Image-based Modeling of PSF Deformation with Application to Limited Angle PET Data.

The point-spread-functions (PSFs) of reconstructed images can be deformed due to detector effects such as resolution blurring and parallax error, data acquisition geometry such as insufficient sampling or limited angular coverage in dual-panel PET systems, or reconstruction imperfections/simplifications. PSF deformation decreases quantitative accuracy and its spatial variation lowers consistency of lesion uptake measurement across the imaging field-of-view (FOV). This can be a significant problem with dual panel PET systems even when using TOF data and image reconstruction models of the detector and data acquisition process. To correct for the spatially variant reconstructed PSF distortions we propose to use an image-based resolution model (IRM) that includes such image PSF deformation effects. Originally the IRM was mostly used for approximating data resolution effects of standard PET systems with full angular coverage in a computationally efficient way, but recently it was also used to mitigate effects of simplified geometric projectors. Our work goes beyond this by including into the IRM reconstruction imperfections caused by combination of the limited angle, parallax errors, and any other (residual) deformation effects and testing it for challenging dual panel data with strongly asymmetric and variable PSF deformations. We applied and tested these concepts using simulated data based on our design for a dedicated breast imaging geometry (B-PET) consisting of dual-panel, time-of-flight (TOF) detectors. We compared two image-based resolution models; i) a simple spatially invariant approximation to PSF deformation, which captures only the general PSF shape through an elongated 3D Gaussian function, and ii) a spatially variant model using a Gaussian mixture model (GMM) to more accurately capture the asymmetric PSF shape in images reconstructed from data acquired with the B-PET scanner geometry. Results demonstrate that while both IRMs decrease the overall uptake bias in the reconstructed image, the second one with the spatially variant and accurate PSF shape model is also able to ameliorate the spatially variant deformation effects to provide consistent uptake results independent of the lesion location within the FOV.

Effects of TOF Resolution Models on Edge Artifacts in PET Reconstruction from Limited-Angle Data.

Limited-angle data, such as data obtained from a dual-panel Breast-PET scanner, result in substantial image blur in directions coinciding with the missing cone of the image spectrum. On systems with time-of-flight (TOF) capabilities, this blur is reduced as given by the TOF uncertainty, with the image spectrum being correspondingly expanded into the missing spectral cone. Modeling of the TOF uncertainty in the reconstruction is expected to deconvolve this residual TOF blurring. We have however observed that, as a tradeoff, this TOF de-blurring process also introduces ringing artifacts at the edges, analogous to the edge effects observed with line-of-response (LOR) resolution modeling, which attempts to deconvolve the blur due to detector resolution effects. However, in the former case, the ringing artifacts are much wider due to the spatial extent of the TOF uncertainty as compared to the width of typical LOR resolution blur. We illustrate and investigate the effects of using matched, as well as under-modeled and over-modeled, TOF kernels on edge artifacts in reconstruction from limited-angle data, and compare them with TOF reconstructions of complete data. Although for the conventional data with full angular coverage the reconstruction is fairly insensitive to the exact size of the TOF kernel and TOF modeling does not produce ringing artifacts, it is not the case for the limited-angle data. We show that it is important to use some form of regularization of the TOF uncertainty deconvolution process within reconstruction of the limited-angle data, such as decreasing the TOF kernel size.

A separable quadratic surrogate total variation minimization algorithm for accelerating accurate CT reconstruction from few-views and limited-angle data.

PURPOSE: Total variation minimization (TVM) is a popular and useful method for accurate CT reconstruction from few-views and limited-angle data. However, the optimization procedure of previous TVM-based algorithms is very time-consuming. The purpose of this paper was to accelerate the high image quality CT reconstruction from few-views and limited-angle data. METHOD: A new optimization algorithm based on the optimization transfer principle is proposed. The proposed algorithm uses TVM as the regularization term of the cost function that ensures the quality of the CT image reconstructed from few-views and limited-angle data. Additionally, half of the square of the difference between the original projection and the forward projection is used as the fidelity term. We then proved that the regularization term, i.e., 2-norm TV, is a convex function. Based on the convexity of the regularization and fidelity terms, a separable quadratic surrogate (SQS) function was proposed to substitute the regularization and fidelity terms. The solution of the cost function can be obtained by minimizing the SQS function and building the next SQS function at the minimum point. RESULTS: Both numerical simulations and simulations using real experimental data showed that the proposed algorithm reconstruct high-quality CT image from few-views and limited-angle data. The differences between the image reconstructed by the proposed algorithm and the images reconstructed by the previous algorithms are very small. However, the proposed algorithm required less than 1/10 time of the computational time of the previous algorithms. The image quality is not assessed in a rigorous way. CONCLUSION: The proposed algorithm can greatly accelerate the accurate CT reconstruction from few-views and limited-angle data relative to previous algorithms.