000257572 001__ 257572
000257572 005__ 20190619220049.0
000257572 02470 $$2ArXiv$$a1808.01961
000257572 037__ $$aARTICLE
000257572 245__ $$aSuper Resolution Phase Retrieval for Sparse Signals
000257572 260__ $$c2018-08-06
000257572 269__ $$a2018-08-06
000257572 336__ $$aJournal Articles
000257572 520__ $$aIn a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the magnitude of its Fourier transform to enable the reconstruction of the original signal. Solving the phase retrieval problem is equivalent to recovering a signal from its auto-correlation function. In this paper, we assume the original signal to be sparse; this is a natural assumption in many applications, such as X-ray crystallography, speckle imaging and blind channel estimation. We propose an algorithm that resolves the phase retrieval problem in three stages: i) we leverage the finite rate of innovation sampling theory to super-resolve the auto-correlation function from a limited number of samples, ii) we design a greedy algorithm that identifies the locations of a sparse solution given the super-resolved auto-correlation function, iii) we recover the amplitudes of the atoms given their locations and the measured auto-correlation function. Unlike traditional approaches that recover a discrete approximation of the underlying signal, our algorithm estimates the signal on a continuous domain, which makes it the first of its kind. Along with the algorithm, we derive its performance bound with a theoretical analysis and propose a set of enhancements to improve its computational complexity and noise resilience. Finally, we demonstrate the benefits of the proposed method via a comparison against Charge Flipping, a notable algorithm in crystallography.
000257572 6531_ $$aLCAV-IVP
000257572 6531_ $$aLCAV-MSP
000257572 700__ $$g175320$$aBaechler, Gilles$$0246557
000257572 700__ $$g248373$$aKrekovic, Miranda$$0248299
000257572 700__ $$g196523$$aRanieri, Juri$$0244415
000257572 700__ $$aChebira, Amina
000257572 700__ $$aYue, M. Lu
000257572 700__ $$0240184$$aVetterli, Martin$$g107537
000257572 8560_ $$fgilles.baechler@epfl.ch
000257572 8564_ $$uhttps://infoscience.epfl.ch/record/257572/files/1808.01961.pdf$$s2194111
000257572 909C0 $$pLCAV$$mpaolo.prandoni@epfl.ch$$mmihailo.kolundzija@epfl.ch$$xU10434$$0252056
000257572 909CO $$qGLOBAL_SET$$pIC$$particle$$ooai:infoscience.epfl.ch:257572
000257572 960__ $$agilles.baechler@epfl.ch
000257572 961__ $$amanon.velasco@epfl.ch
000257572 973__ $$aEPFL$$sSUBMITTED$$rREVIEWED
000257572 980__ $$aARTICLE
000257572 981__ $$aoverwrite