Biomedical subjects

Michael A Fiddy

Publications and source records attributed to Michael A Fiddy.

3 recordsLinked to original sources

PubMed2006

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. We explore the ways in which some significant parameters affect the PDFT estimate. A relationship between estimated spectral values, prior knowledge, and regularization was examined. It allows one to assess the reliability of the estimated spectral values for a given choice of prior estimate and provides a means for optimizing PDFT-based estimators.

Journal Article↗

PubMed2006

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. To estimate linear-functional values of F(r) that have not been measured from those that have been, we need to employ prior information about the object F(r), such as support information or, more generally, estimates of the overall profile of F(r). One way to do this is through minimum-weighted-norm (MWN) estimation, with the prior information used to determine the weights. The MWN approach extends the Gerchberg-Papoulis band-limited extrapolation method and is closely related to matched-filter linear detection, the approximation of the Wiener filter, and to iterative Shannon-entropy-maximization algorithms. Non-linear versions of the MWN method extend the noniterative, Burg, maximum-entropy spectral-estimation procedure.

Algorithms↗

PubMed2006

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. On the basis of numerical computations, the optimum choice of parameters is determined empirically by comparing image reconstructions of the noniterative PDFT algorithm and the proposed iterative scheme.

Algorithms↗