconstruction process. Practical examples of clinical interest including time-resolved peripheral angiography, cardiac perfusion and abdominal perfusion will be presented to show feasibility and general applicability of the L+S method.
Biography: Ricardo Otazo is an Assistant Professor of Radiology at New York University School of Medicine. He received his B.Sc. in Electrical Engineering from Universidad Catolica de Asuncion, Paraguay in 2001, and his M.Sc. and Ph.D. in Electrical Engineering from the University of New Mexico in 2005 and 2007 respectively. His research work aims at developing rapid MRI and low-dose CT techniques using advanced mathematical and physical models based on compressed sensing and low-rank matrix completion.
Globally Optimal Structured Low-Rank Matrix and Tensor Factorization (Speaker: René Vidal)
Abstract: Recently, convex solutions to low-rank matrix factorization problems have received increasing attention in machine learning. However, in many applications the data can display other structures beyond simply being low-rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current low-rank methods. This talk will explore a matrix factorization technique suitable for large datasets that captures additional structure in the factors by using a projective tensor norm, which includes classical image regularizers such as total variation and the nuclear norm as particular cases. Although the resulting optimization problem is not convex, we show that under certain conditions on the factors, any local minimizer for the factors yields a global minimizer for their product. Examples in biomedical video segmentation and hyperspectral compressed recovery show the advantages of our approach on high-dimensional datasets.
Biography: René Vidal is a professor in the Department of Biomedical Engineering at The Johns Hopkins University. He directs the Vision Dynamics and Learning Lab, which is part of the Center for Imaging Science (CIS). He is also a faculty member in the Institute for Computational Medicine (ICM) and the Laboratory for Computational Sensing and Robotics (LCSR). His research areas are biomedical image analysis, computer vision, machine learning, dynamical systems theory and robotics. He is particularly interested in the development of mathematical methods for the interpretation of high-dimensional data. In particular, he developed methods from algebraic geometry, sparse and low-rank representation theory for clustering and classification of high-dimensional data, and methods from dynamical systems theory for modeling and comparison of time series data. Applications include motion segmentation, dynamic texture classification, object and activity recognition in images and videos.