923 resultados para Image data hiding
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Hyperspectral imaging sensors provide image data containing both spectral and spatial information from the Earth surface. The huge data volumes produced by these sensors put stringent requirements on communications, storage, and processing. This paper presents a method, termed hyperspectral signal subspace identification by minimum error (HySime), that infer the signal subspace and determines its dimensionality without any prior knowledge. The identification of this subspace enables a correct dimensionality reduction yielding gains in algorithm performance and complexity and in data storage. HySime method is unsupervised and fully-automatic, i.e., it does not depend on any tuning parameters. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada.
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Tese de Doutoramento (Programa Doutoral em Engenharia Biomédica)
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The structure of the yeast DNA-dependent RNA polymerase I (RNA Pol I), prepared by cryo-negative staining, was studied by electron microscopy. A structural model of the enzyme at a resolution of 1.8 nm was determined from the analysis of isolated molecules and showed an excellent fit with the atomic structure of the RNA Pol II Delta4/7. The high signal-to-noise ratio (SNR) of the stained molecular images revealed a conformational flexibility within the image data set that could be recovered in three-dimensions after implementation of a novel strategy to sort the "open" and "closed" conformations in our heterogeneous data set. This conformational change mapped in the "wall/flap" domain of the second largest subunit (beta-like) and allows a better accessibility of the DNA-binding groove. This displacement of the wall/flap domain could play an important role in the transition between initiation and elongation state of the enzyme. Moreover, a protrusion was apparent in the cryo-negatively stained model, which was absent in the atomic structure and was not detected in previous 3D models of RNA Pol I. This structure could, however, be detected in unstained views of the enzyme obtained from frozen hydrated 2D crystals, indicating that this novel feature is not induced by the staining process. Unexpectedly, negatively charged molybdenum compounds were found to accumulate within the DNA-binding groove, which is best explained by the highly positive electrostatic potential of this region of the molecule, thus, suggesting that the stain distribution reflects the overall surface charge of the molecule.
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X-ray microtomography has become a new tool in earth sciences to obtain non-destructive 3D-image data from geological objects in which variations in mineralogy, chemical composition and/or porosity create sufficient x-ray density contrasts.We present here first, preliminary results of an application to the external and internal morphology of Permian to Recent Larger Foraminifera. We use a SkyScan-1072 high-resolution desk-top micro-CT system. The system has a conical x-ray source with a spot size of about 5µm that runs at 20-100kV, 0-250µA, resulting in a maximal resolution of 5µm. X-ray transmission images are captured by a scintillator coupled via fibre optics to a 1024x1024 pixel 12-bit CCD. The object is placed between the x-ray source and the scintillator on a stub that rotates 360°around its vertical axis in steps as small as 0.24 degrees. Sample size is limited to 2 cm due to the absorption of geologic material for x-rays. The transmission images are back projected using a Feldkamp algorithm into a vertical stack of up to 1000 1Kx1K images that represent horizontal cuts of the object. This calculation takes 2 to several hours on a Double-Processor 2.4GHz PC. The stack of images (.bmp) can be visualized with any 3D-imaging software, used to produce cuts of Larger Foraminifera. Among other applications, the 3D-imaging software furnished by SkyScan can produce 3D-models by defining a threshold density value to distinguish "solid" from "void. Several models with variable threshold values and colors can be imbricated, rotated and cut together. The best results were obtained with microfossils devoid of chamber-filling cements (Permian, Eocene, Recent). However, even slight differences in cement mineralogy/composition can result in surprisingly good x-ray density contrasts.X-ray microtomography may develop into a powerful tool for larger microfossils with a complex internal structure, because it is non-destructive, requires no preparation of the specimens, and produces a true 3D-image data set. We will use these data sets in the future to produce cuts in any direction to compare them with arbitrary cuts of complex microfossils in thin sections. Many groups of benthic and planktonic foraminifera may become more easily determinable in thin section by this way.
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Synchrotron radiation X-ray tomographic microscopy is a nondestructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, we present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis of our data.
