In this paper, a compressive sensing (CS) perspective to exemplar-based speech processing is proposed. Relying on an analytical relationship between CS formulation and statistical speech recognition (Hidden Markov Models - HMM), the automatic speech recognition (ASR) problem is cast as recovery of highdimensional sparse word representation from the observed low-dimensional acoustic features. The acoustic features are exemplars obtained from (deep) neural network sub-word conditional posterior probabilities. Low-dimensional word manifolds are learned using these sub-word posterior exemplars and exploited to construct a linguistic dictionary for sparse representation of word posteriors. Dictionary learning has been found to be a principled way to alleviate the need of having huge collection of exemplars as required in conventional exemplar-based approaches, while still improving the performance. Context appending and collaborative hierarchical sparsity are used to exploit the sequential...