Kyungsang Kim

Dynamic PET reconstruction using temporal patch-based low rank penalty for ROI-based brain kinetic analysis

Dynamic positron emission tomography (PET) is widely used to measure changes in the bio-distribution of radiopharmaceuticals within particular organs of interest over time. However, to retain sufficient temporal resolution, the number of photon counts in each time frame must be limited. Therefore, conventional reconstruction algorithms such as the ordered subset expectation maximization (OSEM) produce noisy reconstruction images, thus degrading the quality of the extracted time activity curves (TACs). To address this issue, many advanced reconstruction algorithms have been developed using various spatio-temporal regularizations. In this paper, we extend earlier results and develop a novel temporal regularization, which exploits the self-similarity of patches that are collected in dynamic images. The main contribution of this paper is to demonstrate that the correlation of patches can be exploited using a low-rank constraint that is insensitive to global intensity variations. The resulting optimization framework is, however, non-Lipschitz and nonconvex due to the Poisson log-likelihood and low-rank penalty terms. Direct application of the conventional Poisson image deconvolution by an augmented Lagrangian (PIDAL) algorithm is, however, problematic due to its large memory requirements, which prevents its parallelization. Thus, we propose a novel optimization framework using the concave-convex procedure (CCCP)

Fully iterative scatter corrected digital breast tomosynthesis using GPU-based fast Monte Carlo simulation and composition ratio update.

PURPOSE In digital breast tomosynthesis (DBT), scatter correction is highly desirable, as it improves image quality at low doses. Because the DBT detector panel is typically stationary during the source rotation, antiscatter grids are not generally compatible with DBT; thus, a software-based scatter correction is required. This work proposes a fully iterative scatter correction method that uses a novel fast Monte Carlo simulation (MCS) with a tissue-composition ratio estimation technique for DBT imaging. METHODS To apply MCS to scatter estimation, the material composition in each voxel should be known. To overcome the lack of prior accurate knowledge of tissue composition for DBT, a tissue-composition ratio is estimated based on the observation that the breast tissues are principally composed of adipose and glandular tissues. Using this approximation, the composition ratio can be estimated from the reconstructed attenuation coefficients, and the scatter distribution can then be estimated by MCS using the composition ratio. The scatter estimation and image reconstruction procedures can be performed iteratively until an acceptable accuracy is achieved. For practical use, (i) the authors have implemented a fast MCS using a graphics processing unit (GPU), (ii) the MCS is simplified to transport only x-rays in the energy range of 10-50 keV, modeling Rayleigh and Compton scattering and the photoelectric effect using the tissue-composition ratio of adipose and glandular tissues, and (iii) downsampling is used because the scatter distribution varies rather smoothly. RESULTS The authors have demonstrated that the proposed method can accurately estimate the scatter distribution, and that the contrast-to-noise ratio of the final reconstructed image is significantly improved. The authors validated the performance of the MCS by changing the tissue thickness, composition ratio, and x-ray energy. The authors confirmed that the tissue-composition ratio estimation was quite accurate under a variety of conditions. Our GPU-based fast MCS implementation took approximately 3 s to generate each angular projection for a 6 cm thick breast, which is believed to make this process acceptable for clinical applications. In addition, the clinical preferences of three radiologists were evaluated; the preference for the proposed method compared to the preference for the convolution-based method was statistically meaningful (p < 0.05, McNemar test). CONCLUSIONS The proposed fully iterative scatter correction method and the GPU-based fast MCS using tissue-composition ratio estimation successfully improved the image quality within a reasonable computational time, which may potentially increase the clinical utility of DBT.

Joint estimation of activity image and attenuation sinogram using time-of-flight positron emission tomography data consistency condition filtering

Abstract. Attenuation correction is essential for quantitative reliability of positron emission tomography (PET) imaging. In time-of-flight (TOF) PET, attenuation sinogram can be determined up to a global constant from noiseless emission data due to the TOF PET data consistency condition. This provides the theoretical basis for jointly estimating both activity image and attenuation sinogram/image directly from TOF PET emission data. Multiple joint estimation methods, such as maximum likelihood activity and attenuation (MLAA) and maximum likelihood attenuation correction factor (MLACF), have already been shown that can produce improved reconstruction results in TOF cases. However, due to the nonconcavity of the joint log-likelihood function and Poisson noise presented in PET data, the iterative method still requires proper initialization and well-designed regularization to prevent convergence to local maxima. To address this issue, we propose a joint estimation of activity image and attenuation sinogram using the TOF PET data consistency condition as an attenuation sinogram filter, and then evaluate the performance of the proposed method using computer simulations.