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Purpose: To develop and evaluate a practical method for the quantification of signal-to-noise ratio (SNR) on coronary MR angiograms (MRA) acquired with parallel imaging.Materials and Methods: To quantify the spatially varying noise due to parallel imaging reconstruction, a new method has been implemented incorporating image data acquisition followed by a fast noise scan during which radio-frequency pulses, cardiac triggering and navigator gating are disabled. The performance of this method was evaluated in a phantom study where SNR measurements were compared with those of a reference standard (multiple repetitions). Subsequently, SNR of myocardium and posterior skeletal muscle was determined on in vivo human coronary MRA.Results: In a phantom, the SNR measured using the proposed method deviated less than 10.1% from the reference method for small geometry factors (<= 2). In vivo, the noise scan for a 10 min coronary MRA acquisition was acquired in 30 s. Higher signal and lower SNR, due to spatially varying noise, were found in myocardium compared with posterior skeletal muscle.Conclusion: SNR quantification based on a fast noise scan is a validated and easy-to-use method when applied to three-dimensional coronary MRA obtained with parallel imaging as long as the geometry factor remains low.
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Coronary magnetic resonance angiography (MRA) is a powerful noninvasive technique with high soft-tissue contrast for the visualization of the coronary anatomy without X-ray exposure. Due to the small dimensions and tortuous nature of the coronary arteries, a high spatial resolution and sufficient volumetric coverage have to be obtained. However, this necessitates scanning times that are typically much longer than one cardiac cycle. By collecting image data during multiple RR intervals, one can successfully acquire coronary MR angiograms. However, constant cardiac contraction and relaxation, as well as respiratory motion, adversely affect image quality. Therefore, sophisticated motion-compensation strategies are needed. Furthermore, a high contrast between the coronary arteries and the surrounding tissue is mandatory. In the present article, challenges and solutions of coronary imaging are discussed, and results obtained in both healthy and diseased states are reviewed. This includes preliminary data obtained with state-of-the-art techniques such as steady-state free precession (SSFP), whole-heart imaging, intravascular contrast agents, coronary vessel wall imaging, and high-field imaging. Simultaneously, the utility of electron beam computed tomography (EBCT) and multidetector computed tomography (MDCT) for the visualization of the coronary arteries is discussed.
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With improved B 0 homogeneity along with satisfactory gradient performance at high magnetic fields, snapshot gradient-recalled echo-planar imaging (GRE-EPI) would perform at long echo times (TEs) on the order of T2*, which intrinsically allows obtaining strongly T2*-weighted images with embedded substantial anatomical details in ultrashort time. The aim of this study was to investigate the feasibility and quality of long TE snapshot GRE-EPI images of rat brain at 9.4 T. When compensating for B 0 inhomogeneities, especially second-order shim terms, a 200 x 200 microm2 in-plane resolution image was reproducibly obtained at long TE (>25 ms). The resulting coronal images at 30 ms had diminished geometric distortions and, thus, embedded substantial anatomical details. Concurrently with the very consistent stability, such GRE-EPI images should permit to resolve functional data not only with high specificity but also with substantial anatomical details, therefore allowing coregistration of the acquired functional data on the same image data set.
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Purpose: SIOPEN scoring of 123I mIBG imaging has been shown to predict response to induction chemotherapy and outcome at diagnosis in children with HRN.Method: Patterns of skeletal 123I mIBG uptake were assigned numerical scores (Mscore) ranging from 0 (no metastasis) to 72 (diffuse metastases) within 12 body areas as described previously. 271 anonymised, paired image data sets acquired at diagnosis and on completion of Rapid COJEC induction chemotherapy were reviewed, constituting a representative sample of 1602 children treated prospectively within the HR-NBL1/SIOPEN trial. Pre-and post-treatment Mscores were compared with bone marrow cytology (BM) and 3 year event free survival (EFS).Results: Results 224/271 patients showed skeletal MIBG-uptake at diagnosis and were evaluable forMIBG-response. Complete response (CR) on MIBG to Rapid COJEC induction was achieved by 66%, 34% and 15% of patients who had pre-treatment Mscores of <18 (n¼65, 29%), 18-44 (n¼95,42%) and Y ´ 45 (n¼64, 28.5%) respectively (chi squared test p<.0001). Mscore at diagnosis and on completion of Rapid COJEC correlated strongly with BM involvement (p<0.0001). The correlation of pre score with post scores and response was highly significant (p<0.001). Most importantly, the 3 year EFS in 47 children with Mscore 0 at diagnosis was 0.68 (A ` 0.07), by comparison with 0.42 (A` 0.06), 0.35 (A` 0.05) and 0.25 (A` 0.06) for patients in pre-treatment score groups <18, 18-44 and Y ´ 45, respectively (p<0.001). AnMscore threshold ofY ´ 45 at diagnosis was associated with significantly worse outcome by comparison with all other Mscore groups (p¼0.029). The 3 year EFS of 0.53 (A` 0.07) of patients in metastatic CR (mIBG and BM) after Rapid Cojec (33%) is clearly superior to patients not achieving metastatic CR (0.24 (A ` 0.04), p¼0.005).Conclusion: SIOPEN scoring of 123I mIBG imaging has been shown to predict response to induction chemotherapy and outcome at diagnosis in children with HRN.
