Abstract

Two-dimensional image reconstruction using Fourier coefficients that are computed directly from the sampled representation of zero crossings is demonstrated. A two-dimensional image of dimensions Nx × Ny is interpreted as a set of Ny independent x-space lines (in gray-scale format) that are arranged uniquely along the y direction. Each line has Nx elements. Reconstruction is achieved first by computing the entire set of Ny one-dimensional Fourier transforms from the measured zero crossings using Newton’s formula. Each Nyth line spectra has Nx Fourier coefficients. The inverse Fourier transform is then applied to each of the line spectra to obtain a set of Ny reconstructed x-space lines. The reconstructed image is obtained by arranging the reconstructed lines properly along the y direction.

© 1993 Optical Society of America

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