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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.