Phase retrieval from noisy data based on sparse approximation of object phase and amplitude
For researchers in optical imaging and computational microscopy, this work offers a robust phase retrieval algorithm that handles heavy noise, enabling shorter exposure times.
The paper develops a variational phase retrieval method using sparse modeling of both amplitude and phase in a transform domain, achieving significant improvements over state-of-the-art methods (e.g., Gerchberg-Saxton, truncated Wirtinger flow) for Poissonian observations, especially under high noise levels corresponding to short exposure times.
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of wavefronts. The transform domain sparsity is applied for the amplitude and phase modeling. It is demonstrated that this modeling results in the essential advantage of the developed algorithm for heavily noisy observations corresponding to a short exposure time in optical experiments. We consider also two simplified versions of this algorithm where the sparsity modeling of phase and amplitude is omitted. In the simulation study we compare the developed algorithms versus the Gerchberg-Saxton and truncation Wirtinger flow algorithms. The latter algorithm being the maximum likelihood based is the state-of-the-art for the phase retrieval from Poissonian observations. For noisy and very noisy observations the proposed algorithm demonstrates a valuable advantage.