Improved quantitation for PET/CT image reconstruction with system modeling and anatomical priors

Accurate quantitation of positron emission tomography (PET) tracer uptake levels in tumors is important for staging and monitoring response to treatment. Quantitative accuracy in PET is particularly poor for small tumors because of system partial volume errors and smoothing operations. This work proposes a reconstruction algorithm to reduce the quantitative errors due to limited system resolution and due to necessary image noise reduction. We propose a method for finding and using the detection system response in the projection matrix of a statistical reconstruction algorithm. In addition, we use aligned anatomical information, available in PET/CT scanners, to govern the penalty term applied during each image update. These improvements are combined with Fourier rebinning in a clinically feasible algorithm for reconstructing fully three-dimensional PET data. Results from simulation and measured studies show improved quantitation of tumor values in terms of bias and variance across multiple tumor sizes and activity levels with the proposed method. At common clinical image noise levels for the detection task, the proposed method reduces the error in maximum tumor values by 11% compared to filtered back-projection and 5% compared to conventional iterative methods.     

MR image reconstruction via guided filter

Magnetic resonance imaging (MRI) reconstruction from the smallest possible set of Fourier samples has been a difficult problem in medical imaging field. In our paper, we present a new approach based on a guided filter for efficient MRI recovery algorithm. The guided filter is an edge-preserving smoothing operator and has better behaviors near edges than the bilateral filter. Our reconstruction method is consist of two steps. First, we propose two cost functions which could be computed efficiently and thus obtain two different images. Second, the guided filter is used with these two obtained images for efficient edge-preserving filtering, and one image is used as the guidance image, the other one is used as a filtered image in the guided filter. In our reconstruction algorithm, we can obtain more details by introducing guided filter. We compare our reconstruction algorithm with some competitive MRI reconstruction techniques in terms of PSNR and visual quality. Simulation results are given to show the performance of our new method.     

Model-based image reconstruction for four-dimensional PET

Positron emission tonography (PET) is useful in diagnosis and radiation treatment planning for a variety of cancers. For patients with cancers in thoracic or upper abdominal region, the respiratory motion produces large distortions in the tumor shape and size, affecting the accuracy in both diagnosis and treatment. Four-dimensional (4D) (gated) PET aims to reduce the motion artifacts and to provide accurate measurement of the tumor volume and the tracer concentration. A major issue in 4D PET is the lack of statistics. Since the collected photons are divided into several frames in the 4D PET scan, the quality of each reconstructed frame degrades as the number of frames increases. The increased noise in each frame heavily degrades the quantitative accuracy of the PET imaging. In this work, we propose a method to enhance the performance of 4D PET by developing a new technique of 4D PET reconstruction with incorporation of an organ motion model derived from 4D-CT images. The method is based on the well-known maximum-likelihood expectation-maximization (ML-EM) algorithm. During the processes of forward- and backward-projection in the ML-EM iterations, all projection data acquired at different phases are combined together to update the emission map with the aid of deformable model, the statistics is therefore greatly improved. The proposed algorithm was first evaluated with computer simulations using a mathematical dynamic phantom. Experiment with a moving physical phantom was then carried out to demonstrate the accuracy of the proposed method and the increase of signal-to-noise ratio over three-dimensional PET. Finally, the 4D PET reconstruction was applied to a patient case.     

PET energy-based scatter estimation and image reconstruction with energy-dependent corrections

In this paper we propose a comprehensive energy-based scatter correction approach for positron emission tomography (PET). We take advantage of the marked difference between the energy spectra of the unscattered and scattered photons, and use the detailed energy information that comes with the list-mode data for the estimation of the scattered events distribution in the data space. Also, inside the maximum-likelihood expectation maximization (ML-EM) image reconstruction algorithm, we introduce energy-dependent factors that individualize the correction terms for each event, given its position and energy information. The central piece of our approach is the two-dimensional detector energy response model represented as a linear combination of four components, each one representing a particular state a PET event can be found in: both photons unscattered, the second scattered while the first not, the first photon scattered while the second not and both photons scattered. For a set of events collected in the vicinity of a point in the projection space, the coefficient of each component is determined by applying a statistical estimator. As a result we obtain the number of scattered events that are in the given set. The model also gives us the variation of scatter fraction with the photon pair energies for that particular position in the data space. A simulation study that demonstrates the proposed methods is presented.     

