Abstract

We consider the problem of reconstructing a function f with bounded support S from finitely many values of its Fourier transform F. Although f cannot be band limited since it has bounded support, it is typically the case that f can be modeled as the restriction to S of a σ-band-limited function, say g. Our reconstruction method is based on such a model for f. Of particular interest is the effect of the choice of $\sigma >0$ on the resolution.

© 2006 Optical Society of America

Reconstruction of compact binary images from limited Fourier amplitude data

V. L. Lo and R. P. Millane
J. Opt. Soc. Am. A 25(10) 2600-2607 (2008)

Image reconstruction: a unifying model for resolution enhancement and data extrapolation. Tutorial

Hsin M. Shieh, Charles L. Byrne, and Michael A. Fiddy
J. Opt. Soc. Am. A 23(2) 258-266 (2006)

Algorithms for reconstruction of partially known, band-limited Fourier-transform pairs from noisy data

Richard Barakat and Garry Newsam
J. Opt. Soc. Am. A 2(11) 2027-2039 (1985)

Noniterative image reconstruction from photon-limited data with the use of self-cross-correlation

Xiaotian Shi and Rabab K. Ward
J. Opt. Soc. Am. A 12(1) 47-57 (1995)

Accurate image reconstruction from few-view and limited-angle data in diffraction tomography

Samuel J. LaRoque, Emil Y. Sidky, and Xiaochuan Pan
J. Opt. Soc. Am. A 25(7) 1772-1782 (2008)