Smoothed amplitude flow-based phase retrieval algorithm

Phase retrieval recovers signals from linear phaseless measurements via minimizing a quadratic or amplitude function, while its loss function is generally either non-convex or non-smooth. Existing methods are used to add a truncation procedure or reweighting to the gradient during the gradient descent process to address the non-smooth problem. However, these methods often cause inconsistency in the search direction and increase the sampling complexity. This paperproposes a smoothed amplitude flow-based phase retrieval (SAFPR) algorithm to solve these problems. By introducing the smoothing function into the phase retrieval problem, the loss function is smoothed, significantly reducing the sampling complexity. Moreover, we also develop a stochastic smooth amplitude flow-based phase retrieval (SSAF) algorithm with practical, scalable, and fast in large-scale applications. Experimental results show that whether SAFPR or SSAF, the number of measurements required to reconstruct the signal entirely is better than the existing most advanced phase retrieval algorithms. The proposed methods also perform well in terms of time cost and convergence rate.