From Phil Schniter's email in More intra-block correlation and sparse sensing matrices we have an implementation of the AMP algoriithm for Dynamic Compressed Sesning: The DCS-AMP homepage is here. The introduction reads:
Dynamic Compressed Sensing (DCS) | Approximate Message Passing (AMP)DCS-AMP is a recently developed Bayesian algorithm for solving the dynamic compressed sensing (DCS) problem in compressed sensing, in cases with (possibly) substantial amplitude correlation across time. The technique leverages recent advances in approximate message passing (AMP) in order to rapidly obtain accurate solutions in high-dimensional settings.
As a reminder the supporting paper is: Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing by Justin Ziniel and Philip Schniter. The abstract reads:
In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efﬁcient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal ﬁltering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety of operating conditions. We further describe the result of applying DCS-AMP to two real dynamic CS datasets, as well as a frequency estimation task, to bolster our claim that DCS-AMP is capable of offering state-of-the-art performance and speed on real-world high-dimensional problems.
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