Fourier rebinning and consistency equations for time-of-flight PET planograms

3D directional gradient L0 norm minimization guided limited-view reconstruction in a dual-panel positron emission mammography

BACKGROUND

Dual-panel PET is often used for local organ imaging, especially breast imaging, due to its simple structure, high sensitivity, good in-plane resolution, and straightforward fusion with other imaging modalities. Nevertheless, because of data loss caused by the dual-panel structure, using conventional image reconstruction methods results in limited-view artifacts and low image quality in dual-panel positron emission mammography (PEM), which may seriously affect the diagnosis. To mitigate the limited-view artifacts in the dual-panel PEM, we propose a 3D directional gradient L₀ norm minimization (3D-DL₀) guided reconstruction method.

METHODS

The detailed derivation and reasonable simplification of the 3D-DL₀ algorithm are given first. Using this algorithm, we then obtain a prior image with edge recovery but contrast loss. To limit the solution space, the 3D-DL₀ prior is introduced into the Maximum a Posteriori reconstruction. Meanwhile, a space-invariant point spread function is also implemented to restore image contrast and boundaries. Finally, the reconstructed images with limited-view artifact suppression are obtained. The proposed method was evaluated using the data acquired from physical phantoms and patients with breast tumors on a commercial dual-panel PET system.

RESULTS

The qualitative and quantitative studies for phantom data and the blind reader study for clinical data show that the proposed method is more effective in reaching a balance between artifact elimination and image contrast improvement compared with various limited-view reconstruction methods. In addition, the iteration process of the method is proved convergent numerically.

CONCLUSIONS

The image quality improvement confirms the potential value of the proposed reconstruction algorithm to address the limited-view problem, and thus improve diagnostic accuracy in dual-panel PEM imaging.

A backprojection kernel (KRNL3D) for very-wide-aperture 3D tomography applied to PET with Multigrid for precise use of time-of-flight data

In 'KRNL3D' we derive a kernel functionK(y₁,y₂,φ) whose backprojections from all directions (θ,φ) in the spherical band∣φ∣<φ¯maxon the celestial sphere, when integrated with respect to solid angle, yieldρ, the 3D Gaussian point response function (PRF) of radius 1. ThisK, when convolved against line integral data from an unknown density functionf, yields an integral formula for the 'mollification'ff=ρ∗f, which is a slightly blurred version off, and which stabilizes the mild ill-posedness. Applied to positron emission tomography that backprojection reconstruction occurs stochastically and one emission event at a time, after needed data corrections. We describe Octave (≈Matlab) codes to tabulateKand to test its use with a large apertureφ¯max=π/3orπ/6. 'KRNL3D-TOF' truncates backprojection to a cylindrical patch about the TOF approximate location of each event. These 'backplacements' decrease the computational cost and limit noise and streaking in one region from contaminating the reconstruction in more distant regions. They also retain the ability to count emission events in an isolated blob despiteverylow event counts, a valuable feature fordynamicstudies of metabolic processes. 'Multigrid' allows further reduction in the radius and lengths of the cylinders, thereby enabling even moreprecise use of the TOF information. This precision should be especially important as researchers decrease the TOF uncertainty in newer generation scanners. Finally, we discuss 'further work' that needs to be done. Our codes are being made freely available athttps://github.com/keithmillerberkeley/PET-codes.

Time of Flight in Perspective: Instrumental and Computational Aspects of Time Resolution in Positron Emission Tomography

The first time-of-flight positron emission tomography (TOF-PET) scanners were developed as early as in the 1980s. However, the poor light output and low detection efficiency of TOF-capable detectors available at the time limited any gain in image quality achieved with these TOF-PET scanners over the traditional non-TOF PET scanners. The discovery of LSO and other Lu-based scintillators revived interest in TOF-PET and led to the development of a second generation of scanners with high sensitivity and spatial resolution in the mid-2000s. The introduction of the silicon photomultiplier (SiPM) has recently yielded a third generation of TOF-PET systems with unprecedented imaging performance. Parallel to these instrumentation developments, much progress has been made in the development of image reconstruction algorithms that better utilize the additional information provided by TOF. Overall, the benefits range from a reduction in image variance (SNR increase), through allowing joint estimation of activity and attenuation, to better reconstructing data from limited angle systems. In this work, we review these developments, focusing on three broad areas: 1) timing theory and factors affecting the time resolution of a TOF-PET system; 2) utilization of TOF information for improved image reconstruction; and 3) quantification of the benefits of TOF compared to non-TOF PET. Finally, we offer a brief outlook on the TOF-PET developments anticipated in the short and longer term. Throughout this work, we aim to maintain a clinically driven perspective, treating TOF as one of multiple (and sometimes competitive) factors that can aid in the optimization of PET imaging performance.

