Undersampled Phase Retrieval via Majorization-Minimization

Abstract

In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce the number of required measurements since a recent theory established that $M\approx 4N$ intensity measurements are necessary and sufficient to recover a generic signal $\mathbf{x}$. In this paper, we propose to exploit the sparsity in the original signal and develop low-complexity algorithms with superior performance based on the majorization-minimization (MM) framework. The proposed algorithms are preferred to existing benchmark methods since at each iteration a simple surrogate problem is solved with a closed-form solution that monotonically decreases the original objective function. Experimental results validate that our algorithms outperform existing up-to-date methods in terms of recovery probability and accuracy, under the same settings.

References in corpus (4)

• Compressive Phase Retrieval via Generalized Approximate Message Passing
• Sparse Phase Retrieval from Short-Time Fourier Measurements
• Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow
• Solving Large-scale Systems of Random Quadratic Equations via Stochastic Truncated Amplitude Flow

Cited by in corpus (10)

• Solving Large-scale Systems of Random Quadratic Equations via Stochastic Truncated Amplitude Flow
• Phase Retrieval for Partially Coherent Observations
• Sparse Phase Retrieval via Truncated Amplitude Flow
• Denoising Poisson Phaseless Measurements via Orthogonal Dictionary Learning
• Phase Retrieval From Binary Measurements
• PDMM: A novel Primal-Dual Majorization-Minimization algorithm for Poisson Phase-Retrieval problem
• Extended Successive Convex Approximation for Phase Retrieval with Dictionary Learning
• A general framework for denoising phaseless diffraction measurements
• Hadamard Wirtinger Flow for Sparse Phase Retrieval
• $L^0$-regularized Variational Methods for Sparse Phase Retrieval