Unfolded Algorithms for Deep Phase Retrieval

Exploring the idea of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements. In this paper, we approach the problem by proposing a hybrid model-based, data-driven deep architecture referred to as Unfolded Phase Retrieval (UPR), which exhibits significant potential in improving the performance of state-of-the-art data-driven and model-based phase retrieval algorithms. The proposed method benefits from the versatility and interpretability of well-established model-based algorithms while simultaneously benefiting from the expressive power of deep neural networks. In particular, our proposed model-based deep architecture is applied to the conventional phase retrieval problem (via the incremental reshaped Wirtinger flow algorithm) and the sparse phase retrieval problem (via the sparse truncated amplitude flow algorithm), showing immense promise in both cases. Furthermore, we consider a joint design of the sensing matrix and the signal processing algorithm and utilize the deep unfolding technique in the process. Our numerical results illustrate the effectiveness of such hybrid model-based and data-driven frameworks and showcase the untapped potential of data-aided methodologies to enhance existing phase retrieval algorithms.