Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm

We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P${}^3$ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P${}^3$ALM for solving the nonconvex phase retrieval problems. Extensive experiments are conducted to show the effectiveness of the proposed methods.

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