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BACKGROUND. Estimation of fractional flow reserve from coronary CTA (FFR-CT) is an established method of assessing the hemodynamic significance of coronary lesions. However, clinical implementation has progressed slowly, partly because of off-site data transfer with long turnaround times for results. OBJECTIVE. The purpose of this study was to evaluate the diagnostic performance of FFR-CT computed on-site with a high-speed deep learning-based algorithm with invasive hemodynamic indexes as the reference standard. METHODS. This retrospective study included 59 patients (46 men, 13 women; mean age, 66.5 ± 10.2 years) who underwent coronary CTA (including calcium scoring) followed within 90 days by invasive angiography with invasive fractional flow reserve (FFR) and/or instantaneous wave-free ratio measurements from December 2014 to October 2021. Coronary artery lesions were considered to have hemodynamically significant stenosis in the presence of invasive FFR of 0.80 or less and/or instantaneous wave-free ratio of 0.89 or less. A single cardiologist evaluated the CTA images using an on-site deep learning-based semiautomated algorithm entailing a 3D computational flow dynamics model to determine FFR-CT for coronary artery lesions detected with invasive angiography. Time for FFR-CT analysis was recorded. FFR-CT analysis was repeated by the same cardiologist in 26 randomly selected examinations and by a different cardiologist in 45 randomly selected examinations. Diagnostic performance and agreement were assessed. RESULTS. A total of 74 lesions were identified with invasive angiography. FFR-CT and invasive FFR had strong correlation (r = 0.81) and, in Bland-Altman analysis, bias of 0.01 and 95% limits of agreement of -0.13 to 0.15. FFR-CT had AUC for hemodynamically significant stenosis of 0.975. At a cutoff of 0.80 or less, FFR-CT had 95.9% accuracy, 93.5% sensitivity, and 97.7% specificity. In 39 lesions with severe calcifications (≥ 400 Agatston units), FFR-CT had AUC of 0.991 and at a cutoff of 0.80, 94.7% sensitivity, 95.0% specificity, and 94.9% accuracy. Mean analysis time per patient was 7 minutes 54 seconds. Intraobserver agreement (intraclass correlation coefficient, 0.85; bias, -0.01; 95% limits of agreement, -0.12 and 0.10) and interobserver agreement (intraclass correlation coefficient, 0.94; bias, -0.01; 95% limits of agreement, -0.08 and 0.07) were good to excellent. CONCLUSION. A high-speed on-site deep learning-based FFR-CT algorithm had excellent diagnostic performance for hemodynamically significant stenosis with high reproducibility. CLINICAL IMPACT. The algorithm should facilitate implementation of FFR-CT technology into routine clinical practice.
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Enfermedad de la Arteria Coronaria , Estenosis Coronaria , Aprendizaje Profundo , Reserva del Flujo Fraccional Miocárdico , Masculino , Humanos , Femenino , Persona de Mediana Edad , Anciano , Enfermedad de la Arteria Coronaria/diagnóstico por imagen , Angiografía Coronaria/métodos , Estudios Retrospectivos , Constricción Patológica , Reproducibilidad de los Resultados , Angiografía por Tomografía Computarizada/métodos , Valor Predictivo de las Pruebas , Algoritmos , Estándares de ReferenciaRESUMEN
It is well known that CT projections are redundant. Over the past decades, significant efforts have been devoted to characterize the data redundancy in different aspects. Very recently, Clackdoyle and Desbat reported a new integral-type data consistency condition (DCC) for truncated 2D parallel-beam projections, which can be applied to a region inside a field of view (FOV) but outside of the convex hull of the compact support of an object. Inspired by their work, here we derive a more general condition for 2D fan-beam geometry with a general scanning trajectory. This extended DCC is verified with simulated projections of the Shepp-Logan phantom and a clinically collected sinogram. Then, we demonstrate an application of the proposed DCC.
