H-FISTA: a hierarchical algorithm for phase retrieval with application to pulsar dynamic spectra

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, unregularized optimization. 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.

Automated summary

A pulsar dynamic spectrum is a digital hologram that encodes information on the propagation paths of signals. We present a new method, called H-FISTA, for phase retrieval in pulsar spectroscopy using the Fast Iterative Shrinkage Thresholding Algorithm. Our algorithm obtains sparse models of the wavefield in a hierarchical approach, leading to a fully dense model that allows the discovery of faint signals. The performance of our method is demonstrated on synthetic test cases and real data.