Statistical image reconstruction from correlated data with applications to PET

Most statistical reconstruction methods for emission tomography are designed for data modeled as conditionally independent Poisson variates. In reality, due to scanner detectors, electronics and data processing, correlations are introduced into the data resulting in dependent variates. In general, these correlations are ignored because they are difficult to measure and lead to computationally challenging statistical reconstruction algorithms. This work addresses the second concern, seeking to simplify the reconstruction of correlated data and provide a more precise image estimate than the conventional independent methods. In general, correlated variates have a large non-diagonal covariance matrix that is computationally challenging to use as a weighting term in a reconstruction algorithm. This work proposes two methods to simplify the use of a non-diagonal covariance matrix as the weighting term by (a) limiting the number of dimensions in which the correlations are modeled and (b) adopting flexible, yet computationally tractable, models for correlation structure. We apply and test these methods with simple simulated PET data and data processed with the Fourier rebinning algorithm which include the one-dimensional correlations in the axial direction and the two-dimensional correlations in the transaxial directions. The methods are incorporated into a penalized weighted least-squares 2D reconstruction and compared with a conventional maximum a posteriori approach.     

Statistical dynamic image reconstruction in state-of-the-art high-resolution PET

Modern high-resolution PET is now more than ever in need of scrutiny into the nature and limitations of the imaging modality itself as well as image reconstruction techniques. In this work, we have reviewed, analysed and addressed the following three considerations within the particular context of state-of-the-art dynamic PET imaging: (i) the typical average numbers of events per line-of-response (LOR) are now (much) less than unity, (ii) due to the physical and biological decay of the activity distribution, one requires robust and efficient reconstruction algorithms applicable to a wide range of statistics and (iii) the computational considerations in dynamic imaging are much enhanced (i.e., more frames to be stored and reconstructed). Within the framework of statistical image reconstruction, we have argued theoretically and shown experimentally that the sinogram non-negativity constraint (when using the delayed-coincidence and/or scatter-subtraction techniques) is especially expected to result in an overestimation bias. Subsequently, two schemes are considered: (a) subtraction techniques in which an image non-negativity constraint has been imposed and (b) implementation of random and scatter estimates inside the reconstruction algorithms, thus enabling direct processing of Poisson-distributed prompts. Both techniques are able to remove the aforementioned bias, while the latter, being better conditioned theoretically, is able to exhibit superior noise characteristics. We have also elaborated upon and verified the applicability of the accelerated list-mode image reconstruction method as a powerful solution for accurate, robust and efficient dynamic reconstructions of high-resolution data (as well as a number of additional benefits in the context of state-of-the-art PET).     

Three penalized EM-type algorithms for PET image reconstruction

Based on Bayes theory, Green introduced the maximum a posteriori (MAP) algorithm to obtain a smoothing reconstruction for positron emission tomography. This algorithm is flexible and convenient for most of the penalties, but it is hard to guarantee convergence. For a common goal, Fessler penalized a weighted least squares (WLS) estimator by a quadratic penalty and then solved it with the successive over-relaxation (SOR) algorithm, however, the algorithm was time-consuming and difficultly parallelized. Anderson proposed another WLS estimator for faster convergence, on which there were few regularization methods studied. For three regularized estimators above, we develop three new expectation maximization (EM) type algorithms to solve them. Unlike MAP and SOR, the proposed algorithms yield update rules by minimizing the auxiliary functions constructed on the previous iterations, which ensure the cost functions monotonically decreasing. Experimental results demonstrated the robustness and effectiveness of the proposed algorithms.     

Three-dimensional image reconstruction for PET by multi-slice rebinning and axial image filtering

A fast method is described for reconstructing volume images from three-dimensional (3D) coincidence data in positron emission tomography (PET). The reconstruction method makes use of all coincidence data acquired by high-sensitivity PET systems that do not have inter-slice absorbers (septa) to restrict the axial acceptance angle. The reconstruction method requires only a small amount of storage and computation, making it well suited for dynamic and whole-body studies. The method consists of three steps: (i) rebinning of coincidence data into a stack of 2D sinograms; (ii) slice-by-slice reconstruction of the sinogram associated with each slice to produce a preliminary 3D image having strong blurring in the axial (z) direction, but with different blurring at different z positions; and (iii) spatially variant filtering of the 3D image in the axial direction (i.e. 1D filtering in z for each x-y column) to produce the final image. The first step involves a new form of the rebinning operation in which multiple sinograms are incremented for each oblique coincidence line (multi-slice rebinning). The axial filtering step is formulated and implemented using the singular value decomposition (SVD). The method has been applied successfully to simulated data and to measured data for different kinds of phantom (multiple point sources, multiple discs, a cylinder with cold spheres, and a 3D brain phantom).     

