Exact iterative reconstruction for the interior problem

Improved Performance of a Multipinhole SPECT for DAT Imaging by Increasing Number of Pinholes at the Expense of Increased Multiplexing

SPECT imaging of dopamine transporters (DAT) in the brain is a widely utilized study to improve the diagnosis of Parkinsonian syndromes, where conventional (parallel-hole and fan-beam) collimators on dual-head scanners are commonly employed. We have designed a multi-pinhole (MPH) collimator to improve the performance of DAT imaging. The MPH collimator focuses on the striatum and hence offers a better trade-off for sensitivity and spatial resolution than the conventional collimators within this clinically most relevant region for DAT imaging. Our original MPH design consisted of 9 pinholes with a background-to-striatal (Bkg/Str) projection multiplexing of 1% only. In this simulation study, we investigated whether further improvements in the performance of MPH imaging could be obtained by increasing the number of pinholes, hence by enhancing the sensitivity and sampling, despite the ambiguity in reconstructing images due to increased multiplexing. We performed analytic simulations of the MPH configurations with 9, 13, and 16 pinholes (aperture diameters: 4-6mm) using a digital phantom modeling DAT imaging. Our quantitative analyses indicated that using 13 (Bkg/Str: 12%) and 16 (Bkg/Str: 22%) pinholes provided better performance than the original 9-pinhole configuration for the acquisition with 2 or 4 angular views, but a similar performance with 8 and 16 views.

The impact of system matrix dimension on small FOV SPECT reconstruction with truncated projections

PURPOSE

A dedicated cardiac hybrid single photon emission computed tomography (SPECT)/CT scanner that uses cadmium zinc telluride detectors and multiple pinhole collimators for stationary acquisition offers many advantages. However, the impact of the reconstruction system matrix (SM) dimension on the reconstructed image quality from truncated projections and 19 angular samples acquired on this scanner has not been extensively investigated. In this study, the authors aimed to investigate the impact of the dimensions of SM and the use of body contour derived from adjunctive CT imaging as an object support in reconstruction on this scanner, in relation to background extracardiac activity.

METHODS

The authors first simulated a generic SPECT/CT system to image four NCAT phantoms with various levels of extracardiac activity and compared the reconstructions using SM in different dimensions and with/without body contour as a support for quantitative evaluations. The authors then compared the reconstructions of 18 patient studies, which were acquired on a GE Discovery NM570c scanner following injection of different radiotracers, including (99m)Tc-Tetrofosmin and (123)I-mIBG, comparing the scanner's default SM that incompletely covers the body with a large SM that incorporates a patient specific full body contour.

RESULTS

The simulation studies showed that the reconstructions using a SM that only partially covers the body yielded artifacts on the edge of the field of view (FOV), overestimation of activity and increased nonuniformity in the blood pool for the phantoms with higher relative levels of extracardiac activity. However, the impact on the quantitative accuracy in the high activity region, such as the myocardium, was subtle. On the other hand, an excessively large SM that enclosed the entire body alleviated the artifacts and reduced overestimation in the blood pool, but yielded slight underestimation in myocardium and defect regions. The reconstruction using the larger SM with body contour yielded the most quantitatively accurate results in all the regions of interest for a range of uptake levels in the extracardiac regions. In patient studies, the SM incorporating patient specific body contour minimized extracardiac artifacts, yielded similar myocardial activity, lower blood pool activity, and subsequently improved myocardium-to-blood pool contrast (p < 0.0001) by an average of 7% (range 0%-18%) across all the patients, compared to the reconstructions using the scanner's default SM.

CONCLUSIONS

Their results demonstrate that using a large SM that incorporates a CT derived body contour in the reconstruction could improve quantitative accuracy within the FOV for clinical studies with high extracardiac activity.

Efficient determination of the uncertainty for the optimization of SPECT system design: a subsampled fisher information matrix

System designs in single photon emission tomography (SPECT) can be evaluated based on the fundamental trade-off between bias and variance that can be achieved in the reconstruction of emission tomograms. This trade off can be derived analytically using the Cramer-Rao type bounds, which imply the calculation and the inversion of the Fisher information matrix (FIM). The inverse of the FIM expresses the uncertainty associated to the tomogram, enabling the comparison of system designs. However, computing, storing and inverting the FIM is not practical with 3-D imaging systems. In order to tackle the problem of the computational load in calculating the inverse of the FIM, a method based on the calculation of the local impulse response and the variance, in a single point, from a single row of the FIM, has been previously proposed for system design. However this approximation (circulant approximation) does not capture the global interdependence between the variables in shift-variant systems such as SPECT, and cannot account e.g., for data truncation or missing data. Our new formulation relies on subsampling the FIM. The FIM is calculated over a subset of voxels arranged in a grid that covers the whole volume. Every element of the FIM at the grid points is calculated exactly, accounting for the acquisition geometry and for the object. This new formulation reduces the computational complexity in estimating the uncertainty, but nevertheless accounts for the global interdependence between the variables, enabling the exploration of design spaces hindered by the circulant approximation. The graphics processing unit accelerated implementation of the algorithm reduces further the computation times, making the algorithm a good candidate for real-time optimization of adaptive imaging systems. This paper describes the subsampled FIM formulation and implementation details. The advantages and limitations of the new approximation are explored, in comparison with the circulant approximation, in the context of design optimization of a parallel-hole collimator SPECT system and of an adaptive imaging system (similar to the commercially available D-SPECT).

