The problem of reconstructing a non-negative function from finitely many values of its Fourier
transform is a problem of approximating one function by another and, as such, is analogous …

Maximum entropy, using the Shannon/Jaynes form-Σ p log p, is an enormously powerful tool
for reconstructing positive, additive images from a wide variety of types of data. The …

The ill-posed problem of restoring object information from finitely many measurements of its
spectrum can be solved by using the best approximation in Hilbert spaces appropriately …

A finite energy signal can be reconstructed from equally spaced samples taken at a rate ρ if
translates of the signal's spectral region by non-zero integer multiples of ρ are disjoint, or …

I discuss approaches to optimally remove noise from images. A generalization of Wiener
filtering to non–Gaussian distributions and wavelets is described, as well as an approach to …

The application of the maximum entropy method of image processing to the problem of
reconstructing an image from the intensities of its Fourier transform is discussed. We present …

Non–parametric function estimation aims to estimate or recover or denoise a function of
interest, perhaps a signal, spectrum or image, that is observed in noise and possibly …

One popular method for the recovery of an ideal intensity image from corrupted or indirect
measurements is regularization: minimize an objective function that enforces a roughness …

Digital image restoration requires some knowledge of the degradation phenomena in order
to attempt an inversion of that degradation. Typically, degradations which are included in the …

We present a sampling theory for a class of binary images with finite rate of innovation (FRI).
Every image in our model is the restriction of 1 {p≤ 0} to the image plane, where 1 denotes …