Image reconstruction from power spectral data

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.