Image reconstruction from power spectral data

Ofer Hadar; E. Gresten; D. A. Weitzman; Dan Arbel

doi:10.1117/12.255081

25 October 1996 Image reconstruction from power spectral data

Ofer Hadar, E. Gresten, D. A. Weitzman, Dan Arbel

Proceedings Volume 2827, Digital Image Recovery and Synthesis III; (1996) https://doi.org/10.1117/12.255081
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

Restoration of images blurred by an optical transfer function (OTF), or additive Gaussian noise which affect the Fourier transform amplitude and phase of the image, are considered. A method for reconstructing a two-dimensional image from power spectral data is presented. It is known that the spatial frequencies at which the Fourier transform F(u,v) of an image equals zero are called the real-plane zeros. It has been shown that real-plane zero locations have a significant effect on the Fourier phase in that they are the end points of phase function branch cuts, and it has been shown that real-plane zero locations can be estimated from Fourier transform magnitude data. Thus, real-plane zeros can be utilized in phase retrieval algorithms to help constrain the possible Fourier transform phase function. The purpose of this research is to recover the Fourier transform phase function from the knowledge of the power spectrum itself. By locating the points at which the Fourier transform intensity data are zero, we approximate a nonfactorizable function by its point-zero factors to recover an estimate of the object. A simple iterative method then successfully refines this phase estimate. The basic idea for the restoration is to separate the point-zeros of the modulation transfer function (MTF) or the additive noise from the point-zeros of the original image. Image restoration results according to the method of phase function retrieval for images degraded by additive noise and linear MTF are also presented.

Citation Download Citation

Ofer Hadar, E. Gresten, D. A. Weitzman, and Dan Arbel "Image reconstruction from power spectral data", Proc. SPIE 2827, Digital Image Recovery and Synthesis III, (25 October 1996); https://doi.org/10.1117/12.255081

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