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Algorithm for the recovery of a real signal from its Hartley-transform modulus only

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Abstract

A new algorithm for the reconstruction of a real signal (image) from its Hartley-transform modulus only is presented, based on the general theory of the amplitude-phase-retrieval problem. The quality of the recovered image is strongly dependent on the properties of the frequency components in the Hartley-transform space and can be significantly improved by extending the band limit of the Hartley-transform spectrum. The accuracy of the recovered image at high-resolution levels depends on the initial image intensity distribution used in the iteration algorithm. To obtain the best recovery of the image, we propose an instructive method to determine the initial image distribution. The influence of noise contained in the Hartley-transform modulus on the convergent solution is also examined in detail.

© 1991 Optical Society of America

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