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This work extends a previously developed research concerning about the use of local model predictive control in differential driven mobile robots. Hence, experimental results are presented as a way to improve the methodology by considering aspects as trajectory accuracy and time performance. In this sense, the cost function and the prediction horizon are important aspects to be considered. The aim of the present work is to test the control method by measuring trajectory tracking accuracy and time performance. Moreover, strategies for the integration with perception system and path planning are briefly introduced. In this sense, monocular image data can be used to plan safety trajectories by using goal attraction potential fields
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This research extends a previously developed work concerning about the use of local model predictive control in mobile robots. Hence, experimental results are presented as a way to improve the methodology by considering aspects as trajectory accuracy and time performance. In this sense, the cost function and the prediction horizon are important aspects to be considered. The platformused is a differential driven robot with a free rotating wheel. The aim of the present work is to test the control method by measuring trajectory tracking accuracy and time performance. Moreover, strategies for the integration with perception system and path planning are also introduced. In this sense, monocular image data provide an occupancy grid where safety trajectories are computed by using goal attraction potential fields
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Blowing and drifting of snow is a major concern for transportation efficiency and road safety in regions where their development is common. One common way to mitigate snow drift on roadways is to install plastic snow fences. Correct design of snow fences is critical for road safety and maintaining the roads open during winter in the US Midwest and other states affected by large snow events during the winter season and to maintain costs related to accumulation of snow on the roads and repair of roads to minimum levels. Of critical importance for road safety is the protection against snow drifting in regions with narrow rights of way, where standard fences cannot be deployed at the recommended distance from the road. Designing snow fences requires sound engineering judgment and a thorough evaluation of the potential for snow blowing and drifting at the construction site. The evaluation includes site-specific design parameters typically obtained with semi-empirical relations characterizing the local transport conditions. Among the critical parameters involved in fence design and assessment of their post-construction efficiency is the quantification of the snow accumulation at fence sites. The present study proposes a joint experimental and numerical approach to monitor snow deposits around snow fences, quantitatively estimate snow deposits in the field, asses the efficiency and improve the design of snow fences. Snow deposit profiles were mapped using GPS based real-time kinematic surveys (RTK) conducted at the monitored field site during and after snow storms. The monitored site allowed testing different snow fence designs under close to identical conditions over four winter seasons. The study also discusses the detailed monitoring system and analysis of weather forecast and meteorological conditions at the monitored sites. A main goal of the present study was to assess the performance of lightweight plastic snow fences with a lower porosity than the typical 50% porosity used in standard designs of such fences. The field data collected during the first winter was used to identify the best design for snow fences with a porosity of 50%. Flow fields obtained from numerical simulations showed that the fence design that worked the best during the first winter induced the formation of an elongated area of small velocity magnitude close to the ground. This information was used to identify other candidates for optimum design of fences with a lower porosity. Two of the designs with a fence porosity of 30% that were found to perform well based on results of numerical simulations were tested in the field during the second winter along with the best performing design for fences with a porosity of 50%. Field data showed that the length of the snow deposit away from the fence was reduced by about 30% for the two proposed lower-porosity (30%) fence designs compared to the best design identified for fences with a porosity of 50%. Moreover, one of the lower-porosity designs tested in the field showed no significant snow deposition within the bottom gap region beneath the fence. Thus, a major outcome of this study is to recommend using plastic snow fences with a porosity of 30%. It is expected that this