Jicun Hu

Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data

This paper proposes a new row-action type iterative algorithm which is appropriate to reconstruct sparse objects from a limited number of projections. The main idea is to use the L/sub 1/ norm to pick up a sparse solution from a set of feasible solutions to the measurement equation. By perturbing the linear program to a quadratic program, we use the duality of nonlinear programming to construct a row-action type iterative algorithm to find the solution. We also prove that the algorithm converges to the solution under mild assumptions. We show that this method works well in the 3-D blood-vessel reconstruction and its computation time is shorter than those of our previous method and MART method. Furthermore, we apply the method to real data measured with the Micro-CT device developed at Marquette University.

An approximate short scan helical FDK cone beam algorithm based on nutating curved surfaces satisfying the Tuy’s condition

Traditionally, short scan helical FDK algorithms have been implemented based on horizontal transaxial slices. However, not every point on the horizontal transaxial slice satisfies Tuys condition for the corresponding (pi+fan angle) segment of helix, which means that some points on the horizontal slices are incompletely sampled and are impossible to be exactly reconstructed. In this paper, we propose and implement an improved but still approximate short scan helical cone beam FDK algorithm based on nutating curved surfaces satisfying the Tuys condition. This surface is defined by averaging PI surfaces emanating the initial and final source points of a (pi+fan angle) segment of helix. One of the key characteristics of the surface is that every point on it satisfies the Tuys condition for the corresponding (pi+fan angle) segment of helix, which means that we can potentially reconstruct every point on the surface exactly. This difference makes the proposed algorithm deliver a better-reconstructed image quality while requiring a smaller detector area than that of traditional FDK methods based on horizontal transaxial slices. Another characteristic of the proposed surface is that every point within the helix belongs to one and only one such surface. Therefore, the location of the short scan segment for the reconstruction of a point in Cartesian coordinate could be precalculated and stored in a look-up table. This enables us to perform reconstruction directly on rectangular grids. We compare the performance of the improved FDK algorithm with that of a quasi-exact algorithm based on data combination technique. The simulation results show that the reconstructed image quality of these two methods is similar.

Dynamic molecular imaging of cardiac innervation using a dual headpinhole SPECT system

Typically 123I-MIBG is used for the study of innervation and function of the sympathetic nervous system in heart failure. The protocol involves two studies: first a planar or SPECT scan is performed to measure initial uptake of the tracer, followed some 3-4 hours later by another study measuring the wash-out of the tracer from the heart. A fast wash-out is indicative of a compromised heart. In this work, a dual head pinhole SPECT system was used for imaging the distribution and kinetics of 123I-MIBG in the myocardium of spontaneous hypertensive rats (SHR) and normotensive Wistar Kyoto (WKY) rats. The system geometry was calibrated based on a nonlinear point projection fitting method using a three-point source phantom. The angle variation effect of the parameters was modeled with a sinusoidal function. A dynamic acquisition was performed by injecting 123I-MIBG into rats immediately after starting the data acquisition. The detectors rotated continuously performing a 360o data acquisition every 90 seconds. We applied the factor analysis (FA)method and region of interest (ROI) sampling method to obtain time activity curves (TACs)in the blood pool and myocardium and then applied two-compartment modeling to estimate the kinetic parameters. Since the initial injection bolus is too fast for obtaining a consistent tomographic data set in the first few minutes of the study, we applied the FA method directly to projections during the first rotation. Then the time active curves for blood and myocardial tissue were obtained from ROI sampling. The method was applied to determine if there were differences in the kinetics between SHR and WKY rats and requires less time by replacing the delayed scan at 3-4 hours after injection with a dynamic acquisition over 90 to 120 minutes. The results of a faster washout and a smaller distribution volume of 123IMIBG near the end of life in the SHR model of hypertrophic cardiomyopthy may be indicative of a failing heart in late stages of heart failure.

