In this paper, a phase retrieval algorithm based on the Incremental Truncation Wirtinger flow (ITWF) and reweighted gradient descent algorithm, which is called Incremental Reweighted Gradient Descent (IRGD). The presented IRGD algorithm is divided into two steps as most optimization algorithms: an initial estimation and an iterative refinement. In the iterative process of the algorithm, we refine the initial estimate value by combining the incremental with the reweighted gradient descent. Compared with WF and other algorithms which needs to pass through the entire data at each time, it has obvious advantages when dealing with large-scale signals. In order to speed up the convergence of iterative estimates and increase the robustness, we use the reweighted method to attach large weights to the reliable gradients and small weights to the spurious ones, and integrate the smoothing function and the relaxation parameter into the gradient descent formula. The simulation experimental results show that it can recover the unknown signal accurately under the given random Gaussian measurement with certain noise, and is superior to the most existing algorithms in convergence speed and success rate under the same condition.
This paper considers the phase retrieval problem of recovering the unknown signal from the given quadratic measurements. A phase retrieval algorithm based on Incremental Truncated Amplitude Flow (ITAF) which combines the ITWF algorithm and the TAF algorithm is proposed. The proposed ITAF algorithm enhances the initialization by performing both of the truncation methods used in ITWF and TAF respectively, and improves the performance in the gradient stage by applying the incremental method proposed in ITWF to the loop stage of TAF. Moreover, the original sampling vector and measurements are preprocessed before initialization according to the variance of the sensing matrix. Simulation experiments verified the feasibility and validity of the proposed ITAF algorithm. The experimental results show that it can obtain higher success rate and faster convergence speed compared with other algorithms. Especially, for the noiseless random Gaussian signals, ITAF can recover any real-valued signal accurately from the magnitude measurements whose number is about 2.5 times of the signal length, which is close to the theoretic limit (about 2 times of the signal length). And it usually converges to the optimal solution within 20 iterations which is much less than the state-of-the-art algorithms.