PET Image Deblurring and Super-Resolution With an MR-Based Joint Entropy Prior

The intrinsically limited spatial resolution of positron emission tomography (PET) confounds image quantitation. This paper presents an image deblurring and super-resolution framework for PET using anatomical guidance provided by high-resolution magnetic resonance (MR) images. The framework relies on image-domain postprocessing of already-reconstructed PET images by means of spatially variant deconvolution stabilized by an MR-based joint entropy penalty function. The method is validated through simulation studies based on the BrainWeb digital phantom, experimental studies based on the Hoffman phantom, and clinical neuroimaging studies pertaining to aging and Alzheimer's disease. The developed technique was compared with direct deconvolution and deconvolution stabilized by a quadratic difference penalty, a total variation penalty, and a Bowsher penalty. The BrainWeb simulation study showed improved image quality and quantitative accuracy measured by contrast-to-noise ratio, structural similarity index, root-mean-square error, and peak signal-to-noise ratio generated by this technique. The Hoffman phantom study indicated noticeable improvement in the structural similarity index (relative to the MR image) and gray-to-white contrast-to-noise ratio. Finally, clinical amyloid and tau imaging studies for Alzheimer's disease showed lowering of the coefficient of variation in several key brain regions associated with two target pathologies.

I. Introduction

Positron emission tomography (PET) is an in vivo medical imaging technique that enables visualization of the distribution of radiotracers that bind to specific molecular targets with functional or physiological significance [1]–[3]. The spatial resolution of PET is intrinsically very limited, thereby hindering its potential as a quantitative imaging tool, particularly for applications involving localized or constricted imaging targets. PET imaging systems capture coincidences of emitted pairs of photons traveling approximately collinearly in opposite directions following positron-electron annihilation events. A number of physical factors, some related to the imaging system hardware, limit PET resolution. These include the non-collinearity of the emitted photon pairs, intercrystal scatter, crystal penetration, and non-zero positron range of PET radionuclides [4]–[6]. Furthermore, it is fairly commonplace to use smoothing penalties during image reconstruction or to apply smoothing filters post-reconstruction for lowering the noise levels in the final images. This image-domain smoothing further compounds the resolution challenge [7]. Attempts to alleviate this challenge have led to the development of sophisticated edge-preserving penalties [8]–[10] or the incorporation of image-domain or sinogram-domain point spread functions (PSFs) in the PET image reconstruction framework [11]–[13]. Some techniques incorporate anatomical information from a segmented magnetic resonance (MR) image to guide the reconstruction process [14]–[19]. In contrast to these reconstruction methods, this paper aims to improve PET quantitation by means of a post-reconstruction processing technique that is applicable to existing images. Post-processing approaches have wider adoptability because they obviate the need for raw data. Furthermore, their relative simplicity resulting from the decoupling of the deblurring and reconstruction problems makes their adoption in a clinical setting easier than that for reconstruction-based tools.