A Kernel Density Estimator-Based Maximum A Posteriori Image Reconstruction Method for Dynamic Emission Tomography Imaging.

By accurately modeling the physics of photon transport into the projection and backprojection operations, iterative SPECT reconstruction methods can reduce the degrading effects of scatter, attenuation and the non-stationary spatial resolution of the camera. Unfortunately, iterative reconstruction methods have required very long computation times, predominately due to the complexity involved in modeling these degrading effects into the projection and backprojection operations. In this study, we describe an approach which allows SPECT iterative reconstruction algorithms to be implemented with a reduction in the number of computations needed. The idea is to pre-process the measured projection data to compensate for scatter and attenuation, as well as to transform the projection data to those which would have been obtained with a stationary system resolution. Results of simulation studies indicate that preprocessing the measured projection data reduces the number of computations needed to perform the projection and backprojection operations, and yields reconstructions which differ minimally from those obtained using the slower standard iterative approach of modeling both photon attenuation and nonstationary blurring in the projection and backprojection steps.

Existing methods to determine the binding potential in brain receptor and transporter studies with single-photon emission computed tomography (SPECT) show a marked dependence on the physical performance of the scanner and on the regions of interest (ROIs) drawn. We examined the influence of the physical performance on the binding potential. The authors tested three gamma cameras (single-, dual- and triple-head) and two reconstruction techniques (conventional filtered back-projection and iterative reconstruction method) to determine the binding potential in brain receptor studies. Both human and organ-like phantom studies were performed. The binding potential was completely dependent on the imaging resolution, on the reconstruction technique used and on the ROIs drawn. The results of the phantom study revealed that the striatum-to-cerebellum ratio was only 37% of the actual one for the single-head, 63% for the dual-head and 72% for the triple-head gamma camera. The multiple head gamma camera with fan-beam collimators and iterative reconstruction with the attenuation based scatter correction is an imaging system of choice which introduces clinically more relevant images and is able to distinguish smaller differences in radioactivity at early stage of disease. However, for quantitative purposes the improvement without the use of the recovery coefficient is not great enough to restore the binding potentials to those of the true ones.

Iterative reconstruction methods in X-ray CT

Iterative algorithms such as maximum likelihood expectation maximization (ML-EM) algorithm are rapidly becoming the standard for image reconstruction in emission computed tomography. The maximum likelihood approach provides images with superior noise characteristics compared to conventional filtered backprojection algorithm. A major drawback of the iterative image reconstruction methods is their high computational cost. In this paper, we develop a new algorithm called the improved ordered subset expectation maximization (IOS-EM) algorithm. This algorithm modifies the number of projections in each subset and the step size (i.e., the relaxation factor) for each iteration in order to recover various frequency components in early iteration steps. In the method presented in this paper, the number of projections in a subset increases and the step size decreases after each iteration. In addition, pixel data are grouped into subdivisions to accelerate image reconstruction. Experimental results show that the IOS-EM algorithm can provide high quality reconstructed images at a small number of iterations.

In this study open-source software (QSPECT) suitable for the iterative reconstruction of single-photon emission computed tomography (SPECT) data is presented. QSPECT implements maximum likelihood expectation maximization and ordered subsets expectation maximization algorithms in a user-friendly graphical interface. The software functionality is described and validation results are presented. Maximum likelihood expectation maximization and ordered subsets expectation maximization algorithms are implemented in C++. The Qt toolkit, a standard C++ framework for developing high-performance cross-platform applications, has been used for the graphical user interface development. QSPECT is tested using original projection data from two clinical SPECT systems: (i) APEX SPX-6/6HR and (ii) Millennium MG. Phantom experiments were carried out to evaluate the quality of reconstructed images in terms of (i) spatial resolution, (ii) sensitivity to activity variations, and (iii) the presence of scatter media. A cardiac phantom was used to simulate a normal and abnormal scenario. Finally, clinical cardiac SPECT images were reconstructed. In all cases, QSPECT results were compared with the clinical systems reconstruction software that uses the standard filtered backprojection algorithm. The reconstructed images show that QSPECT, when compared with standard clinical reconstruction, provides images with higher contrast, reduced background, and better separation of small sources located in small distances. In addition, reconstruction with QSPECT provides more quantitative images, and reduces the background created by scatter media. Finally, the phantom and clinical cardiac images are reconstructed with similar quality. QSPECT is a freely distributed, open-source standalone application that provides real-time, high-quality SPECT images. The software can be further modified to improve reconstruction algorithms, and include more correction techniques, such as, scatter and attenuation correction.

