Compressive sensing (CS) is an emerging £eld that, under appropriate conditions, can signi£-cantly reduce the number of measurements required for a given signal. In many applications, one is interested in multiple signals that may be measured in multiple CS-type measurements, where here each signal corresponds to a sensing "task". In this paper we propose a novel multitask compressive sensing framework based on a Bayesian formalism, where a Dirichlet process (DP) prior is employed, yielding a principled means of simultaneously inferring the appropriate sharing mechanisms as well as CS inversion for each task. A variational Bayesian (VB) inference algorithm is employed to estimate the full posterior on the model parameters.

Abstract-We develop a hidden Markov mixture model based on a Dirichlet process (DP) prior, for representation of the statistics of sequential data for which a single hidden Markov model (HMM) may not be sufficient. The DP prior has an intrinsic clustering property that encourages parameter sharing, and this naturally reveals the proper number of mixture components. The evaluation of posterior distributions for all model parameters is achieved in two ways: 1) via a rigorous Markov chain Monte Carlo method; and 2) approximately and efficiently via a variational Bayes formulation. Using DP HMM mixture models in a Bayesian setting, we propose a novel scheme for music analysis, highlighting the effectiveness of the DP HMM mixture model. Music is treated as a time-series data sequence and each music piece is represented as a mixture of HMMs. We approximate the similarity of two music pieces by computing the distance between the associated HMM mixtures. Experimental results are presented for synthesized sequential data and from classical music clips. Music similarities computed using DP HMM mixture modeling are compared to those computed from Gaussian mixture modeling, for which the mixture modeling is also performed using DP. The results show that the performance of DP HMM mixture modeling exceeds that of the DP Gaussian mixture modeling. Index Terms-Dirichlet process, hidden Markov model (HMM) mixture, Markov chain Monte Carlo (MCMC), music, variationalBayes.

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A new multi-aspect target detection method is presented based on the infinite hidden Markov model (iHMM). The scattering of waves from a target is modeled as an iHMM with the number of underlying states treated as infinite, from which a full posterior distribution on the number of states associated with the targets is inferred and the targetdependent states are learned collectively. A set of Dirichlet processes (DPs) are used to define the rows of the HMM transition matrix and these DPs are linked and shared via a hierarchical Dirichlet process (HDP). Learning and inference for the iHMM are based on a Gibbs sampler. The basic framework is first demonstrated using synthetic data, followed by a detailed analysis of measured acoustic scattering data.

A hidden Markov mixture model is developed using a Dirichlet process (DP) prior, to represent the statistics of sequential data for which a single hidden Markov model (HMM) may not be sufficient. The DP prior has an intrinsic clustering property that encourages parameter sharing, naturally revealing the proper number of mixture components. The evaluation of posterior distributions for all model parameters is achieved via a variational Bayes formulation. We focus on exploring music similarities as an important application, highlighting the effectiveness of the HMM mixture model. Experimental results are presented from classical music clips.