37,499 research outputs found
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
2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis
This work proposes an extension of the 1-D Hilbert Huang transform for the
analysis of images. The proposed method consists in (i) adaptively decomposing
an image into oscillating parts called intrinsic mode functions (IMFs) using a
mode decomposition procedure, and (ii) providing a local spectral analysis of
the obtained IMFs in order to get the local amplitudes, frequencies, and
orientations. For the decomposition step, we propose two robust 2-D mode
decompositions based on non-smooth convex optimization: a "Genuine 2-D"
approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D"
approach, which constrains separately the extrema of lines, columns, and
diagonals. The spectral analysis step is based on Prony annihilation property
that is applied on small square patches of the IMFs. The resulting 2-D
Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure
A new family of high-resolution multivariate spectral estimators
In this paper, we extend the Beta divergence family to multivariate power
spectral densities. Similarly to the scalar case, we show that it smoothly
connects the multivariate Kullback-Leibler divergence with the multivariate
Itakura-Saito distance. We successively study a spectrum approximation problem,
based on the Beta divergence family, which is related to a multivariate
extension of the THREE spectral estimation technique. It is then possible to
characterize a family of solutions to the problem. An upper bound on the
complexity of these solutions will also be provided. Simulations suggest that
the most suitable solution of this family depends on the specific features
required from the estimation problem
Semi-Supervised Sound Source Localization Based on Manifold Regularization
Conventional speaker localization algorithms, based merely on the received
microphone signals, are often sensitive to adverse conditions, such as: high
reverberation or low signal to noise ratio (SNR). In some scenarios, e.g. in
meeting rooms or cars, it can be assumed that the source position is confined
to a predefined area, and the acoustic parameters of the environment are
approximately fixed. Such scenarios give rise to the assumption that the
acoustic samples from the region of interest have a distinct geometrical
structure. In this paper, we show that the high dimensional acoustic samples
indeed lie on a low dimensional manifold and can be embedded into a low
dimensional space. Motivated by this result, we propose a semi-supervised
source localization algorithm which recovers the inverse mapping between the
acoustic samples and their corresponding locations. The idea is to use an
optimization framework based on manifold regularization, that involves
smoothness constraints of possible solutions with respect to the manifold. The
proposed algorithm, termed Manifold Regularization for Localization (MRL), is
implemented in an adaptive manner. The initialization is conducted with only
few labelled samples attached with their respective source locations, and then
the system is gradually adapted as new unlabelled samples (with unknown source
locations) are received. Experimental results show superior localization
performance when compared with a recently presented algorithm based on a
manifold learning approach and with the generalized cross-correlation (GCC)
algorithm as a baseline
Time and spectral domain relative entropy: A new approach to multivariate spectral estimation
The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.Comment: 32 pages, submitted for publicatio
Blind MultiChannel Identification and Equalization for Dereverberation and Noise Reduction based on Convolutive Transfer Function
This paper addresses the problems of blind channel identification and
multichannel equalization for speech dereverberation and noise reduction. The
time-domain cross-relation method is not suitable for blind room impulse
response identification, due to the near-common zeros of the long impulse
responses. We extend the cross-relation method to the short-time Fourier
transform (STFT) domain, in which the time-domain impulse responses are
approximately represented by the convolutive transfer functions (CTFs) with
much less coefficients. The CTFs suffer from the common zeros caused by the
oversampled STFT. We propose to identify CTFs based on the STFT with the
oversampled signals and the critical sampled CTFs, which is a good compromise
between the frequency aliasing of the signals and the common zeros problem of
CTFs. In addition, a normalization of the CTFs is proposed to remove the gain
ambiguity across sub-bands. In the STFT domain, the identified CTFs is used for
multichannel equalization, in which the sparsity of speech signals is
exploited. We propose to perform inverse filtering by minimizing the
-norm of the source signal with the relaxed -norm fitting error
between the micophone signals and the convolution of the estimated source
signal and the CTFs used as a constraint. This method is advantageous in that
the noise can be reduced by relaxing the -norm to a tolerance
corresponding to the noise power, and the tolerance can be automatically set.
The experiments confirm the efficiency of the proposed method even under
conditions with high reverberation levels and intense noise.Comment: 13 pages, 5 figures, 5 table
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