A driving force for the development of new reconstruction algorithms is to achieve better quality images using less information (lower dose, fewer projections, in less time), but under what circumstances do iterative methods become worth the effort? In this paper we propose a framework that enables the performance of reconstruction algorithms to be mapped. Such a framework allows fair comparisons to be made, providing insights into experimental acquisition strategies and methods of quantifying the quality of reconstructions, and identifying the sweet spot for different algorithms.

Small animal positron emission tomography (PET) scanners are being increasingly used as a basic measurement tool in modern biomedical research. The new designs and technologies of these scanners and the modern reconstruction methods have allowed to reach high spatial resolution and sensitivity. Despite their successes, some important issues remain to be addressed in high resolution PET imaging. First, iterative reconstruction methods like maximum likelihood-expectation maximization (MLEM) are known to recover resolution, but also to create noisy images and edge artifacts if some kind of regularization is not imposed. Second, the limit of resolution achievable by iterative methods on high resolution scanners is not quantitatively understood. Third, the use of regularization methods like Sieves or maximum a posteriori (MAP) requires the determination of the optimal values of several adjustable parameter that may be object-dependent. In this work we review these problems in high resolution PET and establish that the origin of them is more related with the physical effects involved in the emission and detection of the radiation during the acquisition than with the kind of iterative reconstruction method chosen. These physical effects (positron range, non-collinearity, scatter inside the object and inside the detector materials) cause that the tube of response (TOR) that connects the voxels with a line of response (LOR) is rather thick. This implies that the higher frequencies of the patient organ structures are not recorded by the scanner and therefore cannot be recovered during the reconstruction. As iterations grow, ML-EM algorithms try to recover higher frequencies in the image. Once that a certain critic frequency is reached, this only maximizes high frequency noise. Using frequency response analyses techniques, we determine the maximum achievable resolution, before edge artifacts spoil the quality of the image, for a particular scanner as a function of the thickness of the TOR, and independently of the reconstruction method employed. With the same techniques, we can deduce well defined stopping criteria for reconstructions methods. Also, criteria for the highest number of subsets which should be used and how the design of the scanners can be optimized when statistical reconstruction methods are employed, is established.

Single-photon emission computed tomography (SPECT) is a method of choice for imaging spatial distributions of radioisotopes. Applications of this method are found in medicine, biomedical research and nuclear industry. This paper deals with improving spatial resolution in SPECT by applying correction for the point-spread function (PSF) in the reconstruction algorithm and optimizing the collimator. Several approaches are considered: the use of a depth-dependent PSF model for a parallel-beam collimator derived from experimental data, the extension of this model to a fan-beam collimator, a triangular approximation of the PSF for reconstruction acceleration, and a method for optimal fan-beam collimator design. An unmatched projector/backprojector ordered subsets expectation maximization (OSEM) algorithm is used for image reconstruction. Experimental results with simulated and physical phantom data of a micro-SPECT system show a significant improvement of spatial resolution with the proposed methods.

CT perfusion (CTP) is obtained cerebrovascular circulation image for assessment of stroke patients; however, at the expense of increased radiation dose by dynamic scan. Iterative reconstruction (IR) method is possible to decrease image noise, it has the potential to reduce radiation dose. The purpose of this study is to assess the visual effect of IR method by using a digital perfusion phantom. The digital perfusion phantom was created by reconstructed filtered back projection (FBP) method and IR method CT images that had five exposure doses. Various exposure dose cerebral blood flow (CBF) images were derived from deconvolution algorithm. Contrast-to-noise ratio (CNR) and visual assessment were compared among the various exposure dose and each reconstructions. Result of low exposure dose with IR method showed, compared with FBP method, high CNR in severe ischemic area, and visual assessment was significantly improvement. IR method is useful for improving image quality of low-dose CTP.

