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.

A new multi-aspect target detection method is presented based on the infinite hidden Markov model (iHMM). The scattering of waves from multiple targets 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 target-dependent 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 an effective Gibbs sampler. The framework is demonstrated using 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.