Phase Retrieval via Wirtinger Flow Algorithm and Its Variants Almost threequarters of the underling information in the light wave field is embodied in the phase. However, the early optical detectors can only record the intensity or amplitude of the light wave field and cannot directly extract the phase information of the light wave field. Therefore, it is necessary to use the measured amplitude or strength to reconstruct the phase information of the object, this problem is denoted phase retrieval. Phase retrieval is a matter of cardinal significance in signal processing and machine learning. The phase retrieval by convex optimization algorithm is ideal but the computational complexity is high. In 2015, Candes proposed a very effective nonconvex optimization algorithmWirtinger flow algorithm which used spectral initialization to get a better initial value and then gradient iteration to get a promised recovery effect. Subsequently, in line with the idea, a large number of variants are devised, such as: Wirtinger flow(WF), Truncated Wirtinger Flow (TWF), Truncated Amplitude Flow (TAF), Reshaped Wirtinger Flow (RWF), Incremental Truncated Wirtinger Flow (ITWF), Incremental Reshaped Wirtinger Flow (IRWF), Robust Wirtinger Flow (RobustWF), Sparse Wirtinger Flow (SWF), MedianTWF, MedianRWF, Generalized Wirtinger Flow (GWF), Accelerated Wirtinger Flow (AWF), Thresholded Wirtinger Flow Revisited (THWFR), Thresholded Wirtinger Flow (THWF), Reweighted Wirtinger Flow (REWF), Wirtinger Flow Method With Optimal Stepsize (WFOS), Stochastic Truncated Wirtinger Flow Algorithm (STWF), Stochastic Truncated Amplitude Flow (STAF), Reweighted Amplitude Flow (RAF), Compressive Reweighted Amplitude Flow (CRAF), SPARse Truncated Amplitude flow (SPARTA) and Sparse Wirtinger Flow Algorithm with Optimal Stepsize (SWFOS), etc. This paper analyzes and summarizes these algorithms according to their characteristics such as: initialization method, step size, iteration times, sample complexity, computational complexity, etc., so that readers can intuitively and clearly see the characteristics of each algorithm. Finally, we provide the website of the source code of some algorithms, facilitate to access and use it for readers.

Signal Reconstruction From Modulo Observations We consider the problem of reconstructing a signal from underdetermined modulo observations (or measurements). This observation model is inspired by a (relatively) less wellknown imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the underdetermined regime with modulo observations is a challenging illposed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the inverse problem limited to two modulo periods, inspired by recent advances in algorithms for phase retrieval under sparsity constraints. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal and provides improved performance over other existing algorithms. We also provide experiments validating our approach on both synthetic and real data to depict its superior performance.