Penalized direct estimation of parametric images in PET

Direct positron emission tomography (PET) reconstruction has been developed for acquiring accurate parametric imaging from raw measurement. Direct reconstruction estimates physiological kinetic parameters in iterative reconstruction process that contains two steps such as updating dynamic images and calculating nonlinear least square (NLS) parameter fitting. Although the quality of dynamic images has been significantly improved using the direct reconstruction, the small kinetic values related to the binding potential are still noisy due to high noise variance of the conventional pixel-by-pixel NLS. To improve the performance, we propose a penalized direct reconstruction that contains the Poisson likelihood, ridge regression with NLS, and total variation (TV) terms. In particular, because the kinetic parameters are three dimensional images and we can assume that the kinetic parameters of neighbor voxels varies smoothly, we can impose a 3-D TV regularization to the kinetic parameter images directly. To solve the cost function, we use a splitting method exploiting an alternating direction method of multipliers (ADMM) algorithm. In computer simulation, we use a segmented brain phantom in which different kinetic parameters are used for different regions. We compare binding potential images of conventional methods and the proposed method. We demonstrate that the proposed method is significantly accurate and improves the quality of binding potential image compared to the conventional direct method.

Low‐dose CT reconstruction using spatially encoded nonlocal penalty

Purpose: Computed tomography (CT) is one of the most used imaging modalities for imaging both symptomatic and asymptomatic patients. However, because of the high demand for lower radiation dose during CT scans, the reconstructed image can suffer from noise and artifacts due to the trade‐off between the image quality and the radiation dose. The purpose of this paper is to improve the image quality of quarter dose images and to select the best hyperparameters using the regular dose image as ground truth. Methods: We first generated the axially stacked two‐dimensional sinograms from the multislice raw projections with flying focal spots using a single slice rebinning method, which is an axially approximate method to provide simple implementation and efficient memory usage. To improve the image quality, a cost function containing the Poisson log‐likelihood and spatially encoded nonlocal penalty is proposed. Specifically, an ordered subsets separable quadratic surrogates (OS‐SQS) method for the log‐likelihood is exploited and the patch‐based similarity constraint with a spatially variant factor is developed to reduce the noise significantly while preserving features. Furthermore, we applied the Nesterovs momentum method for acceleration and the diminishing number of subsets strategy for noise consistency. Fast nonlocal weight calculation is also utilized to reduce the computational cost. Results: Datasets given by the Low Dose CT Grand Challenge were used for the validation, exploiting the training datasets with the regular and quarter dose data. The most important step in this paper was to fine‐tune the hyperparameters to provide the best image for diagnosis. Using the regular dose filtered back‐projection (FBP) image as ground truth, we could carefully select the hyperparameters by conducting a bias and standard deviation study, and we obtained the best images in a fixed number of iterations. We demonstrated that the proposed method with well selected hyperparameters improved the image quality using quarter dose data. The quarter dose proposed method was compared with the regular dose FBP, quarter dose FBP, and quarter dose l1‐based 3‐D TV method. We confirmed that the quarter dose proposed image was comparable to the regular dose FBP image and was better than images using other quarter dose methods. The reconstructed test images of the accreditation (ACR) CT phantom and 20 patients data were evaluated by radiologists at the Mayo clinic, and this method was awarded first place in the Low Dose CT Grand Challenge. Conclusion: We proposed the iterative CT reconstruction method using a spatially encoded nonlocal penalty and ordered subsets separable quadratic surrogates with the Nesterovs momentum and diminishing number of subsets. The results demonstrated that the proposed method with fine‐tuned hyperparameters can significantly improve the image quality and provide accurate diagnostic features at quarter dose. The performance of the proposed method should be further improved for small lesions, and a more thorough evaluation using additional clinical data is required in the future.

Dynamic 3D PET reconstruction for kinetic analysis using patch-based low-rank penalty

Dynamic positron emission tomography (PET) is widely used to identify metabolism over time. However, conventional reconstruction algorithm provides a noisy reconstruction due to the lack of photon counts in each frame. Therefore, the main goal of this paper is to develop a novel spatio-temporal regularization approach that exploits inherent similarities within intra- and inter- frames. One of the main contributions of this paper is to demonstrate that such correlations can be exploited using a low rank constraint of overlapping similarity blocks. The resulting optimization framework is, however, non-smooth and non Lipschitz due to the low-rank penalty terms and Poisson log-likelihood. Therefore, we propose a novel globally convergent optimization method using the concave-convex procedure (CCCP) by exploiting Legendre-Fenchel transform.We confirm that the proposed algorithm can provide significantly improved image quality.

