Recovering missing data in coherent diffraction imaging

Autor:	Barmherzig, David, Barnett, Alex B., Epstein, Charles L., Greengard, Leslie F., Magland, Jeremy F., Rachh, Manas
Rok vydání:	2020
Předmět:	Mathematics - Numerical Analysis Electrical Engineering and Systems Science - Signal Processing High Energy Physics - Experiment 78A46 78A45 42A16 65T40
Druh dokumentu:	Working Paper
Popis:	In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. This signal can be interpreted as the square of the modulus of the Fourier transform of the unknown scattering density. A beam-stop obstructs the forward scattered wave and, hence, the modulus Fourier data from a neighborhood of k=0 cannot be measured. In this note, we describe a linear method for recovering this unmeasured modulus Fourier data from the measured values and an estimate of the support of the image's autocorrelation function without consideration of phase retrieval. We analyze the conditioning of this problem, which grows exponentially with the modulus of the maximum spatial frequency not measured, and the effects of noise. Comment: Version 2 is a substantial revision with a stronger focus on the conditioning of our algorithm
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2002.02874 Zobrazit plný text záznamu View this record from Arxiv