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The present work describes a Bayesian maximum a posteriori (MAP) method using a statistical multiscale wavelet prior model. Rather than using the orthogonal discrete wavelet transform (DWT), this prior is built on the translation invariant wavelet transform (TIWT). The statistical modeling of wavelet coefficients relies on the generalized Gaussian distribution. Image reconstruction is performed in spatial domain with a fast block sequential iteration algorithm. We study theoretically the TIWT MAP method by analyzing the Hessian of the prior function to provide some insights on noise and resolution properties of image reconstruction. We adapt the key concept of local shift invariance and explore how the TIWT MAP algorithm behaves with different scales. It is also shown that larger support wavelet filters do not offer better performance in contrast recovery studies. These theoretical developments are confirmed through simulation studies. The results show that the proposed method is more attractive than other MAP methods using either the conventional Gibbs prior or the DWT-based wavelet prior. Index Terms--Emission tomography, expectation-maximization, image reconstruction, maximum a posteriori, translation invariant, wavelet transform.

In this paper, we present a PET reconstruction method using the wavelet-based maximum a posteriori (MAP) expectation-maximization (EM) algorithm. The proposed method, namely WV-MAP-EM, shows several advantages over conventional methods. It provides an adaptive way for hyperparameter determination. Since the wavelet transform allows the use of fast algorithms, WV-MAP-EM also does not increase the order of computational complexity. The spatial noise behavior (bias/variance and resolution) of the proposed MAP estimator is analyzed. Quantitative comparisons to MAP methods with Markov random field (MRF) prior models point out that our alternative method, wavelet-base method, offers competitive performance in PET image reconstruction. Index Terms--Expectation-maximization (EM), image reconstruction, maximum a posteriori (MAP), positron emission tomography (PET), wavelet transform.

This paper reports on a method for left ventricle three-dimensional (3-D) reconstruction from two orthogonal ventriculograms. The proposed algorithm is voxel-based and takes into account the conical projection geometry associated with the biplane image acquisition equipment. The reconstruction process starts with an initial ellipsoidal approximation derived from the input ventriculograms. This model is subsequently deformed in such a way as to match the input projections. To this end, the object is modeled as a 3-D Markov-Gibbs random field, and an energy function is defined so that it includes one term that models the projections compatibility and another one that includes the space-time regularity constraints. The performance of this reconstruction method is evaluated by considering the reconstruction of mathematically synthesized phantoms and two 3-D binary databases from two orthogonal synthesized projections. The method is also tested using real biplane ventriculograms. In this case, the performance of the reconstruction is expressed in terms of the projection error, which attains values between 9.50% and 11.78% for two biplane sequences including a total of 55 images. Index Terms--Markov random fields, reconstruction from projections, simulated annealing, three-dimensional (3-D) reconstruction, ventriculographic images.

Clinical interventional hemodynamic studies quantify the ventricular function from two-dimensional (2-D) X-ray projection images without having enough information of the actual three-dimensional (3-D) shape of this cardiac cavity. This paper reports a left ventricle 3-D reconstruction method from two orthogonal angiographic projections. This investigation is motivated by the lack of information about the actual 3-D shape of the cardiac cavity. The proposed algorithm works in 3-D space and considers the oblique projection geometry associated with the biplane image acquisition equipment. The reconstruction process starts by performing an approximate reconstruction based on the Cylindrical Closure Operation and the Dempster-Shafer theory. This approximate reconstruction is appropriately deformed in order to match the given projections. The deformation procedure is carried out by an iterative process that, by means of the Dempster--Shafer and the fuzzy integral theory, combines the information provided by the projection error and the connectivity between voxels. The performance of the proposed reconstruction method is evaluated by considering first the reconstruction of two 3-D binary databases from two orthogonal synthetized projections, obtaining errors as low as 6.48%. The method is then tested on real data, where two orthogonal preprocessed angiographic images are used for reconstruction. The performance of the technique, in this case, is assessed by means of the projection error, whose average for both views is 7.5%. The reconstruction method is also tested by performing the 3-D reconstruction of a ventriculographic sequence throughout an entire cardiac cycle. Index Terms--Angiographic images, evidential combination, fuzzy sets, left ventricle, three-dimensional (3-D) reconstruction.

In this paper, a model-based approach to medical image analysis is presented. It is aimed at understanding the influence of the physiological (related to tissue) and physical (related to image modality) processes underlying the image content. This methodology is exemplified by modeling first, the liver and its vascular network, and second, the standard computed tomography (CT) scan acquisition. After a brief survey on vascular modeling literature, a new method, aimed at the generation of growing three-dimensional vascular structures perfusing the tissue, is described. A solution is proposed in order to avoid intersections among vessels belonging to arterial and/or venous trees, which are physiologically connected. Then it is shown how the propagation of contrast material leads to simulate time-dependent sequences of enhanced liver CT slices. Index Terms--Computed tomography (CT), hepatic enhancement, image simulation, physiologically based modeling, vascular network.

In the field of epilepsy, the analysis of stereoelectroencephalographic (SEEG) signals recorded with depth electrodes provides major information on interactions between brain structures during seizures. A comprehensive methodology of comparing SEEG seizure recordings is presented. It proceeds in three steps: 1) segmentation of SEEG signals; 2) characterization and labeling of segments; and 3) comparison of observations coded as sequences of symbol vectors. The third step reports a vectorial extension of the Wagner and Fischer's algorithm to first, quantify similarities between observations and second, extract invariant sequences of events, referred to as spatio-temporal signatures. The study shows that two observations of nonequal duration can be matched by deforming the first one to optimally fit the second, under cost constraints. Results show that the methodology allows to exhibit signatures occurring during epileptic seizures and to point out different types of seizure patterns. The study brings objective results on reproducible interactions between brain structures during ictal periods and may help in the understanding of epileptogenic networks.

This paper presents a three-dimensional edge operator aimed at the detection of anatomical structures in medical imaging. It uses the spatial moments of gray level surface, and operates in three dimensions with any window size. It allows us to estimate the location and the contrast surface, as well as the surface orientation. The computation of the discrete version is reported. Bias and errors due to the spatial sampling and noise are analyzed both at a theoretical and experimental level. The moment-based operator is compared with other well-known edge operators on simple shaped primitives for which the analytical solution is known. The 3D rendering of real data is then provided by merging the operator in a ray-tracing framework.

An improved and very fast algorithm dealing with the extraction of vessels in three-dimensional imaging is described. The approach is based on geometrical moments and a local cylindrical approximation. A robust estimation of vessel and background intensity levels, position, orientation, and diameter of the vessels with adaptive control of key parameters, is provided during vessel tracking. Experimental results are presented for lower limb arteries in multidetector computed tomography scanner. Index Terms--CTA, geometrical moment, three-dimensional segmentation.

The death of biomedical engineering advocate Dr. Pierre Galletti is announced. He was instrumental for bringing recognition to biomedical engineering from the government and the academe. He received his M.D. degree from the University of Lausanne in 1951 and went on to become the first chairman of the Division of Biological and Medical Sciences at Brown University. At the time of his death, Dr. Galletti was a member of the editorial boards of four research journals on biomedical engineering. He is survived by his wife Sonia and son Marc Henri.

A study was conducted to analyze the characteristics of the motion of coronary arteries in two and three dimensions. The main left coronary artery centerlines were determined from digital subtraction angiography image sequences. Local and global motion properties were examined along the sequence. A new numeric was proposed to symbolic image transformation to support the needed facts for knowledge-based motion interpretation.