Recovering missing data in coherent diffraction imaging
Abstract
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 beamstop 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.02874
 Bibcode:
 2020arXiv200202874B
 Keywords:

 Mathematics  Numerical Analysis;
 Electrical Engineering and Systems Science  Signal Processing;
 High Energy Physics  Experiment;
 78A46;
 78A45;
 42A16;
 65T40
 EPrint:
 Version 2 is a substantial revision with a stronger focus on the conditioning of our algorithm