Scott Axelrod

SPIN ECHOES OF NUCLEAR MAGNETIZATION DIFFUSING IN A CONSTANT MAGNETIC FIELD GRADIENT AND IN A RESTRICTED GEOMETRY

We study the influence of restriction on Carr–Purcell–Meiboom–Gill spin echoes response of magnetization of spins diffusing in a bounded region in the presence of a constant magnetic field gradient. Depending on three main length scales: LS pore size, LG dephasing length and LD diffusion length during half-echo time, three main regimes of decay have been identified: free, localization and motionally averaging regime. In localization regime, the decay exponent depends on a fractional power (2/3) of the gradient, denoting a strong breakdown of the second cumulant or the Gaussian phase approximation (GPA). In the other two regimes, the exponent depends on the gradient squared, and the GPA holds. We find that the transition from the localization to the motionally averaging regime happens when the magnetic field gradients approach special values, corresponding to branch points of the eigenvalues. Transition from one regime to another as a function of echo number for a certain range of parameters is discussed. ...

Nuclear magnetic resonance spin echoes for restricted diffusion in an inhomogeneous field: Methods and asymptotic regimes

We develop systematic formulations for calculating the magnetization of spins diffusing in a bounded region in the presence of the surface relaxation and magnetic field inhomogeneity and compute explicitly the relaxation exponent for the Carr–Purcell–Meiboom–Gill spin echoes. The results depend on the echo number n, and three dimensionless parameters: Lρ/LS, D0=(LD/LS)2, the dimensionless diffusion constant, and γ=LD2LS/LG3=Δωτ, the dimensionless gyromagnetic ratio, where the restriction is characterized by a size LS, the magnetic field inhomogeneity by a dephasing length, LG, the diffusion length during half-echo time by LD, and a length Lρ characterizes the surface relaxation. Here Δω is the line broadening and 2τ is the echo period. Depending on the length scales, three main regimes of decay have been identified: short-time, localization, and motionally averaging regimes (MAv). The short-time and the MAv regimes are described well by the cumulant expansion in terms of powers of the “small” parameter ...

Maximum entropy and MCE based HMM stream weight estimation for audio-visual ASR

In this paper, we propose a new fast and flexible algorithm based on the maximum entropy (MAXENT) criterion to estimate stream weights in a state-synchronous multi-stream HMM. The technique is compared to the minimum classification error (MCE) criterion and to a brute-force, grid-search optimization of the WER on both a small and a large vocabulary audio-visual continuous speech recognition task. When estimating global stream weights, the MAXENT approach gives comparable results to the grid-search and the MCE. Estimation of state dependent weights is also considered: We observe significant improvements in both the MAXENT and MCE criteria, which, however, do not result in significant WER gains.

INHOMOGENEITY IN LOCAL MAGNETIC FIELD DUE TO SUSCEPTIBILITY CONTRAST

A method for computing local magnetic field for the case of small permeability or susceptibility contrast is described. The method is illustrated by using an example of a periodic array of cylinders which affords the simplest yet a representative case for visualizing the local fields. The cylinders represent material of one susceptibility such as solid grains in a rock matrix (or tissues in biological systems) and the space outside represents material of another susceptibility such as fluid which fills the pore space (or fluids outside tissues). We calculate the position dependent correction from the continuum to the local field inhomogeneity and go beyond the standard uniform field term. A simple (separate) illustration when the local field diverges is given.

Combination of hidden Markov models with dynamic time warping for speech recognition

We combine hidden Markov models of various topologies and nearest neighbor classification techniques in an exponential modeling framework with a model selection algorithm to obtain significant error rate reductions on an isolated word digit recognition task. This work is a preliminary investigation of large scale modeling techniques to be applied to large vocabulary continuous speech recognition.

