An inverse diffusion problem that appears in Magnetic Resonance dosimetry is studied. The problem is shown to be equivalent to a deconvolution problem with a known kernel. To cope with the singularity of the kernel, nonlinear regularization functionals are considered which can provide regular solutions, reproduce steep gradients and impose positivity constraints. A fast deterministic algorithm for solving the involved non-convex minimization problem is used. Accurate restorations on real 256×256 images are obtained by the algorithm in a few minutes on a 266-MHz PC that allow to precisely quantitate the relative absorbed dose.

Recent studies have demonstrated the potential of dynamic contrast-enhanced magnetic resonance imaging (MRI) describing pulmonary perfusion. However, breathing motion, susceptibility artifacts, and a low signal-to-noise ratio (SNR) make automatic pixel-by-pixel analysis difficult. In the present work, we propose a novel method to compensate for breathing motion. In order to test the feasibility of this method, we enrolled 53 patients with pulmonary embolism (N = 24), chronic obstructive pulmonary disease (COPD) (N = 14), and acute pneumonia (N = 15). A crucial part of the method, an automatic diaphragm detection algorithm, was evaluated in all 53 patients by two independent observers. The accuracy of the method to detect the diaphragm showed a success rate of 92%. Furthermore, a Bayesian noise reduction technique was implemented and tested. This technique significantly reduced the noise level without removing important clinical information. In conclusion, the combination of a motion correction method and a Bayesian noise reduction method offered a rapid, semiautomatic pixel-by-pixel analysis of the lungs with great potential for research and clinical use. © 2001 Wiley-Liss, Inc.

The use of Euler polynomials and Euler numbers allows us to construct a quadrature rule similar to the well-known Euler--MacLaurin quadrature formula, using Euler (instead of Bernoulli) numbers, and even (instead of odd) order derivatives of a given function evaluated at the extrema of the considered interval. An expression of the remainder term and numerical examples are also given. © 2001, Heldermann Verlag. All rights reserved.

The problem of reconstructing a piecewise constant function from a finite number of its Fourier coefficients perturbed by noise is considered. A reconstruction method, based on the computation of the Padè approximants to the Z-transform of the sequence of the noisy Fourier coefficients is proposed. The method is based on the remark that the distribution of the poles of the Padè approximants shows, asymptotically, clusters in the complex plane which allow the identification of the discontinuities of the function. It turns out that the Z-transform is a multiple-valued function and the location of the clusters corresponds to the branch points of such a function. By using this property of the Padè poles, a very effective reconstruction method can be developed. Some numerical experiments are presented to show the feasibility of the method.

We consider a geometric motion associated with the minimization of a curvature dependent functional, which is related to the Willmore functional. Such a functional arises in connection with the image segmentation problem in computer vision theory. We show by using formal asymptotics that the geometric motion can be approximated by the evolution of the zero level set of the solution of a nonlinear fourth-order equation related to the Cahn-Hilliard and Allen-Cahn equations.

A multiphase and multicomponent mathematical model for the fluid dynamics in porous media is described.

An integro-differential equation of Prandtl's type and a collocation method as well as a collocationquadrature method for its approximate solution is studied in weighted spaces of continuous functions.

AVHRR is an imager flying on polar meteorological satellites that, due to its spatial resolution (about 1 km at Nadir view), produces a huge amount of data. A method based on the wavelet packet transform is devised to compress AVHRR images. The method is driven by the compression error (application dependent), so that different types of images have the same quality. The best basis wavelet packet is chosen by L1 norm criterion that was found to be the most suited for the problem at hand. Ability of the compression method to preserve most fine structures of the images even at the highest resolution is demonstrated based on some examples. Comparison with wavelet algorithms is performed.