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Procesamiento de Imagen Asistido por Computador/métodos , Tomografía Computarizada por Rayos X/métodos , Artefactos , Simulación por Computador , Humanos , Fantasmas de ImagenRESUMEN
BACKGROUND: Four-dimensional (4D) wide coverage computed tomography (CT) is an effective imaging modality for measuring the mechanical function of the myocardium. However, repeated CT measurement across a number of heartbeats is still a concern. PURPOSE: A projection-domain noise emulation method is presented to generate accurate low-dose (mA modulated) 4D cardiac CT scans from high-dose scans, enabling protocol optimization to deliver sufficient image quality for functional cardiac analysis while using a dose level that is as low as reasonably achievable (ALARA). METHODS: Given a targeted low-dose mA modulation curve, the proposed noise emulation method injects both quantum and electronic noise of proper magnitude and correlation to the high-dose data in projection domain. A spatially varying (i.e., channel-dependent) detector gain term as well as its calibration method were proposed to further improve the noise emulation accuracy. To determine the ALARA dose threshold, a straightforward projection domain image quality (IQ) metric was proposed that is based on the number of projection rays that do not fall under the non-linear region of the detector response. Experiments were performed to validate the noise emulation method with both phantom and clinical data in terms of visual similarity, contrast-to-noise ratio (CNR), and noise-power spectrum (NPS). RESULTS: For both phantom and clinical data, the low-dose emulated images exhibited similar noise magnitude (CNR difference within 2%), artifacts, and texture to that of the real low-dose images. The proposed channel-dependent detector gain term resulted in additional increase in emulation accuracy. Using the proposed IQ metric, recommended kVp and mA settings were calculated for low dose 4D Cardiac CT acquisitions for patients of different sizes. CONCLUSIONS: A detailed method to estimate system-dependent parameters for a raw-data based low dose emulation framework was described. The method produced realistic noise levels, artifacts, and texture with phantom and clinical studies. The proposed low-dose emulation method can be used to prospectively select patient-specific minimal-dose protocols for functional cardiac CT.
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Corazón , Fantasmas de Imagen , Dosis de Radiación , Relación Señal-Ruido , Humanos , Corazón/diagnóstico por imagen , Tomografía Computarizada Cuatridimensional/métodos , Procesamiento de Imagen Asistido por Computador/métodosRESUMEN
BACKGROUND: Lead placement at the latest mechanically activated left ventricle (LV) segments is strongly correlated with response to cardiac resynchronization therapy (CRT). We demonstrate the feasibility of a cardiac 4DCT motion correction algorithm (ResyncCT) in estimating LV mechanical activation for guiding lead placement in CRT. METHODS: Subjects with full cardiac cycle 4DCT images acquired using a wide-detector CT scanner for CRT planning/upgrade were included. 4DCT images exhibited motion artifact-induced false-dyssynchrony, hindering LV mechanical activation time estimation. Motion-corrupted images were processed with ResyncCT to yield motion-corrected images. Time to onset of shortening (TOS) was estimated in each of 72 endocardial segments. A false-dyssynchrony index (FDI) was used to quantify the extent of motion artifacts in the uncorrected and the ResyncCT images. After motion correction, the change in classification of LV free-wall segments as optimal target sites for lead placement was investigated. RESULTS: Twenty subjects (70.7 â± â13.9 years, 6 female) were analyzed. Motion artifacts in the ResyncCT-processed images were significantly reduced (FDI: 28.9 â± â9.3 â% vs 47.0 â± â6.0 â%, p â< â0.001). In 10 (50 â%) subjects, ResyncCT motion correction yielded statistically different TOS estimates (p â< â0.05). Additionally, 43 â% of LV free-wall segments were reclassified as optimal target sites for lead placement after motion correction. CONCLUSIONS: ResyncCT significantly reduced motion artifacts in wide-detector cardiac 4DCT images, yielded statistically different time to onset of shortening estimates, and changed the location of optimal target sites for lead placement. These results highlight the potential utility of ResyncCT motion correction in CRT planning when using wide-detector 4DCT imaging.
