Check out our SPARTA (Sparse Phase Retrieval via Truncated Amplitude Flow), which provably recovers sparse signals from a small number of magnitude-only measurements. Sparse orthogonality-promoting initialization is developed, which outperforms existing spectral initialization alternatives for phase retrieval of sparse signals.
Check our new paper on stochastic-type algorithms for large-scale phase retrieval problems ‘Solving Large-scale Random Systems of Quadratic Equations via Stochastic Truncated Amplitude Flow.’ Building on truncated amplitude flow (TAF), we propose stochastic variance-reduced gradient (SVRG) algorithms to solve for the orthogonality-promoting initialization instead of the gradient-type power method, and stochastic gradient descent (SGD)-based or Kaczmarz-based iterations to refine the initialization.
Our paper ‘Solving Random Systems of Quadratic Equations via Truncated Generalized Gradient Flow’ was accepted to NIPS 2016, which is to be held in Barcelona, Spain. The proposed algorithm benchmarks the performance of solving generalized phase retrieval under Gaussian random measurements or coded diffraction patterns.
A full version along with Matlab implementations is available at here.