Subspace constrained Gaussian mixture models for speech recognition

A standard approach to automatic speech recognition uses hidden Markov models whose state dependent distributions are Gaussian mixture models. Each Gaussian can be viewed as an exponential model whose features are linear and quadratic monomials in the acoustic vector. We consider here models in which the weight vectors of these exponential models are constrained to lie in an affine subspace shared by all the Gaussians. This class of models includes Gaussian models with linear constraints placed on the precision (inverse covariance) matrices (such as diagonal covariance, maximum likelihood linear transformation, or extended maximum likelihood linear transformation), as well as the LDA/HLDA models used for feature selection which tie the part of the Gaussians in the directions not used for discrimination. In this paper, we present algorithms for training these models using a maximum likelihood criterion. We present experiments on both small vocabulary, resource constrained, grammar-based tasks, as well as large vocabulary, unconstrained resource tasks to explore the rather large parameter space of models that fit within our framework. In particular, we demonstrate significant improvements can be obtained in both word error rate and computational complexity.

Maximum likelihood training of subspaces for inverse covariance modeling

Speech recognition systems typically use mixtures of diagonal Gaussians to model the acoustics. Using Gaussians with a more general covariance structure can give improved performance; EM-LLT and SPAM models give improvements by restricting the inverse covariance to a linear/affine subspace spanned by rank one and full rank matrices respectively. We consider training these subspaces to maximize likelihood. For EMLLT ML training the subspace results in significant gains over the scheme proposed by Olsen and Gopinath (see Proceedings of ICASSP, 2002). For SPAM ML training of the subspace slightly improves performance over the method reported by Axelrod, Gopinath and Olsen (see Proceedings of ICSLP, 2002). For the same subspace size an EMLLT model is more efficient computationally than a SPAM model, while the SPAM model is more accurate. This paper proposes a hybrid method of structuring the inverse covariances that both has good accuracy and is computationally efficient.

Dimensional reduction, covariance modeling, and computational complexity in ASR systems

We study acoustic modeling for speech recognition using mixtures of exponential models with linear and quadratic features tied across all context dependent states. These models are one version of the SPAM models introduced by Axelrod, Gopinath and Olsen (see Proc. ICSLP, 2002). They generalize diagonal covariance, MLLT, EMLLT, and full covariance models. Reduction of the dimension of the acoustic vectors using LDA/HDA projections corresponds to a special case of reducing the exponential model feature space. We see, in one speech recognition task, that SPAM models on an LDA projected space of varying dimensions achieve a significant fraction of the WER improvement in going from MLLT to full covariance modeling, while maintaining the low computational cost of the MLLT models. Further, the feature precomputation cost can be minimized using the hybrid feature technique of Visweswariah, Olsen, Gopinath and Axelrod (see ICASSP 2003); and the number of Gaussians one needs to compute can be greatly reducing using hierarchical clustering of the Gaussians (with fixed feature space). Finally, we show that reducing the quadratic and linear feature spaces separately produces models with better accuracy, but comparable computational complexity, to LDA/HDA based models.

Gaussian mixture modeling with volume preserving nonlinear feature space transforms

The paper introduces a new class of nonlinear feature space transformations in the context of Gaussian mixture models. This class of nonlinear transformations is characterized by computationally efficient training algorithms. Experimental results with quadratic feature space transforms are shown to yield modestly improved recognition performance in a speech recognition context. The quadratic feature space transforms are also shown to be beneficial in an adaptation setting.

Speaker identification using online, frame dependent, and diffusive variance adaptation

In this paper we perform maximum likelihood adaptation of the variances of a Gaussian mixture model (GMM) based on a single acoustic data frame. We show that, in the case of prototype (and frame) dependent scaling of the variances, the adaptation amounts to a simple non-linear warping of the exponent of the Gaussian. We also introduce algorithms to perform “diffusive” variance adaptation, in which a positive constant is added to the model variance. When the constant is prototype independent (but possibly frame and coordinate dimension dependent), this modification of the GMM is equivalent to evolution of it by the diffusion equation of physics, which is guaranteed to increase entropy. Applied to the task of text-independent speaker identification on the LLHDB database, we report relative improvements of up to 28% reduction in speaker identification error rate compared to the unadapted model.