Negative binomial maximum likelihood expectation maximization (NB-MLEM) algorithm for reconstruction of pre-corrected PET data

In recent several years, motivated by the need to reduce radiation doses in CT exams, all of the major CT manufacturers have commercialized different iterative image reconstruction techniques and these innovative techniques were used in clinical routines with increasing popularity. However, due to the intrinsic nonlinearity of these new techniques, the well accepted quantitative image quality assessment metrics such as spatial resolution and contrast to noise ratio are not sufficient to provide the needed quantitative metrics for assessing image quality and for guiding the CT scan protocol optimization. This symposium aims at providing a thorough update to AAPM community on what we have understood in the past for linear CT imaging system, what are the new challenges and opportunities offered by the nonlinear iterative image reconstruction, and what would be the future directions in quantitative image quality assessment that the AAPM community can work together to address the challenges and to adapt the nonlinear image reconstruction methods to routine clinical practice to improve patient care. Three invited speakers will lead the discussions in this symposium.Dr. Ke Li from the University of Wisconsin‐Madison will be presenting the new challenges introduced in model‐based iterative reconstruction (MBIR) method with a focus on how the nonlinear nature of the MBIR reconstruction poses challenges in quantitative image quality metrics such as spatial resolution, noise power spectrum, and the limitations of CNR in protocol optimization which eventually leads to the need of task‐based detectability index as the metric.Dr. Shuai Leng from Mayo Clinic will then present how the CNR metric is insufficient for nonlinear reconstruction algorithms, and how task based model observers can be used to more accurately quantify image quality, and to optimize imaging system and scanning protocols for nonlinear iterative image reconstruction algorithms based on specific imaging task. Practical considerations regarding the application of task based image quality metrics will also be discussed.Dr. Ehsan Samei from Duke University will start the symposium by summarizing a to‐be‐released AAPM Task Group report (TG 233: Performance Evaluation of Computed Tomography Systems). He will cover what has been understood and accepted for linear CT imaging system, what are the new challenges in CT image quality assessment introduced by the nonlinear iterative reconstruction (IR) techniques, and summarize both taskneutral and task‐based metrologies developed in TG 233 to partially address these challenges, and foresee additional challenges in the future. Learning Objectives: Understand the challenges in quantitative image quality assessment introduced by nonlinear iterative reconstruction techniques Understand the challenges and methods in noise performance assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in spatial resolution assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in task‐based observer performance assessment for nonlinear iterative reconstruction techniquesFunding support received from NIH and DOD; Funding support received from GE Healthcare; Funding support received from Siemens AX; Patent royalties received from GE Healthcare; S. Leng, R01 EB071095; U01 EB017185; E. Samei, Research grant, Siemens; Research grant, GE; K. Li, Funding from NIH, DOD and AAPM

