H-FISTA: A hierarchical algorithm for phase retrieval with application to pulsar dynamic spectra by Stefan Osłowski et al. on Tuesday 22 November

A pulsar dynamic spectrum is an inline digital hologram of the interstellar

medium; it encodes information on the propagation paths by which signals have

travelled from source to telescope. To decode the hologram it is necessary to

"retrieve" the phases of the wavefield from intensity measurements, which

directly gauge only the field modulus, by imposing additional constraints on

the model. We present a new method for phase retrieval in the context of pulsar

spectroscopy. Our method makes use of the Fast Iterative Shrinkage Thresholding

Algorithm (FISTA) to obtain sparse models of the wavefield in a hierarchical

approach with progressively increasing depth. Once the tail of the noise

distribution is reached the hierarchy terminates with a final, unregularised

optimisation. The result is a fully dense model of the complex wavefield that

permits the discovery of faint signals by appropriate averaging. We illustrate

the performance of our method on synthetic test cases and on real data. Our

algorithm, which we call H-FISTA, is implemented in the Python programming

language and is freely available.

arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.11129v1