6,822 research outputs found
Compressive Sensing Theory for Optical Systems Described by a Continuous Model
A brief survey of the author and collaborators' work in compressive sensing
applications to continuous imaging models.Comment: Chapter 3 of "Optical Compressive Imaging" edited by Adrian Stern
published by Taylor & Francis 201
Projection-Based and Look Ahead Strategies for Atom Selection
In this paper, we improve iterative greedy search algorithms in which atoms
are selected serially over iterations, i.e., one-by-one over iterations. For
serial atom selection, we devise two new schemes to select an atom from a set
of potential atoms in each iteration. The two new schemes lead to two new
algorithms. For both the algorithms, in each iteration, the set of potential
atoms is found using a standard matched filter. In case of the first scheme, we
propose an orthogonal projection strategy that selects an atom from the set of
potential atoms. Then, for the second scheme, we propose a look ahead strategy
such that the selection of an atom in the current iteration has an effect on
the future iterations. The use of look ahead strategy requires a higher
computational resource. To achieve a trade-off between performance and
complexity, we use the two new schemes in cascade and develop a third new
algorithm. Through experimental evaluations, we compare the proposed algorithms
with existing greedy search and convex relaxation algorithms.Comment: sparsity, compressive sensing; IEEE Trans on Signal Processing 201
Support Recovery of Sparse Signals
We consider the problem of exact support recovery of sparse signals via noisy
measurements. The main focus is the sufficient and necessary conditions on the
number of measurements for support recovery to be reliable. By drawing an
analogy between the problem of support recovery and the problem of channel
coding over the Gaussian multiple access channel, and exploiting mathematical
tools developed for the latter problem, we obtain an information theoretic
framework for analyzing the performance limits of support recovery. Sharp
sufficient and necessary conditions on the number of measurements in terms of
the signal sparsity level and the measurement noise level are derived.
Specifically, when the number of nonzero entries is held fixed, the exact
asymptotics on the number of measurements for support recovery is developed.
When the number of nonzero entries increases in certain manners, we obtain
sufficient conditions tighter than existing results. In addition, we show that
the proposed methodology can deal with a variety of models of sparse signal
recovery, hence demonstrating its potential as an effective analytical tool.Comment: 33 page
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