Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their expressivity when the data distribution is supported on a low-dimensional manifold or has a non-trivial topology. We introduce a novel statistical framework for learning a mixture of local normalizing flows as “chart maps” over the data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation. We learn a suitable atlas of charts for the data manifold via a vector quantized auto-encoder (VQ-AE) and the distributions over them using a conditional flow. We validate experimentally that our probabilistic framework enables existing approaches to better model data distributions over complex manifolds.

Many convolutional neural networks (CNN's) have a feed-forward structure. In this paper, we model a general framework for analyzing the Lipschitz bounds of CNN's and propose a linear program that estimates these bounds. Several CNN's, including the scattering networks, the AlexNet and the GoogleNet, are studied numerically. In these practical numerical examples, estimations of local Lipschitz bounds are compared to these theoretical bounds. Based on the Lipschitz bounds, we next establish concentration inequalities for the output distribution with respect to a stationary random input signal. The Lipschitz bound is further used to perform nonlinear discriminant analysis that measures the separation between features of different classes.

A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility while satisfying its QoS requirements. The user's QoS constraints are specified in terms of the average source rate and an upper bound on the average delay where the delay includes both transmission and queuing delays. The utility function considered here measures energy efficiency and is particularly suitable for wireless networks with energy constraints. The Nash equilibrium solution for the proposed non-cooperative game is derived and a closed-form expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a "size" for the user which is an indication of the amount of network resources consumed by the user. Using this competitive multiuser framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are studied. In addition, analytical expressions are given for users' delay profiles and the delay performance of the users at Nash equilibrium is quantified.

Accurate noise power spectrum estimation in a noisy speech signal is a key challenge problem in speech enhancement. One state-of-the-art approach is the minima controlled recursive averaging (MCRA). This paper presents an enhanced MCRA algorithm (EMCRA), which demonstrates less speech signal leakage and faster response time to follow abrupt changes in the noise power spectrum. Experiments using real speech and noise recordings have validated the superiority of the proposed enhancements. EMCRA shows improvements both in intuitive subjective listening and objective quality measures in terms of higher output SNR and lower output distortion scores.

The purpose of this letter is to prove, for real frames, that signal reconstruction from the absolute value of the frame coefficients is equivalent to solution of a sparse signal optimization problem, namely a minimum lscrp(quasi)norm over a linear constraint. This linear constraint reflects the coefficients relationship within the range of the analysis operator

In this paper we present a new source separation method based on dynamic sparse source signal models. Source signals are modeled in frequency domain as a product of a Bernoulli selection variable with a deterministic but unknown spectral amplitude. The Bernoulli variables are modeled in turn by first order Markov processes with transition probabilities learned from a training database. We consider a video conferencing scenario where the mixing parameters are estimated by the video system. We obtain the MAP signal estimators and show they are implemented by a Vitterbi decoding scheme. We validate this approach by simulations using TIMIT database, and compare the separation performance of this algorithm with our previous extended DUET method

A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility and at the same time satisfy its QoS requirements. The user's QoS constraints are specified in terms of the average source rate and average delay. The utility function considered here measures energy efficiency and the delay includes both transmission and queueing delays. The Nash equilibrium solution for the proposed non-cooperative game is derived and a closed-form expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a "size" for the user which is an indication of the amount of network resources consumed by the user. Using this framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are also studied.

Sparse constraints on signal decompositions are justified by typical sensor data used in a variety of signal processing fields such as acoustics, medical imaging, or wireless, but moreover can lead to more effective algorithms. The specific sparseness assumption used in this work is that the maximum number of statistically independent sources active at any time and frequency point in a mixture of signals is small. This is shown to result from an assumption of sparseness of the sources themselves, and allows us to solve the maximum likelihood formulation of the noninstantaneous acoustic mixing source estimation problem. We consider an additive noise mixing model with an arbitrary number of sensors and possibly more sources than sensors, when sources satisfy the sparseness assumption above. The solution obtained is applicable to an arbitrary number of microphones and sources, but works best when the number of sources simultaneously active at any time frequency point is a small fraction of the total number of sources.

Few source separation and independent component analysis approaches attempt to deal with noisy data. We consider an additive noise mixing model with an arbitrary number of sensors and possibly more sources than sensors (the "degenerate separation problem") when sources are disjointly orthogonal. We show how disjoint orthogonality can be viewed as a limit of a stochastic voice modeling assumption. This is the basis for our approach to noisy model estimation by maximum likelihood, under the direct-path far-field assumptions. The implementation of the derived criterion involves iterating two steps: a partitioning of the time-frequency plane for separation followed by an optimization of the mixing parameter estimates. The solution is applicable to an arbitrary number of microphones and sources. Experimentally, we show the capability of the technique to separate four voices from two, four, six and eight channel recordings in the presence of strong noise.

Multi-channel techniques offer advantages in noise reduction and overall output signal quality when compared to the well studied mono approaches. We present an original multi-channel psychoacoustically motivated noise reduction algorithm that naturally extends the single channel psychoacoustic masking filter previously studied (see Gustafsson, S. et al., ICASSP, p.873-6, 1999). The optimality criterion is designed to satisfy the psychoacoustic masking principle and to minimize the signal total distortion simultaneously. In experiments on real data recorded in a noisy car environment, we show the enhanced performance of the two-channel solution in terms of artifacts and overall tradeoff between artifacts and the amount of noise removed as given by word recognition rates.

Multichannel techniques offer advantages in noise reduction and overall output signal quality when compared to the well studied mono approaches. In this paper we present an original multichannel psychoacoustically motivates noise reduction algorithm that naturally extends the single channel psychoacoustic masking filter previously studied in the literature [S. Gustafsson et al., 1999]. The optimality criterion is designed to simultaneously satisfy the psychoacoustic masking principle and minimize the signal total distortion. In experiments on real data recorded in a noisy car environment, we show the enhanced performance of the two-channel solution in terms of artifacts and overall tradeoff between artifacts and amount of noise removed as given by word recognition rates.

In this paper the windowed Fourier encoding-decoding scheme applied to the multiple description compression problem is analyzed. In the general case, four window functions are needed to define the encoder and decoder, although this number can be reduced to three or two by using time-shift or frequency-shift division schemes. The encoding coefficients are next divided into two groups according to the eveness of either the modulation or translation index. The distortion on each channel is analyzed using the Zak transform. For the optimal windows, explicit representation formulas are obtained and nonlocalization results are proved. Asymptotic formulas of the total distortion and transmission rate are established and the redundancy is shown to trade off between these two.