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Terapia de Resincronización Cardíaca , Insuficiencia Cardíaca , Humanos , Femenino , Terapia de Resincronización Cardíaca/métodos , Insuficiencia Cardíaca/terapia , Valor Predictivo de las Pruebas , Corazón , Ventrículos Cardíacos/diagnóstico por imagen , Resultado del TratamientoRESUMEN
Background: Four-dimensional (4D) wide coverage computed tomography (CT) is an effective imaging modality for measuring the mechanical function of the myocardium. However, repeated CT measurement across a number of heartbeats is still a concern. Purpose: A projection-domain noise emulation method is presented to generate accurate low-dose (mA modulated) 4D cardiac CT scans from high-dose scans, enabling protocol optimization to deliver sufficient image quality for functional cardiac analysis while using a dose level that is as low as reasonably achievable (ALARA). Methods: Given a targeted low-dose mA modulation curve, the proposed noise emulation method injects both quantum and electronic noise of proper magnitude and correlation to the high-dose data in projection domain. A spatially varying (i.e., channel-dependent) detector gain term as well as its calibration method were proposed to further improve the noise emulation accuracy. To determine the ALARA dose threshold, a straightforward projection domain image quality (IQ) metric was proposed that is based on the number of projection rays that do not fall under the non-linear region of the detector response. Experiments were performed to validate the noise emulation method with both phantom and clinical data in terms of visual similarity, contrast-to-noise ratio (CNR), and noise-power spectrum (NPS). Results: For both phantom and clinical data, the low-dose emulated images exhibited similar noise magnitude (CNR difference within 2%), artifacts, and texture to that of the real low-dose images. The proposed channel-dependent detector gain term resulted in additional increase in emulation accuracy. Using the proposed IQ metric, recommended kVp and mA settings were calculated for low dose 4D Cardiac CT acquisitions for patients of different sizes. Conclusions: A detailed method to estimate system-dependent parameters for a raw-data based low dose emulation framework was described. The method produced realistic noise levels, artifacts, and texture with phantom and clinical studies. The proposed low-dose emulation method can be used to prospectively select patient-specific minimal-dose protocols for functional cardiac CT.
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BACKGROUND: The absence of coronary artery calcium (CAC) measured via CT is associated with very favorable prognosis, and current guidelines recommend low-density lipoprotein cholesterol (LDL-c) lowering therapy for individuals with any CAC. This motivates early detection of small granules of CAC; however, calcium scan sensitivity for detecting very low levels of calcium has not been quantified. PURPOSE: In this work, the size limit of detectability of small calcium hydroxyapatite (CaHA) granules with clinical CAC scanning was assessed using validated simulations. METHODS: CT projections of digital 3D mathematical phantoms containing small CaHA granules were simulated analytically; images were reconstructed using a filter designed to reproduce the point spread function of a specific commercial scanner, and a relationship of HU number versus diameter was derived. These simulation results were validated with experimental measurements of HU versus diameter from phantoms containing small granules of CaHA on a GE Revolution CT scanner in the clinic; ground truth measurements of the CaHA granule diameters were obtained using a Zeiss Xradia 510 Versa high-resolution 3D micro-CT imaging system. Using experimental measurements on the clinical CT scanner, detectability was quantified with a detectability index (d') using a non-prewhitened matched filter. The effect of changes to reconstruction slice thickness and reconstruction kernel on granule detectability was evaluated. RESULTS: Under typical clinical calcium scanning and reconstruction conditions, the minimum detectable diameter of a simulated spherical calcium granule with a clinically relevant CaHA density was 0.76 mm. The minimum detectable volume was 2.4 times smaller on images reconstructed at a slice thickness of 0.625 mm compared to 2.5 mm. The detectability index d' increased by a factor of 1.7 when images were reconstructed with 0.625 mm slices compared to 2.5 mm slices. d' did not change when images were reconstructed with the high-resolution BONE filter compared to the less sharp STANDARD resolution filter on the GE Revolution CT. CONCLUSIONS: We have quantified detectability versus size of small calcium granules at the resolution limit of a widely available clinical CT scanner. Detectability increased significantly with reduced slice thickness and did not change with a sharper reconstruction kernel. The simulation can be used to calculate the trade-off between dose and CAC detectability.
