  Compressive Sensing (CS) has recently attracted attention for ECG data
compression. In CS, an ECG signal is projected onto a small set of random
vectors. Recovering the original signal from such compressed measurements
remains a challenging problem. Traditional recovery methods are based on
solving a regularized minimization problem, where a sparsity-promoting prior is
used. In this paper, we propose an alternative iterative recovery algorithm
based on the Plug-and-Play (PnP) method, which has recently become popular for
imaging problems. In PnP, a powerful denoiser is used to implicitly perform
regularization, instead of using hand-crafted regularizers; this has been found
to be more successful than traditional methods. In this work, we use a PnP
version of the Proximal Gradient Descent (PGD) algorithm for ECG recovery. To
ensure mathematical convergence of the PnP algorithm, the signal denoiser in
question needs to satisfy some technical conditions. We use a high-quality ECG
signal denoiser fulfilling this condition by learning a Bayesian prior for
small-sized signal patches. This guarantees that the proposed algorithm
converges to a fixed point irrespective of the initialization. Importantly,
through extensive experiments, we show that the reconstruction quality of the
proposed method is superior to that of state-of-the-art methods.