The meaning of interior tomography

The classic imaging geometry for computed tomography is for the collection of un-truncated projections and the reconstruction of a global image, with the Fourier transform as the theoretical foundation that is intrinsically non-local. Recently, interior tomography research has led to theoretically exact relationships between localities in the projection and image spaces and practically promising reconstruction algorithms. Initially, interior tomography was developed for x-ray computed tomography. Then, it was elevated to have the status of a general imaging principle. Finally, a novel framework known as 'omni-tomography' is being developed for a grand fusion of multiple imaging modalities, allowing tomographic synchrony of diversified features.

Towards high-resolution synchrotron radiation imaging with statistical iterative reconstruction

Synchrotron radiation (SR) X-ray micro-computed tomography (CT) is an effective imaging modality for high-resolution investigation of small objects, with several applications in medicine, biology and industry. However, the limited size of the detector field of view (FOV) restricts the sample dimensions to only a few millimeters. When the sample size is larger than the FOV, images reconstructed using conventional methods suffer from DC-shift and low-frequency artifacts. This classical problem is known as the local tomography or the interior problem. In this paper, a statistical iterative reconstruction method is introduced to eliminate image artifacts resulting from the local tomography. The proposed method, which can be used in several SR imaging applications, enables high-resolution SR imaging with superior image quality compared with conventional methods. Real data obtained from different SR micro-CT applications are used to evaluate the proposed method. Results indicate a noteworthy quality improvement in the image reconstructed from the local tomography measurements.

Null-space function estimation for the interior problem

In single-photon emission computed tomography (SPECT), projection data can be truncated when the camera's field of view is smaller than the object to be imaged. Using truncated projections to reconstruct a region of interest (ROI) is a reality we must face if small detectors are used. The truncated data result in an underdetermined system of imaging equations, which may lead to non-unique solutions. Data sampling and photon attenuation may also affect the solution uniqueness and stability. The uniqueness of the solutions in the ROI can be investigated by studying the null-space functions in the ROI. This paper uses an iterative algorithm to estimate the null-space image, to determine the sampling conditions under which a stable ROI reconstruction is possible with truncated data and to investigate whether attenuation can influence the ROI reconstruction bias. This iterative algorithm is validated by the singular value decomposition method. We show that if the ROI is sufficiently sampled, the null-space image is close to zero inside the ROI, and any almost-zero offset is insignificant in SPECT, because the noise is a much more dominating degradation factor.

Closed-form kinetic parameter estimation solution to the truncated data problem

In a dedicated cardiac single photon emission computed tomography (SPECT) system, the detectors are focused on the heart and the background is truncated in the projections. Reconstruction using truncated data results in biased images, leading to inaccurate kinetic parameter estimates. This paper has developed a closed-form kinetic parameter estimation solution to the dynamic emission imaging problem. This solution is insensitive to the bias in the reconstructed images that is caused by the projection data truncation. This paper introduces two new ideas: (1) it includes background bias as an additional parameter to estimate, and (2) it presents a closed-form solution for compartment models. The method is based on the following two assumptions: (i) the amount of the bias is directly proportional to the truncated activities in the projection data, and (ii) the background concentration is directly proportional to the concentration in the myocardium. In other words, the method assumes that the image slice contains only the heart and the background, without other organs, that the heart is not truncated, and that the background radioactivity is directly proportional to the radioactivity in the blood pool. As long as the background activity can be modeled, the proposed method is applicable regardless of the number of compartments in the model. For simplicity, the proposed method is presented and verified using a single compartment model with computer simulations using both noiseless and noisy projections.

SPECT region of interest reconstruction with truncated transmission and emission data

PURPOSE

The aim of this article is to propose an exact SPECT region of interest (ROI) reconstruction method using truncated transmission and truncated emission data.

METHODS

Recently, the authors published two articles in Physics in Medicine and Biology with two results in SPECT ROI emission image reconstruction. The first result states that if the transmission data are truncated but the emission data are not truncated, the emission image can be exactly reconstructed, provided the entire emission image is inside the region where the transmission data are not truncated. The second result states that if the transmission data are not truncated, the emission ROI can be exactly reconstructed with truncated emission data. This article combines these two results and obtains a new result that the emission ROI can be exactly reconstructed if both transmission and emission data are truncated.

RESULTS

Computer simulations are performed to verify the proposed ROI image reconstruction algorithm.

CONCLUSIONS

Exact SPECT ROI image reconstruction is possible using truncated transmission and emission projections with some prior information about the attenuator and the emission distribution.