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PURPOSE: X-ray computed tomography angiography (CTA) is the modality of choice to noninvasively monitor and diagnose heart disease with coronary artery health and stenosis detection being of particular interest. Reliable, clinically relevant coronary artery imaging mandates high spatiotemporal resolution. However, advances in intrinsic scanner spatial resolution (CT scanners are available which combine nearly 900 detector columns with focal spot oversampling) can be tempered by motion blurring, particularly in patients with unstable heartbeats. As a result, recently numerous methods have been devised to improve coronary CTA imaging. Solutions involving hardware, multisector algorithms, or ß-blockers are limited by cost, oversimplifying assumptions about cardiac motion, and populations showing contraindications to drugs, respectively. This work introduces an inexpensive algorithmic solution that retrospectively improves the temporal resolution of coronary CTA without significantly affecting spatial resolution. METHODS: Given the goal of ruling out coronary stenosis, the method focuses on "deblurring" the coronary arteries. The approach makes no assumptions about cardiac motion, can be used on exams acquired at high heart rates (even over 75 beats/min), and draws on a fast and accurate three-dimensional (3D) nonrigid bidirectional labeled point matching approach to estimate the trajectories of the coronary arteries during image acquisition. Motion compensation is achieved by employing a 3D warping of a series of partial reconstructions based on the estimated motion fields. Each of these partial reconstructions is created from data acquired over a short time interval. For brevity, the algorithm "Subphasic Warp and Add" (SWA) reconstruction. RESULTS: The performance of the new motion estimation-compensation approach was evaluated by a systematic observer study conducted using nine human cardiac CTA exams acquired over a range of average heart rates between 68 and 86 beats/min. Algorithm performance was based-lined against exams reconstructed using standard filtered-backprojection (FBP). The study was performed by three experienced reviewers using the American Heart Association's 15-segment model. All vessel segments were evaluated to quantify their viability to allow a clinical diagnosis before and after motion estimation-compensation using SWA. To the best of the authors' knowledge this is the first such observer study to show that an image processing-based software approach can improve the clinical diagnostic value of CTA for coronary artery evaluation. CONCLUSIONS: Results from the observer study show that the SWA method described here can dramatically reduce coronary artery motion and preserve real pathology, without affecting spatial resolution. In particular, the method successfully mitigated motion artifacts in 75% of all initially nondiagnostic coronary artery segments, and in over 45% of the cases this improvement was enough to make a previously nondiagnostic vessel segment clinically diagnostic.
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Algoritmos , Artefactos , Angiografía Coronaria/métodos , Imagenología Tridimensional/métodos , Reconocimiento de Normas Patrones Automatizadas/métodos , Intensificación de Imagen Radiográfica/métodos , Interpretación de Imagen Radiográfica Asistida por Computador/métodos , Tomografía Computarizada por Rayos X/métodos , Angiografía Coronaria/instrumentación , Humanos , Movimiento (Física) , Fantasmas de Imagen , Reproducibilidad de los Resultados , Sensibilidad y Especificidad , Tomografía Computarizada por Rayos X/instrumentaciónRESUMEN
PURPOSE: We demonstrate the viability of a four-dimensional X-ray computed tomography (4DCT) imaging system to accurately and precisely estimate mechanical activation times of left ventricular (LV) wall motion. Accurate and reproducible timing estimates of LV wall motion may be beneficial in the successful planning and management of cardiac resynchronization therapy (CRT). METHODS: We developed an anthropomorphically accurate in silico LV phantom based on human CT images with programmed septal-lateral wall dyssynchrony. Twenty-six temporal phases of the in silico phantom were used to sample the cardiac cycle of 1 s. For each of the 26 phases, 1 cm thick axial slabs emulating axial CT image volumes were extracted, 3D printed, and imaged using a commercially available CT scanner. A continuous dynamic sinogram was synthesized by blending sinograms from these static phases; the synthesized sinogram emulated the sinogram that would be acquired under true continuous phantom motion. Using the synthesized dynamic sinogram, images were reconstructed at 70 ms intervals spanning the full cardiac cycle; these images exhibited expected motion artifact characteristics seen in images reconstructed from real dynamic data. The motion corrupted images were then processed with a novel motion correction algorithm (ResyncCT) to yield motion corrected images. Five pairs of motion uncorrected and motion corrected images were generated, each corresponding to a different starting gantry angle (0 to 180 degrees in 45 degree increments). Two line profiles perpendicular to the endocardial surface were used to sample local myocardial motion trajectories at the septum and the lateral wall. The mechanical activation time of wall motion was defined as the time at which the endocardial boundary crossed a fixed position defined on either of the two line profiles while moving toward the center of the LV during systolic contraction. The mechanical activation times of these myocardial trajectories estimated from the motion uncorrected and the motion corrected images were then compared with those derived from the static images of the 3D printed phantoms (ground truth). The precision of the timing estimates was obtained from the five different starting gantry angle simulations. RESULTS: The range of estimated mechanical activation times observed across all starting gantry angles was significantly larger for the motion uncorrected images than for the motion corrected images (lateral wall: 58 ± 15 ms vs 12 ± 4 ms, p < 0.005; septal wall: 61 ± 13 ms vs 13 ± 9 ms, p < 0.005). CONCLUSIONS: 4DCT images processed with the ResyncCT motion correction algorithm yield estimates of mechanical activation times of LV wall motion with significantly improved accuracy and precision. The promising results reported in this study highlight the potential utility of 4DCT in estimating the timing of mechanical events of interest for CRT guidance.
