On the relationship between hidden Markov Models and convex functional transforms for simulating scanning probe Microscopy

Models for simulating Scanning Probe Microscopy (SPM) may serve as a reference point for validating experimental data and practice. Generally, simulations use a microscopic model of the sample-probe interaction based on a first-principles approach, or a geometric model of macroscopic distortions due to the probe geometry. Examples of the latter include use of neural networks, the Legendre Transform, and dilation/erosion transforms from mathematical morphology. Dilation and the Legendre Transform fall within a general family of functional transforms, which distort a function by imposing a convex solution.In earlier work, the authors proposed a generalized approach to modeling SPM using a hidden Markov model, wherein both the sample-probe interaction and probe geometry may be taken into account. We present a discussion of the hidden Markov model and its relationship to these convex functional transforms for simulating and restoring SPM images.©2009 SPIE.

Unsupervised intra-lingual and cross-lingual speaker adaptation for HMM-based speech synthesis using two-pass decision tree construction

Hidden Markov model (HMM)-based speech synthesis systems possess several advantages over concatenative synthesis systems. One such advantage is the relative ease with which HMM-based systems are adapted to speakers not present in the training dataset. Speaker adaptation methods used in the field of HMM-based automatic speech recognition (ASR) are adopted for this task. In the case of unsupervised speaker adaptation, previous work has used a supplementary set of acoustic models to estimate the transcription of the adaptation data. This paper first presents an approach to the unsupervised speaker adaptation task for HMM-based speech synthesis models which avoids the need for such supplementary acoustic models. This is achieved by defining a mapping between HMM-based synthesis models and ASR-style models, via a two-pass decision tree construction process. Second, it is shown that this mapping also enables unsupervised adaptation of HMM-based speech synthesis models without the need to perform linguistic analysis of the estimated transcription of the adaptation data. Third, this paper demonstrates how this technique lends itself to the task of unsupervised cross-lingual adaptation of HMM-based speech synthesis models, and explains the advantages of such an approach. Finally, listener evaluations reveal that the proposed unsupervised adaptation methods deliver performance approaching that of supervised adaptation.

State estimation schemes for independent component coupled hidden Markov models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results. © Taylor & Francis Group, LLC.