Scalable Solvers of Random Quadratic Equations via Stochastic Truncated Amplitude Flow - 2017 PROJECT TITLE :Scalable Solvers of Random Quadratic Equations via Stochastic Truncated Amplitude Flow - 2017ABSTRACT:A novel approach termed stochastic truncated amplitude flow (STAF) is developed to reconstruct an unknown n-dimensional real-/complicated-valued signal x from m “phaseless” quadratic equations of the form ?i = I(ai, x)I. This problem, also called section retrieval from magnitude-solely info, is NP-exhausting normally. Adopting an amplitude-primarily based nonconvex formulation, STAF results in an iterative solver comprising two stages: s1) Orthogonality-promoting initialization through a stochastic variance reduced gradient algorithm; and, s2) a series of iterative refinements of the initialization using stochastic truncated gradient iterations. Both stages involve one equation per iteration, so rendering STAF a easy, scalable, and quick approach amenable to giant-scale implementations that are helpful when n is large. When aii= 1m are independent Gaussian, STAF provably recovers precisely any x ? Rn exponentially fast based mostly on order of n quadratic equations. STAF is also robust within the presence of additive noise of bounded support. Simulated tests involving real Gaussian ai vectors demonstrate that STAF empirically reconstructs any x ? Rnexactly from about 2.3n magnitude-solely measurements, outperforming state-of-the-art approaches and narrowing the gap from the data-theoretic range of equations m = 2n - one. Extensive experiments using synthetic data and real pictures corroborate markedly improved performance of STAF over existing alternatives. Did you like this research project? To get this research project Guidelines, Training and Code... Click Here facebook twitter google+ linkedin stumble pinterest Low-Rank Physical Model Recovery From Low-Rank Signal Approximation - 2017 Sparsity And Low-Rank Amplitude Based Blind Source Separation - 2017