67,104 research outputs found
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
Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling
Solving linear regression problems based on the total least-squares (TLS)
criterion has well-documented merits in various applications, where
perturbations appear both in the data vector as well as in the regression
matrix. However, existing TLS approaches do not account for sparsity possibly
present in the unknown vector of regression coefficients. On the other hand,
sparsity is the key attribute exploited by modern compressive sampling and
variable selection approaches to linear regression, which include noise in the
data, but do not account for perturbations in the regression matrix. The
present paper fills this gap by formulating and solving TLS optimization
problems under sparsity constraints. Near-optimum and reduced-complexity
suboptimum sparse (S-) TLS algorithms are developed to address the perturbed
compressive sampling (and the related dictionary learning) challenge, when
there is a mismatch between the true and adopted bases over which the unknown
vector is sparse. The novel S-TLS schemes also allow for perturbations in the
regression matrix of the least-absolute selection and shrinkage selection
operator (Lasso), and endow TLS approaches with ability to cope with sparse,
under-determined "errors-in-variables" models. Interesting generalizations can
further exploit prior knowledge on the perturbations to obtain novel weighted
and structured S-TLS solvers. Analysis and simulations demonstrate the
practical impact of S-TLS in calibrating the mismatch effects of contemporary
grid-based approaches to cognitive radio sensing, and robust
direction-of-arrival estimation using antenna arrays.Comment: 30 pages, 10 figures, submitted to IEEE Transactions on Signal
Processin
Structured variable selection and estimation
In linear regression problems with related predictors, it is desirable to do
variable selection and estimation by maintaining the hierarchical or structural
relationships among predictors. In this paper we propose non-negative garrote
methods that can naturally incorporate such relationships defined through
effect heredity principles or marginality principles. We show that the methods
are very easy to compute and enjoy nice theoretical properties. We also show
that the methods can be easily extended to deal with more general regression
problems such as generalized linear models. Simulations and real examples are
used to illustrate the merits of the proposed methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS254 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
OMP-type Algorithm with Structured Sparsity Patterns for Multipath Radar Signals
A transmitted, unknown radar signal is observed at the receiver through more
than one path in additive noise. The aim is to recover the waveform of the
intercepted signal and to simultaneously estimate the direction of arrival
(DOA). We propose an approach exploiting the parsimonious time-frequency
representation of the signal by applying a new OMP-type algorithm for
structured sparsity patterns. An important issue is the scalability of the
proposed algorithm since high-dimensional models shall be used for radar
signals. Monte-Carlo simulations for modulated signals illustrate the good
performance of the method even for low signal-to-noise ratios and a gain of 20
dB for the DOA estimation compared to some elementary method
Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG
The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS)
algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K
training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set
Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport
In this work, we propose a novel method for quantifying distances between
Toeplitz structured covariance matrices. By exploiting the spectral
representation of Toeplitz matrices, the proposed distance measure is defined
based on an optimal mass transport problem in the spectral domain. This may
then be interpreted in the covariance domain, suggesting a natural way of
interpolating and extrapolating Toeplitz matrices, such that the positive
semi-definiteness and the Toeplitz structure of these matrices are preserved.
The proposed distance measure is also shown to be contractive with respect to
both additive and multiplicative noise, and thereby allows for a quantification
of the decreased distance between signals when these are corrupted by noise.
Finally, we illustrate how this approach can be used for several applications
in signal processing. In particular, we consider interpolation and
extrapolation of Toeplitz matrices, as well as clustering problems and tracking
of slowly varying stochastic processes
Structured random measurements in signal processing
Compressed sensing and its extensions have recently triggered interest in
randomized signal acquisition. A key finding is that random measurements
provide sparse signal reconstruction guarantees for efficient and stable
algorithms with a minimal number of samples. While this was first shown for
(unstructured) Gaussian random measurement matrices, applications require
certain structure of the measurements leading to structured random measurement
matrices. Near optimal recovery guarantees for such structured measurements
have been developed over the past years in a variety of contexts. This article
surveys the theory in three scenarios: compressed sensing (sparse recovery),
low rank matrix recovery, and phaseless estimation. The random measurement
matrices to be considered include random partial Fourier matrices, partial
random circulant matrices (subsampled convolutions), matrix completion, and
phase estimation from magnitudes of Fourier type measurements. The article
concludes with a brief discussion of the mathematical techniques for the
analysis of such structured random measurements.Comment: 22 pages, 2 figure
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