73,258 research outputs found
Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation
We consider the estimation of a signal from the knowledge of its noisy linear
random Gaussian projections. A few examples where this problem is relevant are
compressed sensing, sparse superposition codes, and code division multiple
access. There has been a number of works considering the mutual information for
this problem using the replica method from statistical physics. Here we put
these considerations on a firm rigorous basis. First, we show, using a
Guerra-Toninelli type interpolation, that the replica formula yields an upper
bound to the exact mutual information. Secondly, for many relevant practical
cases, we present a converse lower bound via a method that uses spatial
coupling, state evolution analysis and the I-MMSE theorem. This yields a single
letter formula for the mutual information and the minimal-mean-square error for
random Gaussian linear estimation of all discrete bounded signals. In addition,
we prove that the low complexity approximate message-passing algorithm is
optimal outside of the so-called hard phase, in the sense that it
asymptotically reaches the minimal-mean-square error. In this work spatial
coupling is used primarily as a proof technique. However our results also prove
two important features of spatially coupled noisy linear random Gaussian
estimation. First there is no algorithmically hard phase. This means that for
such systems approximate message-passing always reaches the minimal-mean-square
error. Secondly, in a proper limit the mutual information associated to such
systems is the same as the one of uncoupled linear random Gaussian estimation
Deep Learning for Environmentally Robust Speech Recognition: An Overview of Recent Developments
Eliminating the negative effect of non-stationary environmental noise is a
long-standing research topic for automatic speech recognition that stills
remains an important challenge. Data-driven supervised approaches, including
ones based on deep neural networks, have recently emerged as potential
alternatives to traditional unsupervised approaches and with sufficient
training, can alleviate the shortcomings of the unsupervised methods in various
real-life acoustic environments. In this light, we review recently developed,
representative deep learning approaches for tackling non-stationary additive
and convolutional degradation of speech with the aim of providing guidelines
for those involved in the development of environmentally robust speech
recognition systems. We separately discuss single- and multi-channel techniques
developed for the front-end and back-end of speech recognition systems, as well
as joint front-end and back-end training frameworks
Noise Corruption of Empirical Mode Decomposition and Its Effect on Instantaneous Frequency
Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing
nonstationary data that provides a localized time-frequency representation by
decomposing the data into adaptively defined modes. EMD can be used to estimate
a signal's instantaneous frequency (IF) but suffers from poor performance in
the presence of noise. To produce a meaningful IF, each mode of the
decomposition must be nearly monochromatic, a condition that is not guaranteed
by the algorithm and fails to be met when the signal is corrupted by noise. In
this work, the extraction of modes containing both signal and noise is
identified as the cause of poor IF estimation. The specific mechanism by which
such "transition" modes are extracted is detailed and builds on the observation
of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing
pure noise. The mechanism is shown to be dependent on spectral leak between
modes and the phase of the underlying signal. These ideas are developed through
the use of simple signals and are tested on a synthetic seismic waveform.Comment: 28 pages, 19 figures. High quality color figures available on Daniel
Kaslovsky's website: http://amath.colorado.edu/student/kaslovsk
Estimation de la fréquence instantanée des signaux FM par opérateur d'énergie Psi_B
Psi_B energy operator is an extension of the cross Teager-Kaiser energy operator which is an non-linear energy tracking operator to deal with complex signals and its usefulness for non-stationary signals analysis has been demonstrated. In this letter two new properties of Psi_B are established. The first property is the link between Psi_B and the dynamic signal which is a generalization of the Instantaneous Frequency (IF). The second property obtained for frequency modulated signals is a simple way to estimate the IF. These properties confirm the interest of Psi_B operator to track the non-stationary of a signal. Results of IF estimation in noisy environment of a non-linear FM signal are presented and comparison to Wigner-Ville distribution and Hilbert transform-based method is provided
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