Approximate Message Passing (AMP) has been shown to be a superior method for
inference problems, such as the recovery of signals from sets of noisy,
lower-dimensionality measurements, both in terms of reconstruction accuracy and
in computational efficiency. However, AMP suffers from serious convergence
issues in contexts that do not exactly match its assumptions. We propose a new
approach to stabilizing AMP in these contexts by applying AMP updates to
individual coefficients rather than in parallel. Our results show that this
change to the AMP iteration can provide theoretically expected, but hitherto
unobtainable, performance for problems on which the standard AMP iteration
diverges. Additionally, we find that the computational costs of this swept
coefficient update scheme is not unduly burdensome, allowing it to be applied
efficiently to signals of large dimensionality.Comment: 11 pages, 3 figures, implementation available at
https://github.com/eric-tramel/SwAMP-Dem