1,489 research outputs found
Adaptive low rank and sparse decomposition of video using compressive sensing
We address the problem of reconstructing and analyzing surveillance videos
using compressive sensing. We develop a new method that performs video
reconstruction by low rank and sparse decomposition adaptively. Background
subtraction becomes part of the reconstruction. In our method, a background
model is used in which the background is learned adaptively as the compressive
measurements are processed. The adaptive method has low latency, and is more
robust than previous methods. We will present experimental results to
demonstrate the advantages of the proposed method.Comment: Accepted ICIP 201
Video Compressive Sensing for Dynamic MRI
We present a video compressive sensing framework, termed kt-CSLDS, to
accelerate the image acquisition process of dynamic magnetic resonance imaging
(MRI). We are inspired by a state-of-the-art model for video compressive
sensing that utilizes a linear dynamical system (LDS) to model the motion
manifold. Given compressive measurements, the state sequence of an LDS can be
first estimated using system identification techniques. We then reconstruct the
observation matrix using a joint structured sparsity assumption. In particular,
we minimize an objective function with a mixture of wavelet sparsity and joint
sparsity within the observation matrix. We derive an efficient convex
optimization algorithm through alternating direction method of multipliers
(ADMM), and provide a theoretical guarantee for global convergence. We
demonstrate the performance of our approach for video compressive sensing, in
terms of reconstruction accuracy. We also investigate the impact of various
sampling strategies. We apply this framework to accelerate the acquisition
process of dynamic MRI and show it achieves the best reconstruction accuracy
with the least computational time compared with existing algorithms in the
literature.Comment: 30 pages, 9 figure
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
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
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