arXiv subjects

Ali Golmakani

Publications and source records attributed to Ali Golmakani.

4 recordsLinked to original sources

arXiv2023

A weighted-variance variational autoencoder model for speech enhancement

We address speech enhancement based on variational autoencoders, which involves learning a speech prior distribution in the time-frequency (TF) domain. A zero-mean complex-valued Gaussian distribution is usually assumed for the generative model, where the speech information is encoded in the variance as a function of a latent variable. In contrast to this commonly used approach, we propose a weighted variance generative model, where the contribution of each spectrogram time-frame in parameter learning is weighted. We impose a Gamma prior distribution on the weights, which would effectively lead to a Student's t-distribution instead of Gaussian for speech generative modeling. We develop efficient training and speech enhancement algorithms based on the proposed generative model. Our experimental results on spectrogram auto-encoding and speech enhancement demonstrate the effectiveness and robustness of the proposed approach compared to the standard unweighted variance model.

cs.SD↗

arXiv2022

Audio-visual speech enhancement with a deep Kalman filter generative model

Deep latent variable generative models based on variational autoencoder (VAE) have shown promising performance for audiovisual speech enhancement (AVSE). The underlying idea is to learn a VAEbased audiovisual prior distribution for clean speech data, and then combine it with a statistical noise model to recover a speech signal from a noisy audio recording and video (lip images) of the target speaker. Existing generative models developed for AVSE do not take into account the sequential nature of speech data, which prevents them from fully incorporating the power of visual data. In this paper, we present an audiovisual deep Kalman filter (AV-DKF) generative model which assumes a first-order Markov chain model for the latent variables and effectively fuses audiovisual data. Moreover, we develop an efficient inference methodology to estimate speech signals at test time. We conduct a set of experiments to compare different variants of generative models for speech enhancement. The results demonstrate the superiority of the AV-DKF model compared with both its audio-only version and the non-sequential audio-only and audiovisual VAE-based models.

cs.CV↗

arXiv2020

Rigorous numerics for critical orbits in the quadratic family

We develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps $f_a (x) = a - x^2$. We illustrate the effectiveness of our approach by constructing a dynamically defined partition $\mathcal P$ of the parameter interval $Ω=[1.4, 2]$ into almost 4 million subintervals, for each of which we compute to high precision the orbits of the critical points up to some time $N$ and other dynamically relevant quantities, several of which can vary greatly, possibly spanning several orders of magnitude. We also subdivide $\mathcal P$ into a family $\mathcal P^{+}$ of intervals which we call stochastic intervals and a family $\mathcal P^{-}$ of intervals which we call regular intervals. We numerically prove that each interval $ω\in \mathcal P^{+}$ has an escape time, which roughly means that some iterate of the critical point taken over all the parameters in $ω$ has considerable width in the phase space. This suggests, in turn, that most parameters belonging to the intervals in $\mathcal P^{+}$ are stochastic and most parameters belonging to the intervals in $\mathcal P^{-}$ are regular, thus the names. We prove that the intervals in $\mathcal P^{+}$ occupy almost 90% of the total measure of $Ω$. The software and the data is freely available at http://www.pawelpilarczyk.com/quadr/, and a web page is provided for carrying out the calculations. The ideas and procedures can be easily generalized to apply to other parametrized families of dynamical systems.

math.DS↗

arXiv2015

Uniform expansivity outside the critical neighborhood in the quadratic family

We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We compute a possibly small radius of the critical neighborhood, and a lower bound for the corresponding expansivity exponent outside this neighborhood, valid for all the parameters in each of the intervals. We illustrate and study the distribution of the radii and these exponents. The results of our computations are mathematically rigorous. The source code of the software and the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/..

math.DS↗