5,405 research outputs found
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
Sparse Signal Processing Concepts for Efficient 5G System Design
As it becomes increasingly apparent that 4G will not be able to meet the
emerging demands of future mobile communication systems, the question what
could make up a 5G system, what are the crucial challenges and what are the key
drivers is part of intensive, ongoing discussions. Partly due to the advent of
compressive sensing, methods that can optimally exploit sparsity in signals
have received tremendous attention in recent years. In this paper we will
describe a variety of scenarios in which signal sparsity arises naturally in 5G
wireless systems. Signal sparsity and the associated rich collection of tools
and algorithms will thus be a viable source for innovation in 5G wireless
system design. We will discribe applications of this sparse signal processing
paradigm in MIMO random access, cloud radio access networks, compressive
channel-source network coding, and embedded security. We will also emphasize
important open problem that may arise in 5G system design, for which sparsity
will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces
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