Characterization of a PET camera optimized for prostate imaging

We present the characterization of a positron emission tomograph for prostate imaging that centers a patient between a pair of external curved detector banks (ellipse: 45 cm minor, 70 cm major axis). The distance between detector banks adjusts to allow patient access and to position the detectors as closely as possible for maximum sensitivity with patients of various sizes. Each bank is composed of two axial rows of 20 HR+ block detectors for a total of 80 detectors in the camera. The individual detectors are angled in the transaxial plane to point towards the prostate to reduce resolution degradation in that region. The detectors are read out by modified HRRT data acquisition electronics. Compared to a standard whole-body PET camera, our dedicated-prostate camera has the same sensitivity and resolution, less background (less randoms and lower scatter fraction) and a lower cost. We have completed construction of the camera. Characterization data and reconstructed images of several phantoms are shown. Sensitivity of a point source in the center is 946 cps/muCi. Spatial resolution is 4 mm FWHM in the central region

A new approach of dynamic pinhole SPECT imaging for evaluation of sympathetic nervous system function in animal models of cardiac hypertrophy

Typically 123I-MIBG is used for the study of innervation and function of the sympathetic nervous system in heart failure. The protocol involves two studies: first a planar or SPECT scan is performed to measure initial uptake of the tracer, followed some 3-4 hours later by another study measuring the wash-out of the tracer from the heart. A fast wash-out is indicative of a compromised heart. In this work, a dual head pinhole SPECT system was used for imaging the distribution and kinetics of 123I-MIBG in the myocardium of spontaneous hypertensive rats (SHR) and normotensive Wistar Kyoto (WKY) rats. The system geometry was calibrated based on a nonlinear point projection fitting method using a three-point source phantom. The angle variation effect of the parameters was modeled with a sinusoidal function. A dynamic acquisition was performed by injecting 123I-MIBG into rats immediately after starting the data acquisition. The detectors rotated continuously traversing 360deg every 90 seconds. We applied the FADS method to obtain time activity curves in the blood pool and myocardium. Since the initial injection bolus is too fast to obtain a consistent tomographic data set in the first minute of the study, we applied the FADS method directly to projections during the first rotation. In the future, the method will be applied to determine if there are differences in the kinetics between SHR and WKY rats. This approach requires less time by replacing the delayed scan at 3-4 hours after injection with a dynamic acquisition of 90 to 120 minutes

Sparse object reconstruction from a limited number of projections using the linear programming

This paper proposes a simple row-action type iterative algorithm which is appropriate to reconstruct sparse objects from a limited number of projections. The main idea is to use the L/sub 1/ norm to pick up a sparse solution from a set of feasible solutions to the measurement equation. By perturbing the linear program to a quadratic program, we use the duality of the nonlinear programming to construct a row-action type iterative algorithm to find a solution, we also prove that the algorithm converges for any initial image. We show that this method works well in the 3D blood-vessel reconstruction and its computation time is shorter compared to our previous method.

A short scan helical FDK cone beam algorithm based on surfaces satisfying the Tuy's condition

FDK method is the most popular cone beam algorithm to date. Traditionally, short scan helical FDK algorithms have been implemented based on horizontal transaxial slices. However, not even, point on the horizontal transaxial slice satisfies Tuys condition for the corresponding (pi+fan angle) segment of helix, which means that some points on the horizontal slices are incompletely sampled and are impossible to be exactly reconstructed In this paper, we propose and implement an improved short scan helical cone beam FDK algorithm based on nutating curved surfaces satisfying the Tuys condition. This surface is defined by averaging PI surfaces emanating the initial and final source points of a (pi+fan angle) segment of helix. One of the key characteristics of the surface is that every point on it satisfies the Tuys condition for the corresponding (pi+fan angle) segment of helix, which means that we can potentially reconstruct every point on the surface exactly. This difference makes the proposed algorithm deliver a better-reconstructed image quality while requiring a smaller detector area than that of traditional FDK methods based on horizontal transaxial slices. Another characteristics of the proposed surface is that every point in the object space belongs to one and only one such surface. Therefore, the location of the short scan segment for reconstruction of a point in Cartesian coordinate can be pre-calculated and stored in a look up table. This enables us to perform reconstruction directly on rectangular grids. We compare the performance of the improved FDK algorithm with that of a quasi-exact algorithm based on data combination technique. The simulation results show that the reconstructed image quality of these two methods is about the same. We also provide a qualitative analysis of the link between the improved FDK and exact methods. The computational requirement of the proposed algorithm is the same as that of the traditional FDK method. We validate the proposed algorithm with a disc phantom