A novel depth-of-interaction rebinning strategy for ultrahigh resolution PET

Small animal positron emission tomography (PET) imaging often requires high resolution (∼few hundred microns) to enable accurate quantitation in small structures such as animal brains. Recently, we have developed a prototype ultrahigh resolution depth-of-interaction (DOI) PET system that uses CdZnTe detectors with a detector pixel size of 350 μm and eight DOI layers with a 250 μm depth resolution. Due to the large number of line-of-response (LOR) combinations of DOIs, the system matrix for reconstruction is 64 times larger than that without DOI. While a high resolution virtual ring geometry can be employed to simplify the system matrix and create a sinogram, the LORs in such a sinogram tend to be sparse and irregular, leading to potential degradation of the reconstructed image quality. In this paper, we propose a novel high resolution sinogram rebinning method in which a uniform sub-sampling DOI strategy is employed. However, even with the high resolution rebinning strategy, the reconstructed image tends to be very noisy due to insufficient photon counts in many high resolution sinogram pixels. To reduce noise effects, we developed a penalized maximum likelihood reconstruction framework with the Poisson log-likelihood and a non-convex total variation penalty. Here, an ordered subsets separable quadratic surrogate and alternating direction method of multipliers are utilized to solve the optimization. To evaluate the performance of the proposed sub-sampling method and the penalized maximum likelihood reconstruction technique, we perform simulations and preliminary point source experiments. By comparing the reconstructed images and profiles based on sinograms without DOI, with rebinned DOI and with sub-sampled DOI, we demonstrate that the proposed method with sub-sampled DOIs can significantly improve the image quality with lower dose and yield a high resolution of  <300 μm.

Penalized MLAA with spatially-encoded anatomic prior in TOF PET/MR

PET/MR scanner has been developed for both molecular and morphological assessment with great potentials. In the PET/MR scan, the attenuation correction is still a problem. One method is the MR-based attenuation correction that generates the synthetic CT images from MR images. However, the lack of bone signal and the bias from the synthetic CT image can degrade the PET image quality. Another method is a maximum likelihood reconstruction of activity and attenuation (MLAA) using the time-of-flight (TOF) PET emission data, however, the noise component is considerably high from TOF PET data. To address this issue, we propose a penalized MLAA using a spatially-encoded anatomic MR prior, which jointly use a patch-based spatially-encoded similarity weight of MR image to improve the attenuation image quality. In addition, we propose a non-divergence criteria using a consistency condition in the iterative process. We exploit an alternating direction method of multipliers (ADMM) algorithm to optimize the cost function. In computer simulations, we demonstrate that the proposed method outperform the conventional MLAA.

Dual-energy CT Reconstruction using Guided Image Filtering

Dual-energy computed tomography (CT) has become widely applied due to its advantages like reducing beam-hardening artefacts and providing more accurate attenuation measurements. Compared with traditional CT (using single X-ray spectrum), dual-energy CT performs much better especially when some material cannot be easily distinguished by one X-ray spectrum. When doing dual-energy CT reconstruction, it is a basic principal to fully exploit the information of the data from both high and low energies. Here we propose a novel dual-energy CT reconstruction method using the guided image filtering algorithm and the commonly used transmission image reconstruction method: separable quadratic surrogates (SQS). As a patch-based image processing algorithm, guided image filtering has nice properties of edge-preserving smoothing and relatively high computational efficiency. It can be used in structure-transferring between two images, filtering-based feathering/matting and dehazing. On the other hand, the SQS algorithm is an ordered subsets algorithm for penalty likelihood image reconstruction in transmission tomography. It can rapidly decrease the objective function value in the early iterations. In this paper, the ideas of guided image filtering and SQS are explained. We study the basic principle and main advantages of guided image filtering and SQS, and tell how we combine these two methods to do dual-energy CT reconstruction. After that, we did computed simulation (with simulated Poisson noise) to validate our idea, and make comparison with other methods. The results show that the quality of both images can be improved in a satisfying convergence speed.

Direct parametric imaging of reversible tracers using partial dynamic data

Direct parametric estimation in positron emission tomography (PET) has been developed to compute the voxel-based kinetic parameters in the reconstruction process, obtaining more accurate physiological information of tracer uptake. Although the direct parametric imaging can achieve accurate kinetic analysis, the long acquisition time is still painful, particularly for sick and old patients. To address this issue, we explore the feasibility to estimate voxel-based kinetic parameters using partial dynamic data, specifically the first and last 10 minutes of a typical dynamic scan. To improve the quality of the direct parametric imaging with partial dynamic data, we propose a novel penalized direct estimation method containing log-likelihood, ridge regression and patch-based joint similarity penalty of kinetic images, in which the structural similarity weight of K1 can be used for improving the features in other kinetic images (k2 ∼ k4). In our optimization, the alternating direction method of multipliers (ADMM) with a separable quadratic surrogate (SQS) is exploited. We validate the proposed method using a brain phantom, and demonstrate that the proposed method outperforms the conventional direct estimation methods even using partial dynamic data.