PROJECT TITLE :
Phase Retrieval via Reweighted Amplitude Flow - 2018
This Project deals with finding an n-dimensional solution x to a system of quadratic equations of the shape y i = || 2 for one = i = m, which is additionally known as the generalized phase retrieval drawback. For this NP-onerous problem, a completely unique approach is developed for minimizing the amplitude-primarily based leastsquares empirical loss, that starts with a weighted maximal correlation initialization obtainable through a few power or Lanczos iterations, followed by successive refinements based on a sequence of iteratively reweighted gradient iterations. The 2 stages (initialization and gradient flow) distinguish themselves from previous contributions by the inclusion of a contemporary (re)weighting regularization procedure. For bound random measurement models, the novel theme is shown to be in a position to recover the true solution x in time proportional to reading the data (a i ; y i ) one =i=m. This holds with high chance and while not further assumption on the signal vector x to be recovered, only if the number m of equations is a few constant c > 0 times the quantity n of unknowns in the signal vector, namely m > cn. Empirically, the upshots of this contribution are: first, (almost) a hundredp.c excellent signal recovery in the high-dimensional (say n = 200zero) regime given solely an information-theoretic limit variety of noiseless equations, particularly m = 2n - 1, in the important Gaussian case; and second, (nearly) optimal statistical accuracy in the presence of additive noise of bounded support. Finally, substantial numerical tests using each artificial knowledge and real images corroborate markedly improved recovery performance and computational efficiency of the novel theme relative to the state-of-the-art approaches.
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