A Fast Gradient-Based Iterative Algorithm for Undersampled Phase Retrieval

This letter develops a fast iterative shrinkage-thresholding algorithm, which can efficiently tackle the issue in undersampled phase retrieval. First, using the gradient framework and proximal regularization theory, the undersampled phase retrieval problem is formulated as an optimization in terms of least-absolute-shrinkage-and-selection-operator form with (ℓ
₂
+ ℓ
₁
)-norm minimization in the case of sparse signals. A gradient-based phase retrieval via majorization- minimization technique (G-PRIME) is applied to solve a quadratic approximation of the original problem, which, however, suffers a slow convergence rate. Then, an extension of the G-PRIME algorithm is derived to further accelerate the convergence rate, in which an additional iteration is chosen with a marginal increase in computational complexity. Experimental results show that the proposed algorithm outperforms the state-of-the-art approaches in terms of the convergence rate.