Rate-distortion analysis of joint compression and classification: Application to HMM state (pose) estimation via multi-aspect scattering data

Rate-distortion analysis is applied to a joint compression and classification problem. It is used to derive a bound for the minimum rate R to encode data to achieve a desired distortion D, denoted as R(D). Here a Lagrangian distortion is used to consider both the Euclidean distortion in reconstructing the original data and the classification performance. An iterative algorithm based on an alternating minimization procedure is proposed to calculate the bound. This rate-distortion framework is then applied to a joint compression and pose estimation problem based on a sequence of scattered waveforms measured at multiple target-sensor orientations.; An HMM-Markov model (HMM-MM) is proposed as the statistical description for the source---multi-aspect scattering data, as required by the rate-distortion analysis. The statistical variation of the scattered fields with variable target-sensor orientation is characterized via a hidden Markov model (HMM), a state of which corresponds to a generally contiguous set of target-sensor orientations over which the angular-dependent scattered fields are stationary. The statistical variation of the transient waveforms within each HMM state is modeled via a Markov model using a physics-based alphabet, including wavefront, resonance and time-delay. Results from five underwater elastic targets have shown that the model is able to accurately describe the scattering data. By using this HMM representation, pose estimation reduces to estimating the underlying HMM states from a sequence of observations.; After deriving the rate-distortion function R( D), we demonstrate that discrete-HMM performance based on Lloyd encoding is far from this bound. Performance is improved via block coding, based on Bayes-VQ. Results are presented for multi-aspect acoustic scattering from underwater elastic targets, using measured and synthesized data. Although the examples presented here are for multi-aspect scattering and pose estimation, the results are of general applicability to discrete-HMM state estimation.