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Tomografía Computarizada Cuatridimensional , Ventrículos Cardíacos , Artefactos , Tomografía Computarizada Cuatridimensional/métodos , Ventrículos Cardíacos/diagnóstico por imagen , Humanos , Movimiento (Física) , Fantasmas de ImagenRESUMEN
This review paper aims to summarize cardiac CT blooming artifacts, how they present clinically and what their root causes and potential solutions are. A literature survey was performed covering any publications with a specific interest in calcium blooming and stent blooming in cardiac CT. The claims from literature are compared and interpreted, aiming at narrowing down the root causes and most promising solutions for blooming artifacts. More than 30 journal publications were identified with specific relevance to blooming artifacts. The main reported causes of blooming artifacts are the partial volume effect, motion artifacts and beam hardening. The proposed solutions are classified as high-resolution CT hardware, high-resolution CT reconstruction, subtraction techniques and post-processing techniques, with a special emphasis on deep learning (DL) techniques. The partial volume effect is the leading cause of blooming artifacts. The partial volume effect can be minimized by increasing the CT spatial resolution through higher-resolution CT hardware or advanced high-resolution CT reconstruction. In addition, DL techniques have shown great promise to correct for blooming artifacts. A combination of these techniques could avoid repeat scans for subtraction techniques.
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PURPOSE: Standard four-dimensional computed tomography (4DCT) cardiac reconstructions typically include spiraling artifacts that depend not only on the motion of the heart but also on the gantry angle range over which the data was acquired. We seek to reduce these motion artifacts and, thereby, improve the accuracy of left ventricular wall positions in 4DCT image series. METHODS: We use a motion artifact reduction approach (ResyncCT) that is based largely on conjugate pairs of partial angle reconstruction (PAR) images. After identifying the key locations where motion artifacts exist in the uncorrected images, paired subvolumes within the PAR images are analyzed with a modified cross-correlation function in order to estimate 3D velocity and acceleration vectors at these locations. A subsequent motion compensation process (also based on PAR images) includes the creation of a dense motion field, followed by a backproject-and-warp style compensation. The algorithm was tested on a 3D printed phantom, which represents the left ventricle (LV) and on challenging clinical cases corrupted by severe artifacts. RESULTS: The results from our preliminary phantom test as well as from clinical cardiac scans show crisp endocardial edges and resolved double-wall artifacts. When viewed as a temporal series, the corrected images exhibit a much smoother motion of the LV endocardial boundary as compared to the uncorrected images. In addition, quantitative results from our phantom studies show that ResyncCT processing reduces endocardial surface distance errors from 0.9 ± 0.8 to 0.2 ± 0.1 mm. CONCLUSIONS: The ResyncCT algorithm was shown to be effective in reducing motion artifacts and restoring accurate wall positions. Some perspectives on the use of conjugate-PAR images and on techniques for CT motion artifact reduction more generally are also given.
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Artefactos , Tomografía Computarizada Cuatridimensional , Algoritmos , Tomografía Computarizada Cuatridimensional/métodos , Ventrículos Cardíacos/diagnóstico por imagen , Movimiento (Física) , Fantasmas de ImagenRESUMEN
The spatial resolution of diagnostic Computed Tomography (CT) has increased substantially, and 3D isotropic sub-millimeter spatial resolution in both axial and helical scan modes is routinely available in the clinic. However, driven by advanced clinical applications, the pursuit for higher spatial resolution and free of aliasing artifacts in diagnostic CT has never stopped. A method to accommodate focal spot wobbling at an arbitrary number of projection views per gantry rotation in CT is presented and evaluated here. The method employs a beta-correction scheme in the row-wise fan-to-parallel rebinning to transform the native cone beam geometry into the cone-parallel geometry under which existing 3D weighted cone beam filtered backprojection algorithms can be utilized for image reconstruction. The experimental evaluation shows that the row-wise fan-to-parallel rebinning with the beta-correction can increase the quantitative in-plane spatial resolution (Modulation Transfer Function) substantially, while the visual spatial resolution can be enhanced significantly. Consequently, the architectural designers of CT scanners are no longer constrained to choosing the number of projection views per rotation determined by gantry geometry. Instead, they can choose the number of projection views per rotation to optimize the trade-offs between in-plane spatial resolution and noise characteristics. Therefore, the presented method is of practical relevance in the architectural design of state-of-the-art diagnostic CT.
