Guy Demoment

Maximum entropy image reconstruction in X-ray and diffraction tomography

The authors propose a Bayesian approach with maximum-entropy (ME) priors to reconstruct an object from either the Fourier domain data (the Fourier transform of diffracted field measurements) in the case of diffraction tomography, or directly from the original projection data in the case of X-ray tomography. The objective function obtained is composed of a quadratic term resulting from chi(2) statistics and an entropy term that is minimized using variational techniques and a conjugate-gradient iterative method. The computational cost and practical implementation of the algorithm are discussed. Some simulated results in X-ray and diffraction tomography are given to compare this method to the classical ones.

Maximum entropy Fourier synthesis with application to diffraction tomography

In diffraction tomography, the generalized Radon theorem relates the Fourier transform (FT) of the diffracted field to the two-dimensional FT of the diffracting object. The relationship stands on algebraic contours, which are semicircles in the case of Born or Rytov first-order linear approximations. But the corresponding data are not sufficient to determine uniquely the solution. We propose a maximum entropy method to reconstruct the object from either the Fourier domain data or directly from the original diffracted field measurements. To do this, we give a new definition for the entropy of an object considered as a function of R(2) to C. To take into account the presence of noise, a chi-squared statistic is added to the entropy measure. The objective function thus obtained is minimized using variational techniques and a conjugate-gradient iterative method. The computational cost and practical implementation of the algorithm are discussed. Some simulated results are given which compare this new method with the classical ones.

Range Resolution Improvement by a Fast Deconvolution Method

Range resolution improvement in ultrasonic echography is considered as an estimation problem which is solved using a new fast minimum variance de-convolution algorithm specially designed for a microprocessor-based on-line processing. This method is used to accurately study the lenses and fundus of the eye and to follow variations of an arterial wall thickness during the cardiac cycle.

Algorithm for on Line Deconvolution of Echographic Signals

The information contained in the signal received from an insonified medium is only partly extracted in conventional echography.

Global parametric search and left ventricular identification

A mathematical model of left ventricular (LV) function in the dog has been developed. Based on a time-varying systolic elastance, the fitting procedure combined a local search according to a second-order method with a global heuristic search and provided beat-to-beat uncertainty intervals for each of the model parameters. Experiments were performed on anesthetized open-chest dogs in which the LV pressure and aortic flow were measured. The model formulated for the LV elastance appeared to be satisfactory for different contracting conditions including isovolumic or auxobaric beats. The study was focused on the maximal isovolumic elastance which, unlike the end-systolic elastance, has been found to be independent of both the preload and afterload and closely dependent on the contractile state of the LV.

Aperture synthesis in astronomical radio-interferometry using maximum entropy on the mean

A new algorithm for aperture synthesis in radio-astronomy is presented. It is based on the principle of the maximum entropy on the mean. The procedure jointly performs estimation of the unknown phase aberrations which composes the Fourier data and image reconstruction. It partly derives from a preexisting imaging method developed in the field of crystallography. A simulated example of the aperture synthesis indicates the efficiency of the method.

Algorithmes adaptatifs et récursifs : structures de calcul et problèmes de parallélisme

RésuméLes algorithmes rapides de factorisation ďune matrice proche-de-Tœplitz possèdent une structure de calcul commune du type treillis vectoriel, quel que soit le mode de récurrence adopté. Les auteurs étudient dans cet article les problèmes que pose leur mise en œuvre en parallèle sur des processeurs de traitement du signal qui ne permettent pas de coder simplement la transformation vectorielle correspondante.AbstractFast algorithms that factorize close-to-Tœplitz matrices may be imbedded in the same vector recursions, whenever using order or time recursion. In this paper we study the problems raised when these algorithms are implemented on digital signal processors that do not easily code this vector recursion.

Range Resolution Improvement with a New Signal Processor Implementing a Fast Kalman Estimator

In this communication we describe the results obtained with the solution we developed to improve the range resolution of existing echographic appliances. This solution consists in a fast minimum variance estimator implemented with a specialized signal processor that can be inserted in a conventional echographic system. This solution is well dedicated in situations where the time distortion of the transducer may be considered independently from other distorting effects. This is the situation in the study of a layered medium satisfying a one-dimensional wave equation (for example in ophtalmology). This is also the case in echotomography where the spatial filtering induced in the reconstructed images by this time distortion can be corrected before data entry in the tomographic processing.