Penalized Direct Estimation of Parametric PET Image

Objectives Direct reconstruction of parametric PET image estimates voxel-wise physiological kinetic parameters from PET raw data, and therefore achieves superior performance compared with traditional in-direct methods. Conventional direct estimation calculates kinetic parameters without spatial constraint or with spatial constraint in the intensity image. The image quality of resulting parametric image could be very sensitive to the variation of pixel-wise dynamic intensity changes because of the severe ill-poseness of the estimation problem. We develop and validate a penalized direct estimation for parametric PET image reconstruction using a 3-D total variation (TV) regularization in parametric image domain to improve the robustness and accuracy of our direct estimation. We also compare the performance of the proposed method with the conventional direct reconstruction with or without a dynamic image-based TV regularization.

Methods The cost function of proposed method contains the Poisson likelihood, ridge regression and kinetic-based 3-D TV terms. We used a separable quadratic surrogate (SQS) algorithm to minimize the Poisson likelihood. Ridge regression is applied to extract kinetic parameters from dynamic images with non-linear least square (NLS) fitting. To optimize the cost function, we exploit an alternating direction method of multipliers (ADMM) algorithm that is very efficient for optimizing multiple regularization terms in a cost function. To evaluate the proposed method, we used a segmented brain phantom with different kinetic parameters in various regions of interest (ROIs). The PET geometry is similar to the HRRT scanner, and the Poisson noise is imposed in raw dynamic measurements. Two-tissue compartment model with reversible tracer is used (K1, k2, k3, k4) in the simulation. We compared qualities of binding potential images (k3/k4) using the conventional direct reconstruction, the direct reconstruction with a dynamic image-based TV regularization, and the proposed method. To evaluate the quantitative performance, the binding potential image and ROI-based bias and standard deviation plots are demonstrated (ROI-1: caudate, accumbens, lateral ventrical and putamen; ROI-2: thalamus and pallidum).

Results In comparison of binding potential images in figure 1(a), the quality of binding potential image using the proposed method was significantly improved and outperforms other methods. Bias and standard deviation plots demonstrated that the proposed method significantly improves the quantitative performance. In particular, biases and standard deviations of two target ROIs were (i) 0.094±1.60/ 0.102±0.88, (ii) 0.098±0.45/ 0.079±0.21 and (iii) 0.086±0.14/ 0.066±0.11 for (i) the conventional direct reconstruction, (ii) direct reconstruction using a dynamic image-based TV and (iii) the proposed method, respectively. Both the bias and standard deviation of the proposed method were the smallest.

Conclusions The penalized direct estimation of parametric image reconstruction outperforms the conventional direct reconstruction methods qualitatively and quantitatively. In the near future, we will further validate the proposed method using clinical data.

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