10,639 research outputs found
Joint Block-Sparse Recovery Using Simultaneous BOMP/BOLS
We consider the greedy algorithms for the joint recovery of high-dimensional
sparse signals based on the block multiple measurement vector (BMMV) model in
compressed sensing (CS). To this end, we first put forth two versions of
simultaneous block orthogonal least squares (S-BOLS) as the baseline for the
OLS framework. Their cornerstone is to sequentially check and select the
support block to minimize the residual power. Then, parallel performance
analysis for the existing simultaneous block orthogonal matching pursuit
(S-BOMP) and the two proposed S-BOLS algorithms is developed. It indicates that
under the conditions based on the mutual incoherence property (MIP) and the
decaying magnitude structure of the nonzero blocks of the signal, the
algorithms select all the significant blocks before possibly choosing incorrect
ones. In addition, we further consider the problem of sufficient data volume
for reliable recovery, and provide its MIP-based bounds in closed-form. These
results together highlight the key role of the block characteristic in
addressing the weak-sparse issue, i.e., the scenario where the overall sparsity
is too large. The derived theoretical results are also universally valid for
conventional block-greedy algorithms and non-block algorithms by setting the
number of measurement vectors and the block length to 1, respectively.Comment: This work has been submitted to the IEEE for possible publicatio
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
This paper demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with nonzero entries in dimension given random linear measurements of that signal. This is a massive improvement over previous results, which require measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems
Recovery of Sparse Signals Using Multiple Orthogonal Least Squares
We study the problem of recovering sparse signals from compressed linear
measurements. This problem, often referred to as sparse recovery or sparse
reconstruction, has generated a great deal of interest in recent years. To
recover the sparse signals, we propose a new method called multiple orthogonal
least squares (MOLS), which extends the well-known orthogonal least squares
(OLS) algorithm by allowing multiple indices to be chosen per iteration.
Owing to inclusion of multiple support indices in each selection, the MOLS
algorithm converges in much fewer iterations and improves the computational
efficiency over the conventional OLS algorithm. Theoretical analysis shows that
MOLS () performs exact recovery of all -sparse signals within
iterations if the measurement matrix satisfies the restricted isometry property
(RIP) with isometry constant The recovery performance of MOLS in the noisy scenario is also
studied. It is shown that stable recovery of sparse signals can be achieved
with the MOLS algorithm when the signal-to-noise ratio (SNR) scales linearly
with the sparsity level of input signals
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
TV-min and Greedy Pursuit for Constrained Joint Sparsity and Application to Inverse Scattering
This paper proposes a general framework for compressed sensing of constrained
joint sparsity (CJS) which includes total variation minimization (TV-min) as an
example. TV- and 2-norm error bounds, independent of the ambient dimension, are
derived for the CJS version of Basis Pursuit and Orthogonal Matching Pursuit.
As an application the results extend Cand`es, Romberg and Tao's proof of exact
recovery of piecewise constant objects with noiseless incomplete Fourier data
to the case of noisy data.Comment: Mathematics and Mechanics of Complex Systems (2013
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