8,903 research outputs found
Stochastic Analysis of the LMS Algorithm for System Identification with Subspace Inputs
This paper studies the behavior of the low rank LMS adaptive algorithm for the general case in which the input transformation may not capture the exact input subspace. It is shown that the Independence Theory and the independent additive noise model are not applicable to this case. A new theoretical model for the weight mean and fluctuation behaviors is developed which incorporates the correlation between successive data vectors (as opposed to the Independence Theory model). The new theory is applied to a network echo cancellation scheme which uses partial-Haar input vector transformations. Comparison of the new model predictions with Monte Carlo simulations shows good-to-excellent agreement, certainly much better than predicted by the Independence Theory based model available in the literature
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
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Machine Learning for Fluid Mechanics
The field of fluid mechanics is rapidly advancing, driven by unprecedented
volumes of data from field measurements, experiments and large-scale
simulations at multiple spatiotemporal scales. Machine learning offers a wealth
of techniques to extract information from data that could be translated into
knowledge about the underlying fluid mechanics. Moreover, machine learning
algorithms can augment domain knowledge and automate tasks related to flow
control and optimization. This article presents an overview of past history,
current developments, and emerging opportunities of machine learning for fluid
mechanics. It outlines fundamental machine learning methodologies and discusses
their uses for understanding, modeling, optimizing, and controlling fluid
flows. The strengths and limitations of these methods are addressed from the
perspective of scientific inquiry that considers data as an inherent part of
modeling, experimentation, and simulation. Machine learning provides a powerful
information processing framework that can enrich, and possibly even transform,
current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202
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