Solving Large-scale Systems of Random Quadratic Equations via Stochastic Truncated Amplitude Flow

Building upon but considerably broadening the scope of truncated amplitude flow (TAF), our algorithm termed stochastic truncated amplitude flow (STAF) is a novel two-stage iterative solution algorithm to solve systems of random quadratic equations. Specifically, STAF performs simple yet effective stochastic iterations in stages: In stage one, we introduce a stochastic variance-reduced gradient (SVRG) algorithm to solve the orthogonality-promoting initialization problem; and stage two refines the initial estimate by successive updates of stochastic truncated amplitude-based gradient iterations. Both stages process one datum (equation) per iteration yet still guarantee a linear convergence rate, rendering STAF a competitive algorithm amenable to large-scale imaging applications. Tests on synthetic data and real images corroborate advantages of STAF over the state-of-the-art algorithms.

Exact recovery performance of STAF relative to the state-of-the-art approaches from noiseless Gaussian random measurements.

Convergence speed of STAF relative to the state-of-the-art approaches from noiseless Gaussian random measurements.