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Algoritmos , Tomografía Computarizada de Haz Cónico/métodos , Procesamiento de Imagen Asistido por Computador/métodos , Artefactos , Fantasmas de Imagen , TungstenoRESUMEN
This paper describes a flexible new methodology for accurate cone beam reconstruction with source positions on a curve (or set of curves). The inversion formulas employed by this methodology are based on first backprojecting a simple derivative in the projection space and then applying a Hilbert transform inversion in the image space. The local nature of the projection space filtering distinguishes this approach from conventional filtered-backprojection methods. This characteristic together with a degree of flexibility in choosing the direction of the Hilbert transform used for inversion offers two important features for the design of data acquisition geometries and reconstruction algorithms. First, the size of the detector necessary to acquire sufficient data for accurate reconstruction of a given region is often smaller than that required by previously documented approaches. In other words, more data truncation is allowed. Second, redundant data can be incorporated for the purpose of noise reduction. The validity of the inversion formulas along with the application of these two properties are illustrated with reconstructions from computer simulated data. In particular, in the helical cone beam geometry, it is shown that 1) intermittent transaxial truncation has no effect on the reconstruction in a central region which means that wider patients can be accommodated on existing scanners, and more importantly that radiation exposure can be reduced for region of interest imaging and 2) at maximum pitch the data outside the Tam-Danielsson window can be used to reduce image noise and thereby improve dose utilization. Furthermore, the degree of axial truncation tolerated by our approach for saddle trajectories is shown to be larger than that of previous methods.
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Algoritmos , Imagenología Tridimensional/métodos , Reconocimiento de Normas Patrones Automatizadas/métodos , Interpretación de Imagen Radiográfica Asistida por Computador/métodos , Tomografía Computarizada Espiral/métodos , Inteligencia Artificial , Análisis por Conglomerados , Cabeza/diagnóstico por imagen , Humanos , Almacenamiento y Recuperación de la Información/métodos , Fantasmas de Imagen , Intensificación de Imagen Radiográfica/métodos , Reproducibilidad de los Resultados , Dispersión de Radiación , Sensibilidad y EspecificidadRESUMEN
The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image. Formulae for performing the DBP step in fanbeam geometry are also presented. The advantage of this two-step Hilbert transform approach is that in certain situations, regions of interest (ROIs) can be reconstructed from truncated projection data. Simulation results are presented that illustrate very similar reconstructed image quality using the new method compared to standard filtered backprojection, and that show the capability to correctly handle truncated projections. In particular, a simulation is presented of a wide patient whose projections are truncated laterally yet for which highly accurate ROI reconstruction is obtained.
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Procesamiento de Imagen Asistido por Computador/métodos , Intensificación de Imagen Radiográfica/métodos , Interpretación de Imagen Radiográfica Asistida por Computador/métodos , Algoritmos , Humanos , Modelos Estadísticos , Modelos Teóricos , Fantasmas de Imagen , Tomografía Computarizada por Rayos X/métodosRESUMEN
This paper investigates cone-beam tomography for a wide class of x-ray source trajectories called saddles. In particular, a mathematical analysis of the number of intersections between a saddle and an arbitrary plane is given. This analysis demonstrates that axially truncated cone-beam projections acquired along a saddle can be used for exact reconstruction at any point in a large volume. The reconstruction can be achieved either using a new algorithm presented herein or using a formula recently introduced by Katsevich (2003 Int. J. Math. Math. Sci. 21 1305-21). The shape of the reconstructed volume and the properties of saddles make saddles attractive for cardiac imaging. Three examples of saddles are presented with a discussion of implementation on devices similar to modern C-arm systems and multislice CT scanners. Reconstruction with one of these saddles has been tested using computer-simulated data, with and without truncation. The imaged phantom for the truncated data is a FORBILD head phantom (representing the heart) that has been modified and embedded inside the FORBILD thorax phantom. The non-truncated data were generated by excluding the thorax. The reconstructed images demonstrate the accuracy of the mathematical results.