In many sensing scenarios, the observed scattered waveforms must be quantized for subsequent transmission over a communication channel. Rate-distortion theory plays an important role in defining the bit rate required to achieve a desired distortion. The distortion is typically defined in the context of signal reconstruction, with the goal of achieving high-fidelity synthesis of the compressed data. For sensing applications, however, the objective is often not simply signal reconstruction but classification performance as well. Other related metrics include target-pose estimation. In this paper, we consider multiaspect wave scattering, in which classification and pose estimation are performed based on the quantized scattering data. Moreover, rate-distortion theory is employed to place bounds on pose-estimation performance when both the target identity and pose are unknown a priori. It is demonstrated that block-coding with Bayes-VQ may yield performance approaching the bound. Example results are presented for measured acoustic waveforms scattered from underwater elastic targets.