On the Mathematics of EEG and MEG in Spheroidal Geometry
On the Relations Between 2D and 3D Fractal Dimensions: Theoretical Approach and Clinical Application in Bone Imaging
The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The question which arises however is to know to which extent it is possible to get an exact determination of the...
On the weak solutions of the forward problem in EEG.
Parameterization and R-peak error estimations of ECG signals using independent component analysis.
Range characterization of Radon transforms on quaternionic projective spaces.
Range characterization of Radon transforms on quaternionic projective spaces.
Recognition of atherosclerotic plaques and their extended dimensioning with computerized tomography angiography imaging
In this paper the authors raise the issue of automatic discrimination of atherosclerotic plaques within an artery lumen based on numerical and statistical thresholding of Computerized Tomography Angiographic (CTA) images and their advanced dimensioning as a support for preoperative vessel assessment. For the study, a set of tomograms of the aorta, as well as the ilio-femoral and femoral arteries were examined. In each case a sequence of about 130-480 images of the artery cutoff planes were analyzed...
Reconstruction algorithms for an inverse medium problem
In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the number, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability...
Reconstruction and Quantification of Diffusion Tensor Imaging-Derived Cardiac Fibre and Sheet Structure in Ventricular Regions used in Studies of Excitation Propagation
Detailed descriptions of cardiac geometry and architecture are necessary for examining and understanding structural changes to the myocardium that are the result of pathologies, for interpreting the results of experimental studies of propagation, and for use as a three-dimensional orthotropically anisotropic model for the computational reconstruction of propagation during arrhythmias. Diffusion tensor imaging (DTI) provides a means to reconstruct fibre and sheet orientation throughout the ventricles....
Removal of ocular artifacts in the EEG through wavelet transform without using an EOG reference channel.
Rotation to physiological factors revised
Reconstruction of underlying physiological structures from a sequence of images is a long-standing problem which has been solved by factor analysis with a success. This paper tries to return to roots of the problem, to exploit the available findings and to propose an improved paradigm.
Segmentation of breast cancer fine needle biopsy cytological images
This paper describes three cytological image segmentation methods. The analysis includes the watershed algorithm, active contouring and a cellular automata GrowCut method. One can also find here a description of image pre-processing, Hough transform based pre-segmentation and an automatic nuclei localization mechanism used in our approach. Preliminary experimental results collected on a benchmark database present the quality of the methods in the analyzed issue. The discussion of common errors and...
Segmentation of MRI data by means of nonlinear diffusion
The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...
Singular Perturbations For Heart Image Segmentation Tracking
In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.
Solutions of inverse problems with potential application for breast tumour detection using microwave measurements.
System matrix computation for iterative reconstruction algorithms in SPECT based on direct measurements
A method for system matrix calculation in the case of iterative reconstruction algorithms in SPECT was implemented and tested. Due to a complex mathematical description of the geometry of the detector set-up, we developed a method for system matrix computation that is based on direct measurements of the detector response. In this approach, the influence of the acquisition equipment on the image formation is measured directly. The objective was to obtain the best quality of reconstructed images with...
Testing for periodicity in signals: An application to detect partial upper airway obstruction during sleep.
The complete ellipsoidal shell-model in EEG imaging.
The Gauss center research in multiscale scientific computation.
The potential distribution due to a dipole source in the fetal heart: A numerical model of the maternal abdomen.