Incorporating accurate statistical modeling in PET: reconstruction for whole-body imaging

Tese de doutoramento em Biofísica, apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2007The thesis is devoted to image reconstruction in 3D whole-body PET imaging. OSEM ( Ordered Subsets Expectation maximization ) is a statistical algorithm that assumes Poisson data. However, corrections for physical effects (attenuation, scattered and random coincidences) and detector efficiency remove the Poisson characteristics of these data. The Fourier Rebinning (FORE), that combines 3D imaging with fast 2D reconstructions, requires corrected data. Thus, if it will be used or whenever data are corrected prior to OSEM, the need to restore the Poisson-like characteristics is present. Restoring Poisson-like data, i.e., making the variance equal to the mean, was achieved through the use of weighted OSEM algorithms. One of them is the NECOSEM, relying on the NEC weighting transformation. The distinctive feature of this algorithm is the NEC multiplicative factor, defined as the ratio between the mean and the variance. With real clinical data this is critical, since there is only one value collected for each bin the data value itself. For simulated data, if we keep track of the values for these two statistical moments, the exact values for the NEC weights can be calculated. We have compared the performance of five different weighted algorithms (FORE+AWOSEM, FORE+NECOSEM, ANWOSEM3D, SPOSEM3D and NECOSEM3D) on the basis of tumor detectablity. The comparison was done for simulated and clinical data. In the former case an analytical simulator was used. This is the ideal situation, since all the weighting factors can be exactly determined. For comparing the performance of the algorithms, we used the Non-Prewhitening Matched Filter (NPWMF) numerical observer. With some knowledge obtained from the simulation study we proceeded to the reconstruction of clinical data. In that case, it was necessary to devise a strategy for estimating the NEC weighting factors. The comparison between reconstructed images was done by a physician largely familiar with whole-body PET imaging

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Image processing techniques in nuclear medicine

The application of image processing techniques to radionuclide images acquired on a gamma camera - computer system has been investigated. Hepatic perfusion imaging studies with 99Tcm-tin colloid were performed in patients with primary colorectal carcimma. The hepatic perfusion index performed poorly in the detection of those patients with occult or overt hepatic metastastes, as did mean transit times of liver colloid flow derived from deconvolution analysis. A discriminant function was developed which separated those patients with occult metastases from those without liver disease. A fully automatic algorithm to derive a left ventricular edge from each frame of an ECG gated cardiac blood pool study was developed and validated in patient studies. Left ventricular ejection fractions calculated from count rates within the edge were reproducible and correlated well with ejection fractions derived from the same images by a manual technique, and with ejection fractions derived from left ventricular cineangiography. Studies were performed in patients to evaluate the effectiveness of tomographic imaging of the myocardial perfusion imaging agent 99Tcm-tBIN for detection of ischaemic heart disease. Tomographic reconstructions in the planes of the axes of the left ventricle gave better results than transaxial reconstructions or planar imaging. Choice of the optimum reconstruction filter for use in tomography using 99Tcm-tBIN was examined by means of patient am phantom studies. These showed that more accurate diagnoses and better reconstructions were obtained with smoothing filters than by the use of sharp reconstruction filters. This work shows that optimum image processing techniques must be established to attain the best possible results with new radiopharmaceuticals for nuclear medicine investigations

