Methods and systems are described for sensing and recovery of a biological signal using generative-model-based compressive sensing. A transformation is applied to sparsify the quasi-periodic signal removing morphology parameters and leaving temporal parameters. The sparsified signal is sampled and the sampled signal data is transmitted to a base station. A homotopy recovery algorithm is applied to the received sampled signal data by the base station to recover the temporal parameters of the biological signal. Generative modelling is applied using previously captured morphology parameters to generate a reconstructed signal. Finally, the reconstructed signal is adjusted and scaled based on the recovered temporal parameters to provide a reconstructed signal that is diagnostically equivalent to the original biological signal.