We consider the problem of reconstructing an object function f(r) from finitely many linear functional values. In our main application, the function f(r) is a tomographic image, and the data areâ€¦ (More)

The prior discrete Fourier transform (PDFT) is a linear spectral estimator that provides a solution that is both data consistent and of minimum weighted norm through the use of a suitably designedâ€¦ (More)

Image reconstruction from limited number of sampled data typically leads to infinitely many data-consistent solutions, and it is usually difficult to specify an accurate image even in the absence ofâ€¦ (More)

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, itâ€¦ (More)

A method is proposed to reconstruct signals from incomplete data. The method, which can be interpreted both as a discrete implementation of the so-called prior discrete Fourier transform (PDFT)â€¦ (More)

In reconstructing an object function F(r) from finitely many noisy linear-functional values integral of F(r)Gn(r)dr we face the problem that finite data, noisy or not, are insufficient to specifyâ€¦ (More)

The ambiguity involved in reconstructing an image from limited Fourier data is removed using a new technique that incorporates prior knowledge of the location of regions containing small-scaleâ€¦ (More)