lower-porosity design will continue to work well for even more severe snow events or for successive snow events occurring during the same winter. The approach advocated in the present study allowed making general recommendations for optimizing the design of lower-porosity plastic snow fences. This approach can be extended to improve the design of other types of snow fences. Some preliminary work for living snow fences is also discussed. Another major contribution of this study is to propose, develop protocols and test a novel technique based on close range photogrammetry (CRP) to quantify the snow deposits trapped snow fences. As image data can be acquired continuously, the time evolution of the volume of snow retained by a snow fence during a storm or during a whole winter season can, in principle, be obtained. Moreover, CRP is a non-intrusive method that eliminates the need to perform man-made measurements during the storms, which are difficult and sometimes dangerous to perform. Presently, there is lots of empiricism in the design of snow fences due to lack of data on fence storage capacity on how snow deposits change with the fence design and snow storm characteristics and in the estimation of the main parameters used by the state DOTs to design snow fences at a given site. The availability of such information from CRP measurements should provide critical data for the evaluation of the performance of a certain snow fence design that is tested by the IDOT. As part of the present study, the novel CRP method is tested at several sites. The present study also discusses some attempts and preliminary work to determine the snow relocation coefficient which is one of the main variables that has to be estimated by IDOT engineers when using the standard snow fence design software (Snow Drift Profiler, Tabler, 2006). Our analysis showed that standard empirical formulas did not produce reasonable values when applied at the Iowa test sites monitored as part of the present study and that simple methods to estimate this variable are not reliable. The present study makes recommendations for the development of a new methodology based on Large Scale Particle Image Velocimetry that can directly measure the snow drift fluxes and the amount of snow relocated by the fence.
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Contrast enhancement is an image processing technique where the objective is to preprocess the image so that relevant information can be either seen or further processed more reliably. These techniques are typically applied when the image itself or the device used for image reproduction provides poor visibility and distinguishability of different regions of interest inthe image. In most studies, the emphasis is on the visualization of image data,but this human observer biased goal often results to images which are not optimal for automated processing. The main contribution of this study is to express the contrast enhancement as a mapping from N-channel image data to 1-channel gray-level image, and to devise a projection method which results to an image with minimal error to the correct contrast image. The projection, the minimum-error contrast image, possess the optimal contrast between the regions of interest in the image. The method is based on estimation of the probability density distributions of the region values, and it employs Bayesian inference to establish the minimum error projection.
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Atherosclerosis is a chronic cardiovascular disease that involves the thicken¬ing of the artery walls as well as the formation of plaques (lesions) causing the narrowing of the lumens, in vessels such as the aorta, the coronary and the carotid arteries. Magnetic resonance imaging (MRI) is a promising modality for the assessment of atherosclerosis, as it is a non-invasive and patient-friendly procedure that does not use ionizing radiation. MRI offers high soft tissue con¬trast already without the need of intravenous contrast media; while modifica¬tion of the MR pulse sequences allows for further adjustment of the contrast for specific diagnostic needs. As such, MRI can create angiographic images of the vessel lumens to assess stenoses at the late stage of the disease, as well as blood flow-suppressed images for the early investigation of the vessel wall and the characterization of the atherosclerotic plaques. However, despite the great technical progress that occurred over the past two decades, MRI is intrinsically a low sensitive technique and some limitations still exist in terms of accuracy and performance. A major challenge for coronary artery imaging is respiratory motion. State- of-the-art diaphragmatic navigators rely on an indirect measure of motion, per¬form a ID correction, and have long and unpredictable scan time. In response, self-navigation (SM) strategies have recently been introduced that offer 100% scan efficiency