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.

Constrained discriminative mapping transforms for unsupervised speaker adaptation

Discriminative mapping transforms (DMTs) is an approach to robustly adding discriminative training to unsupervised linear adaptation transforms. In unsupervised adaptation DMTs are more robust to unreliable transcriptions than directly estimating adaptation transforms in a discriminative fashion. They were previously proposed for use with MLLR transforms with the associated need to explicitly transform the model parameters. In this work the DMT is extended to CMLLR transforms. As these operate in the feature space, it is only necessary to apply a different linear transform at the front-end rather than modifying the model parameters. This is useful for rapidly changing speakers/environments. The performance of DMTs with CMLLR was evaluated on the WSJ 20k task. Experimental results show that DMTs based on constrained linear transforms yield 3% to 6% relative gain over MLE transforms in unsupervised speaker adaptation. © 2011 IEEE.