In this work the dynamic compressive sensing (CS) problem of recoveringsparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linearmeasurements is explored from a Bayesian perspective. While there has been ahandful of previously proposed Bayesian dynamic CS algorithms in theliterature, the ability to perform inference on high-dimensional problems in acomputationally efficient manner remains elusive. In response, we propose aprobabilistic dynamic CS signal model that captures both amplitude and supportcorrelation structure, and describe an approximate message passing algorithmthat performs soft signal estimation and support detection with a computationalcomplexity that is linear in all problem dimensions. The algorithm, DCS-AMP,can perform either causal filtering or non-causal smoothing, and is capable oflearning model parameters adaptively from the data through anexpectation-maximization learning procedure. We provide numerical evidence thatDCS-AMP performs within 3 dB of oracle bounds on synthetic data under a varietyof operating conditions. We further describe the result of applying DCS-AMP totwo real dynamic CS datasets, as well as a frequency estimation task, tobolster our claim that DCS-AMP is capable of offering state-of-the-artperformance and speed on real-world high-dimensional problems.
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