BackgroundPositron Emission Tomography (PET), Computed Tomography (CT), PET/CT and Single Photon Emission Tomography (SPECT) are non-invasive imaging tools used for creating two dimensional (2D) cross section images of three dimensional (3D) objects. PET and SPECT have the potential of providing functional or biochemical information by measuring distribution and kinetics of radiolabelled molecules, whereas CT visualizes X-ray density in tissues in the body. PET/CT provides fused images representing both functional and anatomical information with better precision in localization than PET alone.Images generated by these types of techniques are generally noisy, thereby impairing the imaging potential and affecting the precision in quantitative values derived from the images. It is crucial to explore and understand the properties of noise in these imaging techniques. Here we used autocorrelation function (ACF) specifically to describe noise correlation and its non-isotropic behaviour in experimentally generated images of PET, CT, PET/CT and SPECT.MethodsExperiments were performed using phantoms with different shapes. In PET and PET/CT studies, data were acquired in 2D acquisition mode and reconstructed by both analytical filter back projection (FBP) and iterative, ordered subsets expectation maximisation (OSEM) methods. In the PET/CT studies, different magnitudes of X-ray dose in the transmission were employed by using different mA settings for the X-ray tube. In the CT studies, data were acquired using different slice thickness with and without applied dose reduction function and the images were reconstructed by FBP. SPECT studies were performed in 2D, reconstructed using FBP and OSEM, using post 3D filtering. ACF images were generated from the primary images, and profiles across the ACF images were used to describe the noise correlation in different directions. The variance of noise across the images was visualised as images and with profiles across these images.ResultsThe most important finding was that the pattern of noise correlation is rotation symmetric or isotropic, independent of object shape in PET and PET/CT images reconstructed using the iterative method. This is, however, not the case in FBP images when the shape of phantom is not circular. Also CT images reconstructed using FBP show the same non-isotropic pattern independent of slice thickness and utilization of care dose function. SPECT images show an isotropic correlation of the noise independent of object shape or applied reconstruction algorithm. Noise in PET/CT images was identical independent of the applied X-ray dose in the transmission part (CT), indicating that the noise from transmission with the applied doses does not propagate into the PET images showing that the noise from the emission part is dominant. The results indicate that in human studies it is possible to utilize a low dose in transmission part while maintaining the noise behaviour and the quality of the images.ConclusionThe combined effect of noise correlation for asymmetric objects and a varying noise variance across the image field significantly complicates the interpretation of the images when statistical methods are used, such as with statistical estimates of precision in average values, use of statistical parametric mapping methods and principal component analysis. Hence it is recommended that iterative reconstruction methods are used for such applications. However, it is possible to calculate the noise analytically in images reconstructed by FBP, while it is not possible to do the same calculation in images reconstructed by iterative methods. Therefore for performing statistical methods of analysis which depend on knowing the noise, FBP would be preferred.

Small animal PET scanners require high spatial resolution (<1 mm) and good sensitivity. To obtain high resolution images, iterative reconstruction methods, like OSEM, applied to image reconstruction in three-dimensional (3D) positron emission tomography (PET), have superior performance over analytical reconstruction algorithms like FBP. However, the high computational cost of iterative methods remains a serious drawback to their development and clinical routine use. The increase in performance of current computers should make iterative image reconstruction fast enough to attain clinical viability. However, dealing with the large number of probability coefficients for the response of the system in high-resolution PET scanners becomes a difficult task that prevents the algorithms from reaching peak performance. Taking into account all possible axial, in-plane and other symmetries, we have reduced the storage needs what allows us to store the whole response of the system in dynamic memory of ordinary industry standard computers, so that the reconstruction algorithm can achieve near peak performance

The authors present the results of comparing 3D transform and iterative reconstruction methods with measured PET data from the HEAD PENN-PET scanner, which has a very large axial acceptance angle of 27 deg. The algorithms compared are the 3D-reprojection (3DRP) method, the iterative algebraic reconstruction technique (ART), and the maximum likelihood (ML-EM) algorithm. For the iterative methods, alternatives to the cubic voxel basis functions are also implemented. The comparisons are based on a series of figures of merit, including the point-spread function, the contrast recovery coefficient, and signal to noise ratios (SNR). The results show that the ART method implemented with the new basis functions requires only 1 cycle through the data to produce images with measured SNR values comparable to or better than the 3DRP method. The ML-EM method requires 6 to 8 iterations for the test phantom used and produced images with significantly lower SNR values. These are in agreement with previous simulation studies. >

The authors present the results of comparing 3-D transform and iterative reconstruction methods with measured PET data from the HEAD PENN-PET scanner, which has a very large axial acceptance angle of 27/spl deg/. The algorithms compared are the 3-D-reprojection (3DRP) method, the iterative algebraic reconstruction technique (ART), and the maximum likelihood (ML-EM) algorithm. For the iterative methods, alternatives to the cubic voxel basis functions are also implemented. The comparisons are based on a series of figures of merit, including the point-spread function, the contrast recovery coefficient, and signal-to-noise ratios (SNR). The results show that the ART method implemented with the new basis functions requires only one cycle through the data to produce images with measured SNR values comparable to or better than the 3DRP method. The ML-EM method was run for 10 iterations and produced images with lower SNR values for the test phantom used. With the exception of the ML-EM results, these are in agreement with the authors' previous simulation studies.