Kannan Achan

Phase unwrapping by minimizing Kikuchi free energy

Phase unwrapping in 2-dimensional topologies is an important problem that has several applications in radar and satellite imaging. The s um product algorithm (belief propagation) gives excellent results for the phase unwrapping problem. In this work, we present a gradient smoothing technique that uses higher order surface models to produce very smooth surfaces and report an improvement in the solution obtained. In a recent important work, Yedidia et. al have showed the theoretical connections between belief propagation algorithms and free energy in statistical physics. Based on this, we present a model that uses the Kikuchi technique to compute better posterior marginals than those produced by sum product algorithm.

Robust variational speech separation using fewer microphones than speakers

A variational inference algorithm for robust speech separation, capable of recovering the underlying speech sources even in the case of more sources than microphone observations, is presented. The algorithm is based upon a generative probabilistic model that fuses time-delay of arrival (TDOA) information with prior information about the speakers and application, to produce an optimal estimate of the underlying speech sources. Simulation results are presented for the case of two, three and four underlying sources and two microphone observations corrupted by noise. The resulting SNR gains (32 dB with two sources, 23 dB with three sources, and 16 dB with four sources) are significantly higher than previous speech separation techniques.

A segment based probabilistic generative model of speech

We present a purely time domain approach to speech processing which identifies waveform samples at the boundaries between glottal pulse periods (in voiced speech) or at the boundaries of unvoiced segments. An efficient algorithm for inferring these boundaries and estimating the average spectra of voiced and unvoiced regions is derived from a simple probabilistic generative model. Competitive results are presented on pitch tracking, voiced/unvoiced detection and timescale modification; all these tasks and several others can be performed using the single segmentation provided by inference in the model.

Learning to cluster using local neighborhood structure

This paper introduces an approach for clustering/classification which is based on the use of local, high-order structure present in the data. For some problems, this local structure might be more relevant for classification than other measures of point similarity used by popular unsupervised and semi-supervised clustering methods. Under this approach, changes in the class label are associated to changes in the local properties of the data. Using this idea, we also pursue to learn how to cluster given examples of clustered data (including from different datasets). We make these concepts formal by presenting a probability model that captures their fundamentals and show that in this setting, learning to cluster is a well defined and tractable task. Based on probabilistic inference methods, we then present an algorithm for computing the posterior probability distribution of class labels for each data point. Experiments in the domain of spatial grouping and functional gene classification are used to illustrate and test these concepts.

Translating images by unsupervised estimation of switching filters

We propose a method for altering pixel statistics of one image according to another (source) image. Given an input or observed image (probably degraded by one or more unknown processes), and a source image exhibiting the general patch (group of pixels) properties expected in the input image (before degradation), we seek to infer the original image and the process that affected it to produce the observed image. The foundation of our approach is to transform known image patches with desired statistics to patches found in the input image using a finite set of filters or transformations. These transformations are unknown; thus they also must be estimated. We cast this problem as an approximate probabilistic inference problem and show how it can be approached using belief propagation and expectation maximization. Experimental results for joint image restoration and filter estimation are presented.