Resolution enhancement of imaging small-scale portions in a compactly supported function.

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-scale features of interest. The prior discrete Fourier transform (PDFT) method for image reconstruction incorporates prior knowledge of the support, and perhaps general shape, of the object function being reconstructed through the use of a weight function. The new approach extends the PDFT by allowing different weight functions to modulate the different spatial frequency components of the reconstructed image.

Resolution enhancement in computerized tomographic imaging.

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 are integrals of f(r) along thin strips. Because the data are limited, resolution can be enhanced through the inclusion of prior knowledge.

Image reconstruction from limited Fourier data.

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 sigma-band-limited function, say g. Our reconstruction method is based on such a model for f.

Iterative image reconstruction using prior knowledge.

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) spectral estimation technique and as a variant of the algebraic reconstruction technique, allows one to incorporate prior information about the reconstructed signal to improve the resolution of the signal estimated. The context of diffraction tomography and image reconstruction from samples of the far-field scattering amplitude are used to explore the performance of the method.

Accuracy of extrapolated data as a function of prior knowledge and regularization.

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 designed Hilbert space. The PDFT has been successfully used in imaging applications to improve resolution and overcome the nonuniqueness associated with having only finitely many spectral measurements. With the use of an appropriate prior function, the resolution of the reconstructed image can be improved dramatically.

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

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 specify F(r) uniquely. Estimates based on the finite data may succeed in recovering broad features of F(r), but may fail to resolve important detail. Linear and nonlinear, model-based data extrapolation procedures can be used to improve resolution, but at the cost of sensitivity to noise.