and increased ease of use. SN detects respiratory motion di¬rectly from the image data obtained at the level of the heart, and retrospectively corrects the same data before final image reconstruction. Thus, SN holds po-tential for multi-dimensional motion compensation. To this regard, this thesis presents novel SN methods that estimate 2D and 3D motion parameters from aliased sub-images that are obtained from the same raw data composing the final image. Combination of all corrected sub-images produces a final image with reduced motion artifacts for the visualization of the coronaries. The first study (section 2.2, 2D Self-Navigation with Compressed Sensing) consists of a method for 2D translational motion compensation. Here, the use of com- pressed sensing (CS) reconstruction is proposed and investigated to support motion detection by reducing aliasing artifacts. In healthy human subjects, CS demonstrated an improvement in motion detection accuracy with simula¬tions on in vivo data, while improved coronary artery visualization was demon¬strated on in vivo free-breathing acquisitions. However, the motion of the heart induced by respiration has been shown to occur in three dimensions and to be more complex than a simple translation. Therefore, the second study (section 2.3,3D Self-Navigation) consists of a method for 3D affine motion correction rather than 2D only. Here, different techniques were adopted to reduce background signal contribution in respiratory motion tracking, as this can be adversely affected by the static tissue that surrounds the heart. The proposed method demonstrated to improve conspicuity and vi¬sualization of coronary arteries in healthy and cardiovascular disease patient cohorts in comparison to a conventional ID SN method. In the third study (section 2.4, 3D Self-Navigation with Compressed Sensing), the same tracking methods were used to obtain sub-images sorted according to the respiratory position. Then, instead of motion correction, a compressed sensing reconstruction was performed on all sorted sub-image data. This process ex¬ploits the consistency of the sorted data to reduce aliasing artifacts such that the sub-image corresponding to the end-expiratory phase can directly be used to visualize the coronaries. In a healthy volunteer cohort, this strategy improved conspicuity and visualization of the coronary arteries when compared to a con¬ventional ID SN method. For the visualization of the vessel wall and atherosclerotic plaques, the state- of-the-art dual inversion recovery (DIR) technique is able to suppress the signal coming from flowing blood and provide positive wall-lumen contrast. How¬ever, optimal contrast may be difficult to obtain and is subject to RR variability. Furthermore, DIR imaging is time-inefficient and multislice acquisitions may lead to prolonged scanning times. In response and as a fourth study of this thesis (chapter 3, Vessel Wall MRI of the Carotid Arteries), a phase-sensitive DIR method has been implemented and tested in the carotid arteries of a healthy volunteer cohort. By exploiting the phase information of images acquired after DIR, the proposed phase-sensitive method enhances wall-lumen contrast while widens the window of opportunity for image acquisition. As a result, a 3-fold increase in volumetric coverage is obtained at no extra cost in scanning time, while image quality is improved. In conclusion, this thesis presented novel methods to address some of the main challenges for MRI of atherosclerosis: the suppression of motion and flow artifacts for improved visualization of vessel lumens, walls and plaques. Such methods showed to significantly improve image quality in human healthy sub¬jects, as well as scan efficiency and ease-of-use of MRI. Extensive validation is now warranted in patient populations to ascertain their diagnostic perfor¬mance. Eventually, these methods may bring the use of atherosclerosis MRI closer to the clinical practice. Résumé L'athérosclérose est une maladie cardiovasculaire chronique qui implique le épaississement de la paroi des artères, ainsi que la formation de plaques (lé¬sions) provoquant le rétrécissement des lumières, dans des vaisseaux tels que l'aorte, les coronaires et les artères carotides. L'imagerie par résonance magné¬tique (IRM) est une modalité prometteuse pour l'évaluation de l'athérosclérose, car il s'agit d'une procédure non-invasive et conviviale pour les patients, qui n'utilise pas des rayonnements ionisants. L'IRM offre un contraste des tissus mous très élevé sans avoir besoin de médias de contraste intraveineux, tan¬dis que la modification des séquences d'impulsions de RM permet en outre le réglage du contraste pour des besoins diagnostiques spécifiques. À ce titre, l'IRM peut créer des images angiographiques des lumières des vaisseaux pour évaluer les sténoses à la fin du stade de la maladie, ainsi que des images avec suppression du flux sanguin pour une