3D reconstruction in PET cameras with irregular sampling and depth of interaction

Abstract

Abstract--We present 3D reconstruction algorithms that address fully 3D tomographic reconstruction using septa-less, stationary, and rectangular cameras. The field of view (FOV) encompasses the entire volume enclosed by detector modules capable of measuring depth of interaction (DOI). The Filtered Backprojection based algorithms incorporate DOI, accommodate irregular sampling, and minimize interpolation in the data by defining lines of response between the measured interaction points. We use fixed-width, evenly spaced radial bins in order to use the FFT, but use irregular angular sampling to minimize the number of unnormalizable zero efficiency sinogram bins. To address persisting low efficiency bins, we perform 2D nearest neighbor radial smoothing, employ a semi-iterative procedure to estimate the unsampled data, and mash the "in plane" and the first oblique projections to reconstruct the 2D image in the 3DRP algorithm. We present artifact free, essentially spatially isotropic images of Monte Carlo data with FWHM resolutions of 1.50 mm, 2.25 mm, and 3.00 mm at the center, in the bulk, and at the edges and corners of the FOV respectively.I. INTRODUCTION E are developing high-resolution PET cameras optimized for breast and axillary node imaging [1]. To maximize camera sensitivity, we a) pack the camera modules into a rectangular shape to minimize gaps between them, b) use the entire volume enclosed by the modules as the imaging field, and c) operate the cameras in exclusively septa-less mode. The geometry of the camera precludes motion during the scan. We therefore measure the depth of interaction (DOI) to increase the sampling rate of the camera and to reconstruct isotropic images free of artifacts, especially radial elongation. We measure the DOI by taking the ratio of the signals received by photodetectors in front and at the back of the scintillation crystals in the detector modules [2]. The DOI is measured in discrete fractions of the length of the crystals, modeling the crystals as being subdivided into 8 smaller crystals or DOI "bins."We have previously presented results of 2D Fourier-based reconstruction methods for Monte Carlo data from a simulated camera [3]. From our 2D studies, we determined that we can nearly eliminate unnormalizable zero efficiency

Positron Emission Mammography

“…The image reconstruction task for this scanner has been subject of an intense work. In an initial stage, image reconstruction was performed with a filtered backprojection based reconstruction algorithm that took into account the existence of DOI information and the irregular angular sampling of the scanner [43,44]. Later, a list mode penalized maximum likelihood algorithm using Gaussian priors was developed [40,45,46].…”

Development of the LBNL positron emission mammography camera

“…We have developed and tested both filtered backprojection reconstruction algorithms (2-D [10] and 3-D [11]) and a list mode regularized maximum likelihood reconstruction algorithm [12] using Monte Carlo data. The rectangular geometry and the capability of measuring DOI result in irregular sampling in the sinogram space.…”

Lesion detection and quantitation of positron emission mammography

“…Dedicated PET, commonly referred to as positron emission mammography (PEM), has been developed for imaging breast [1], [2], [3], [4]. Comparing to whole body PET scanners, PEM scanners are built with much less number of detector modules and have higher sensitivity.…”

“…For this scanner, we have developed image reconstruction algorithms, including a filtered backprojection algorithm [4] and a list mode likelihood reconstruction algorithm [5]. In [6] we have also theoretically studied the resolution and noise properties of the list mode reconstruction.…”