Region of interest motion compensation for PET image reconstruction

A motion-incorporated reconstruction (MIR) method for gated PET imaging has recently been developed by several authors to correct for respiratory motion artifacts in PET imaging. This method however relies on a motion map derived from images (4D PET or 4D CT) of the entire field of view (FOV). In this study we present a region of interest (ROI)-based extension to this method, whereby only the motion map of a user-defined ROI is required and motion incorporation during image reconstruction is solely performed within the ROI. A phantom study and an NCAT computer simulation study were performed to test the feasibility of this method. The phantom study showed that the ROI-based MIR produced results that are within 1.26% of those obtained by the full image-based MIR approach when using the same accurate motion information. The NCAT phantom study on the other hand, further verified that motion of features of interest in an image can be estimated more efficiently and potentially more accurately using the ROI-based approach. A reduction of motion estimation time from 450 s to 30 and 73 s was achieved for two different ROIs respectively. In addition, the ROI-based approach showed a reduction in registration error of 43% for one ROI, which effectively reduced quantification bias by 44% and 32% using mean and maximum voxel values, respectively.     

3.5D dynamic PET image reconstruction incorporating kinetics-based clusters

Standard 3D dynamic positron emission tomographic (PET) imaging consists of independent image reconstructions of individual frames followed by application of appropriate kinetic model to the time activity curves at the voxel or region-of-interest (ROI). The emerging field of 4D PET reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple frames within the image reconstruction task. Here we propose a novel reconstruction framework aiming to enhance quantitative accuracy of parametric images via introduction of priors based on voxel kinetics, as generated via clustering of preliminary reconstructed dynamic images to define clustered neighborhoods of voxels with similar kinetics. This is then followed by straightforward maximum a posteriori (MAP) 3D PET reconstruction as applied to individual frames; and as such the method is labeled '3.5D' image reconstruction. The use of cluster-based priors has the advantage of further enhancing quantitative performance in dynamic PET imaging, because: (a) there are typically more voxels in clusters than in conventional local neighborhoods, and (b) neighboring voxels with distinct kinetics are less likely to be clustered together. Using realistic simulated (11)C-raclopride dynamic PET data, the quantitative performance of the proposed method was investigated. Parametric distribution-volume (DV) and DV ratio (DVR) images were estimated from dynamic image reconstructions using (a) maximum-likelihood expectation maximization (MLEM), and MAP reconstructions using (b) the quadratic prior (QP-MAP), (c) the Green prior (GP-MAP) and (d, e) two proposed cluster-based priors (CP-U-MAP and CP-W-MAP), followed by graphical modeling, and were qualitatively and quantitatively compared for 11 ROIs. Overall, the proposed dynamic PET reconstruction methodology resulted in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) for parametric DV and DVR images. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomography. The proposed method was shown to outperform the conventional method in visual as well as quantitative accuracy improvements (in terms of noise versus regional DVR value performance).     

Model-based normalization for iterative 3D PET image reconstruction

We describe a method for normalization in 3D PET for use with maximum a posteriori (MAP) or other iterative model-based image reconstruction methods. This approach is an extension of previous factored normalization methods in which we include separate factors for detector sensitivity, geometric response, block effects and deadtime. Since our MAP reconstruction approach already models some of the geometric factors in the forward projection, the normalization factors must be modified to account only for effects not already included in the model. We describe a maximum likelihood approach to joint estimation of the count-rate independent normalization factors, which we apply to data from a uniform cylindrical source. We then compute block-wise and block-profile deadtime correction factors using singles and coincidence data, respectively, from a multiframe cylindrical source. We have applied this method for reconstruction of data from the Concorde microPET P4 scanner. Quantitative evaluation of this method using well-counter measurements of activity in a multicompartment phantom compares favourably with normalization based directly on cylindrical source measurements.     

Live level set: a hybrid method of livewire and level set for medical image segmentation

Livewire and level set are popular methods for medical image segmentation. In this article, the authors propose a hybrid method of livewire and level set, termed the live level set (LLS). The LLS replaces the one graph update iteration in the classic livewire with two iterations of graph updates. The first iteration generates an initial contour for a level set computation. The level set distance is then factored back into the cost function in the second iteration of graph update. The authors validated LLS using synthetic images. The results show that the performance of the LLS is superior to both the classic live wire and traditional level set methods in terms of accuracy, reproducibility, smoothness and running time. They also qualitatively evaluated the LLS using real clinical data.     