première enquête des parois des vais¬seaux et une caractérisation des plaques d'athérosclérose. Cependant, malgré les grands progrès techniques qui ont eu lieu au cours des deux dernières dé¬cennies, l'IRM est une technique peu sensible et certaines limitations existent encore en termes de précision et de performance. Un des principaux défis pour l'imagerie de l'artère coronaire est le mou¬vement respiratoire. Les navigateurs diaphragmatiques de pointe comptent sur une mesure indirecte de mouvement, effectuent une correction 1D, et ont un temps d'acquisition long et imprévisible. En réponse, les stratégies d'auto- navigation (self-navigation: SN) ont été introduites récemment et offrent 100% d'efficacité d'acquisition et une meilleure facilité d'utilisation. Les SN détectent le mouvement respiratoire directement à partir des données brutes de l'image obtenue au niveau du coeur, et rétrospectivement corrigent ces mêmes données avant la reconstruction finale de l'image. Ainsi, les SN détiennent un poten¬tiel pour une compensation multidimensionnelle du mouvement. A cet égard, cette thèse présente de nouvelles méthodes SN qui estiment les paramètres de mouvement 2D et 3D à partir de sous-images qui sont obtenues à partir des mêmes données brutes qui composent l'image finale. La combinaison de toutes les sous-images corrigées produit une image finale pour la visualisation des coronaires ou les artefacts du mouvement sont réduits. La première étude (section 2.2,2D Self-Navigation with Compressed Sensing) traite d'une méthode pour une compensation 2D de mouvement de translation. Ici, on étudie l'utilisation de la reconstruction d'acquisition comprimée (compressed sensing: CS) pour soutenir la détection de mouvement en réduisant les artefacts de sous-échantillonnage. Chez des sujets humains sains, CS a démontré une amélioration de la précision de la détection de mouvement avec des simula¬tions sur des données in vivo, tandis que la visualisation de l'artère coronaire sur des acquisitions de respiration libre in vivo a aussi été améliorée. Pourtant, le mouvement du coeur induite par la respiration se produit en trois dimensions et il est plus complexe qu'un simple déplacement. Par conséquent, la deuxième étude (section 2.3, 3D Self-Navigation) traite d'une méthode de cor¬rection du mouvement 3D plutôt que 2D uniquement. Ici, différentes tech¬niques ont été adoptées pour réduire la contribution du signal du fond dans le suivi de mouvement respiratoire, qui peut être influencé négativement par le tissu statique qui entoure le coeur. La méthode proposée a démontré une amélioration, par rapport à la procédure classique SN de correction 1D, de la visualisation des artères coronaires dans le groupe de sujets sains et des pa¬tients avec maladies cardio-vasculaires. Dans la troisième étude (section 2.4,3D Self-Navigation with Compressed Sensing), les mêmes méthodes de suivi ont été utilisées pour obtenir des sous-images triées selon la position respiratoire. Au lieu de la correction du mouvement, une reconstruction de CS a été réalisée sur toutes les sous-images triées. Cette procédure exploite la cohérence des données pour réduire les artefacts de sous- échantillonnage de telle sorte que la sous-image correspondant à la phase de fin d'expiration peut directement être utilisée pour visualiser les coronaires. Dans un échantillon de volontaires en bonne santé, cette stratégie a amélioré la netteté et la visualisation des artères coronaires par rapport à une méthode classique SN ID. Pour la visualisation des parois des vaisseaux et de plaques d'athérosclérose, la technique de pointe avec double récupération d'inversion (DIR) est capa¬ble de supprimer le signal provenant du sang et de fournir un contraste posi¬tif entre la paroi et la lumière. Pourtant, il est difficile d'obtenir un contraste optimal car cela est soumis à la variabilité du rythme cardiaque. Par ailleurs, l'imagerie DIR est inefficace du point de vue du temps et les acquisitions "mul- tislice" peuvent conduire à des temps de scan prolongés. En réponse à ce prob¬lème et comme quatrième étude de cette thèse (chapitre 3, Vessel Wall MRI of the Carotid Arteries), une méthode de DIR phase-sensitive a été implémenté et testé
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Steganography is an information hiding application which aims tohide secret data imperceptibly into a cover object. In this paper, we describe anovel coding method based on Z2Z4-additive codes in which data is embeddedby distorting each cover symbol by one unit at most (+-1-steganography). Thismethod is optimal and solves the problem encountered by the most e cientmethods known today, concerning the treatment of boundary values. Theperformance of this new technique is compared with that of the mentionedmethods and with the well-known rate-distortion upper bound to conclude thata higher payload can be obtained for a given distortion by using the proposedmethod.