Topics in image reconstruction for high resolution positron emission tomography

Les problèmes mal posés représentent un sujet d'intérêt interdisciplinaire qui surgires dans la télédétection et des applications d'imagerie. Cependant, il subsiste des questions cruciales pour l'application réussie de la théorie à une modalité d'imagerie. La tomographie d'émission par positron (TEP) est une technique d'imagerie non-invasive qui permet d'évaluer des processus biochimiques se déroulant à l'intérieur d'organismes in vivo. La TEP est un outil avantageux pour la recherche sur la physiologie normale chez l'humain ou l'animal, pour le diagnostic et le suivi thérapeutique du cancer, et l'étude des pathologies dans le coeur et dans le cerveau. La TEP partage plusieurs similarités avec d'autres modalités d'imagerie tomographiques, mais pour exploiter pleinement sa capacité à extraire le maximum d'information à partir des projections, la TEP doit utiliser des algorithmes de reconstruction d'images à la fois sophistiquée et pratiques. Plusieurs aspects de la reconstruction d'images TEP ont été explorés dans le présent travail. Les contributions suivantes sont d'objet de ce travail: Un modèle viable de la matrice de transition du système a été élaboré, utilisant la fonction de réponse analytique des détecteurs basée sur l'atténuation linéaire des rayons y dans un banc de détecteur. Nous avons aussi démontré que l'utilisation d'un modèle simplifié pour le calcul de la matrice du système conduit à des artefacts dans l'image. (IEEE Trans. Nucl. Sei., 2000) );> La modélisation analytique de la dépendance décrite à l'égard de la statistique des images a simplifié l'utilisation de la règle d'arrêt par contre-vérification (CV) et a permis d'accélérer la reconstruction statistique itérative. Cette règle peut être utilisée au lieu du procédé CV original pour des projections aux taux de comptage élevés, lorsque la règle CV produit des images raisonnablement précises. (IEEE Trans. Nucl. Sei., 2001) Nous avons proposé une méthodologie de régularisation utilisant la décomposition en valeur propre (DVP) de la matrice du système basée sur l'analyse de la résolution spatiale. L'analyse des caractéristiques du spectre de valeurs propres nous a permis d'identifier la relation qui existe entre le niveau optimal de troncation du spectre pour la reconstruction DVP et la résolution optimale dans l'image reconstruite. (IEEE Trans. Nucl. Sei., 2001) Nous avons proposé une nouvelle technique linéaire de reconstruction d'image événement-par-événement basée sur la matrice pseudo-inverse régularisée du système. L'algorithme représente une façon rapide de mettre à jour une image, potentiellement en temps réel, et permet, en principe, la visualisation instantanée de distribution de la radioactivité durant l'acquisition des données tomographiques. L'image ainsi calculée est la solution minimisant les moindres carrés du problème inverse régularisé.Abstract: Ill-posed problems are a topic of an interdisciplinary interest arising in remote sensing and non-invasive imaging. However, there are issues crucial for successful application of the theory to a given imaging modality. Positron emission tomography (PET) is a non-invasive imaging technique that allows assessing biochemical processes taking place in an organism in vivo. PET is a valuable tool in investigation of normal human or animal physiology, diagnosing and staging cancer, heart and brain disorders. PET is similar to other tomographie imaging techniques in many ways, but to reach its full potential and to extract maximum information from projection data, PET has to use accurate, yet practical, image reconstruction algorithms. Several topics related to PET image reconstruction have been explored in the present dissertation. The following contributions have been made: (1) A system matrix model has been developed using an analytic detector response function based on linear attenuation of [gamma]-rays in a detector array. It has been demonstrated that the use of an oversimplified system model for the computation of a system matrix results in image artefacts. (IEEE Trans. Nucl. Sci., 2000); (2) The dependence on total counts modelled analytically was used to simplify utilisation of the cross-validation (CV) stopping rule and accelerate statistical iterative reconstruction. It can be utilised instead of the original CV procedure for high-count projection data, when the CV yields reasonably accurate images. (IEEE Trans. Nucl. Sci., 2001); (3) A regularisation methodology employing singular value decomposition (SVD) of the system matrix was proposed based on the spatial resolution analysis. A characteristic property of the singular value spectrum shape was found that revealed a relationship between the optimal truncation level to be used with the truncated SVD reconstruction and the optimal reconstructed image resolution. (IEEE Trans. Nucl. Sci., 2001); (4) A novel event-by-event linear image reconstruction technique based on a regularised pseudo-inverse of the system matrix was proposed. The algorithm provides a fast way to update an image potentially in real time and allows, in principle, for the instant visualisation of the radioactivity distribution while the object is still being scanned. The computed image estimate is the minimum-norm least-squares solution of the regularised inverse problem

The context dependence of network response properties in the primary visual cortex of the primate and cat

In the mammalian visual system, stimulus context was investigated with respect to the ways it influenced neuronal mean response magnitude (the average number of spikes fired per second), response temporal structure (the timing of spikes with respect to one another), and the extent to which distributed neurones fired spikes synchronous due to synaptic interaction between them. Neurones were presented with bipartite grating stimuli, in which the spatio-temporal relationship between the grating activating the excitatory receptive field and that presented to the surrounding visual space could be varied systematically. Simultaneous extracellular recordings were made of the responses of up to four single neurones separated by 750-1000µm, in the lateral geniculate nucleus (LGN) of the thalamus in the cat, or the primary visual cortex (V1) of non-human primates or cats. Changing context systematically influenced the activity of groups of cells. The responses of 83% of primate V1 cells to discontinuous stimuli, in which the centre/surround orientation difference was greater than 45°, contained stronger oscillations at frequencies below 80Hz, than responses to continuous stimuli. Many cat and primate V1 neurones exhibited elevated response magnitudes to such stimuli. In primate V1, the strength of a cell's oscillatory discharge was dependent on stimulus configuration rather than response magnitude. In the LGN and V1, cell pairs with different orientation preferences fired synchronised responses when stimulated by specific discontinuous grating configurations. Stimulus specific synchronised LGN input, and reciprocal excitatory and inhibitory cortico-cortical connections could generate these properties of cells, and the network in which they exist. A model is proposed to account for the function significance of contour discontinuities in generating coherent neural representations of objects in the visual world. It involves response synchronisation in horizontal, feedforward and feedback interactions, within and between the LGN, V1, V2 and V4