Online detector response calculations for high-resolution PET image reconstruction

Positron emission tomography systems are best described by a linear shift-varying model. However, image reconstruction often assumes simplified shift-invariant models to the detriment of image quality and quantitative accuracy. We investigated a shift-varying model of the geometrical system response based on an analytical formulation. The model was incorporated within a list-mode, fully 3D iterative reconstruction process in which the system response coefficients are calculated online on a graphics processing unit (GPU). The implementation requires less than 512 Mb of GPU memory and can process two million events per minute (forward and backprojection). For small detector volume elements, the analytical model compared well to reference calculations. Images reconstructed with the shift-varying model achieved higher quality and quantitative accuracy than those that used a simpler shift-invariant model. For an 8 mm sphere in a warm background, the contrast recovery was 95.8% for the shift-varying model versus 85.9% for the shift-invariant model. In addition, the spatial resolution was more uniform across the field-of-view: for an array of 1.75 mm hot spheres in air, the variation in reconstructed sphere size was 0.5 mm RMS for the shift-invariant model, compared to 0.07 mm RMS for the shift-varying model.     

Joint model of motion and anatomy for PET image reconstruction

Anatomy-based positron emission tomography (PET) image enhancement techniques have been shown to have the potential for improving PET image quality. However, these techniques assume an accurate alignment between the anatomical and the functional images, which is not always valid when imaging the chest due to respiratory motion. In this article, we present a joint model of both motion and anatomical information by integrating a motion-incorporated PET imaging system model with an anatomy-based maximum a posteriori image reconstruction algorithm. The mismatched anatomical information due to motion can thus be effectively utilized through this joint model. A computer simulation and a phantom study were conducted to assess the efficacy of the joint model, whereby motion and anatomical information were either modeled separately or combined. The reconstructed images in each case were compared to corresponding reference images obtained using a quadratic image prior based maximum a posteriori reconstruction algorithm for quantitative accuracy. Results of these studies indicated that while modeling anatomical information or motion alone improved the PET image quantitation accuracy, a larger improvement in accuracy was achieved when using the joint model. In the computer simulation study and using similar image noise levels, the improvement in quantitation accuracy compared to the reference images was 5.3% and 19.8% when using anatomical or motion information alone, respectively, and 35.5% when using the joint model. In the phantom study, these results were 5.6%, 5.8%, and 19.8%, respectively. These results suggest that motion compensation is important in order to effectively utilize anatomical information in chest imaging using PET. The joint motion-anatomy model presented in this paper provides a promising solution to this problem.     

A robust state-space kinetics-guided framework for dynamic PET image reconstruction

Dynamic PET image reconstruction is a challenging issue due to the low SNR and the large quantity of spatio-temporal data. We propose a robust state-space image reconstruction (SSIR) framework for activity reconstruction in dynamic PET. Unlike statistically-based frame-by-frame methods, tracer kinetic modeling is incorporated to provide physiological guidance for the reconstruction, harnessing the temporal information of the dynamic data. Dynamic reconstruction is formulated in a state-space representation, where a compartmental model describes the kinetic processes in a continuous-time system equation, and the imaging data are expressed in a discrete measurement equation. Tracer activity concentrations are treated as the state variables, and are estimated from the dynamic data. Sampled-data H(∞) filtering is adopted for robust estimation. H(∞) filtering makes no assumptions on the system and measurement statistics, and guarantees bounded estimation error for finite-energy disturbances, leading to robust performance for dynamic data with low SNR and/or errors. This alternative reconstruction approach could help us to deal with unpredictable situations in imaging (e.g. data corruption from failed detector blocks) or inaccurate noise models. Experiments on synthetic phantom and patient PET data are performed to demonstrate feasibility of the SSIR framework, and to explore its potential advantages over frame-by-frame statistical reconstruction approaches.     

Improved compressed sensing-based cone-beam CT reconstruction using adaptive prior image constraints

Volumetric cone-beam CT (CBCT) images are acquired repeatedly during a course of radiation therapy and a natural question to ask is whether CBCT images obtained earlier in the process can be utilized as prior knowledge to reduce patient imaging dose in subsequent scans. The purpose of this work is to develop an adaptive prior image constrained compressed sensing (APICCS) method to solve this problem. Reconstructed images using full projections are taken on the first day of radiation therapy treatment and are used as prior images. The subsequent scans are acquired using a protocol of sparse projections. In the proposed APICCS algorithm, the prior images are utilized as an initial guess and are incorporated into the objective function in the compressed sensing (CS)-based iterative reconstruction process. Furthermore, the prior information is employed to detect any possible mismatched regions between the prior and current images for improved reconstruction. For this purpose, the prior images and the reconstructed images are classified into three anatomical regions: air, soft tissue and bone. Mismatched regions are identified by local differences of the corresponding groups in the two classified sets of images. A distance transformation is then introduced to convert the information into an adaptive voxel-dependent relaxation map. In constructing the relaxation map, the matched regions (unchanged anatomy) between the prior and current images are assigned with smaller weight values, which are translated into less influence on the CS iterative reconstruction process. On the other hand, the mismatched regions (changed anatomy) are associated with larger values and the regions are updated more by the new projection data, thus avoiding any possible adverse effects of prior images. The APICCS approach was systematically assessed by using patient data acquired under standard and low-dose protocols for qualitative and quantitative comparisons. The APICCS method provides an effective way for us to enhance the image quality at the matched regions between the prior and current images compared to the existing PICCS algorithm. Compared to the current CBCT imaging protocols, the APICCS algorithm allows an imaging dose reduction of 10-40 times due to the greatly reduced number of projections and lower x-ray tube current level coming from the low-dose protocol.     

Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT

Recent advances in murine cardiac studies with three-dimensional (3D) cone beam micro-CT used a retrospective gating technique. However, this sampling technique results in a limited number of projections with an irregular angular distribution due to the temporal resolution requirements and radiation dose restrictions. Both angular irregularity and undersampling complicate the reconstruction process, since they cause significant streaking artifacts. This work provides an iterative reconstruction solution to address this particular challenge. A sparseness prior regularized weighted l2 norm optimization is proposed to mitigate streaking artifacts based on the fact that most medical images are compressible. Total variation is implemented in this work as the regularizer for its simplicity. Comparison studies are conducted on a 3D cardiac mouse phantom generated with experimental data. After optimization, the method is applied to in vivo cardiac micro-CT data.     

Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation

The performance of the level set segmentation is subject to appropriate initialization and optimal configuration of controlling parameters, which require substantial manual intervention. A new fuzzy level set algorithm is proposed in this paper to facilitate medical image segmentation. It is able to directly evolve from the initial segmentation by spatial fuzzy clustering. The controlling parameters of level set evolution are also estimated from the results of fuzzy clustering. Moreover the fuzzy level set algorithm is enhanced with locally regularized evolution. Such improvements facilitate level set manipulation and lead to more robust segmentation. Performance evaluation of the proposed algorithm was carried on medical images from different modalities. The results confirm its effectiveness for medical image segmentation.     

Bayesian algorithms for PET image reconstruction with mean curvature and Gauss curvature diffusion regularizations

The basic mathematical problem behind PET is an inverse problem. Due to the inherent ill-posedness of this inverse problem, the reconstructed images will have noise and edge artifacts. A roughness penalty is often imposed on the solution to control noise and stabilize the solution, but the difficulty is to avoid the smoothing of edges. In this paper, we propose two new types of Bayesian one-step-late reconstruction approaches which utilize two different prior regularizations: the mean curvature (MC) diffusion function and the Gauss curvature (GC) diffusion function. As they have been studied in image processing for removing noise, these two prior regularizations encourage preserving the edge while the reconstructed images are smoothed. Moreover, the GC constraint can preserve smaller structures which cannot be preserved by MC. The simulation results show that the proposed algorithms outperform the quadratic function and total variation approaches in terms of preserving the edges during emission reconstruction.     

Segmentation of mouse dynamic PET images using a multiphase level set method

Image segmentation plays an important role in medical diagnosis. Here we propose an image segmentation method for four-dimensional mouse dynamic PET images. We consider that voxels inside each organ have similar time activity curves. The use of tracer dynamic information allows us to separate regions that have similar integrated activities in a static image but with different temporal responses. We develop a multiphase level set method that utilizes both the spatial and temporal information in a dynamic PET data set. Different weighting factors are assigned to each image frame based on the noise level and activity difference among organs of interest. We used a weighted absolute difference function in the data matching term to increase the robustness of the estimate and to avoid over-partition of regions with high contrast. We validated the proposed method using computer simulated dynamic PET data, as well as real mouse data from a microPET scanner, and compared the results with those of a dynamic clustering method. The results show that the proposed method results in smoother segments with the less number of misclassified voxels.