2D feasibility study of joint reconstruction of attenuation and activity in limited angle TOF-PET

Several research groups are studying organ-dedicated limited angle positron emission tomography (PET) systems to optimize performance-cost ratio, sensitivity, access to the patient and/or flexibility. Often open systems are considered, typically consisting of two detector panels of various sizes. Such systems provide incomplete sampling due to limited angular coverage and/or truncation, which leads to artefacts in the reconstructed activity images. In addition, these organ-dedicated PET systems are usually stand-alone systems, and as a result, no attenuation information can be obtained from anatomical images acquired in the same imaging session. It has been shown that the use of time-of-flight information reduces incomplete data artefacts and enables the joint estimation of the activity and the attenuation factors. In this work, we explore with simple 2D simulations the performance and stability of a joint reconstruction algorithm, for imaging with a limited angle PET system. The reconstruction is based on the so-called MLACF (Maximum Likelihood Attenuation Correction Factors) algorithm and uses linear attenuation coefficients in a known-tissue-class region to obtain absolute quantification. Different panel sizes and different time-of-flight (TOF) resolutions are considered. The noise propagation is compared to that of MLEM reconstruction with exact attenuation correction (AC) for the same PET system. The results show that with good TOF resolution, images of good visual quality can be obtained. If also a good scatter correction can be implemented, quantitative PET imaging will be possible. Further research, in particular on scatter correction, is required.

One-View Time-of-Flight Positron Emission Tomography Reconstruction

The time-of-flight (TOF) information makes Orlov's condition not necessary for positron emission tomography (PET) imaging. One-view imaging has never been attempted before. This paper investigates whether one-view imaging is possible. We claim that it is possible to obtain an image with measurements from only one-view, provided the TOF time resolution is good enough and the photon counts are high enough. In fact, the image value at a point can be reconstructed by measurements along one line-of-response (LOR) that passes through the point of interest. The region-of-interest (ROI) can be reconstructed with ray-by-ray deblurring methods, which make TOF PET a local tomography system. One-view imaging is a severely ill-posed problem if the TOF resolution is not good enough. One indicator of an ill-posed problem is the ringing artifacts in the reconstruction. We show that ringing artifacts can be eliminated by using the nonnegativity constraint for the dot-like objects with a zero background.

Practical joint reconstruction of activity and attenuation with autonomous scaling for time-of-flight PET

Recent research has showed that attenuation images can be determined from emission data, jointly with activity images, up to a scaling constant when utilizing the time-of-flight (TOF) information. We aim to develop practical CT-less joint reconstruction for clinical TOF PET scanners to obtain quantitatively accurate activity and attenuation images. In this work, we present a joint reconstruction of activity and attenuation based on MLAA (maximum likelihood reconstruction of attenuation and activity) with autonomous scaling determination and joint TOF scatter estimation from TOF PET data. Our idea for scaling is to use a selected volume of interest (VOI) in a reconstructed attenuation image with known attenuation, e.g. a liver in patient imaging. First, we construct a unit attenuation medium which has a similar, though not necessarily the same, support to the imaged emission object. All detectable LORs intersecting the unit medium have an attenuation factor of e -1≈ 0.3679, i.e. the line integral of linear attenuation coefficients is one. The scaling factor can then be determined from the difference between the reconstructed attenuation image and the known attenuation within the selected VOI normalized by the unit attenuation medium. A four-step iterative joint reconstruction algorithm is developed. In each iteration, (1) first the activity is updated using TOF OSEM from TOF list-mode data; (2) then the attenuation image is updated using XMLTR-a extended MLTR from non-TOF LOR sinograms; (3) a scaling factor is determined based on the selected VOI and both activity and attenuation images are updated using the estimated scaling; and (4) scatter is estimated using TOF single scatter simulation with the jointly reconstructed activity and attenuation images. The performance of joint reconstruction is studied using simulated data from a generic whole-body clinical TOF PET scanner and a long axial FOV research PET scanner as well as 3D experimental data from the PennPET Explorer scanner. We show that the proposed joint reconstruction with proper autonomous scaling provides low bias results comparable to the reference reconstruction with known attenuation.

Analytic time-of-flight positron emission tomography reconstruction: three-dimensional case

In a positron emission tomography (PET) scanner, the time-of-flight (TOF) information gives us rough event position along the line-of-response (LOR). Using the TOF information for PET image reconstruction is able to reduce image noise. The state-of-the-art TOF PET image reconstruction uses iterative algorithms. This study introduces an analytic TOF PET algorithm that focuses on three-dimensional (3D) reconstruction. The proposed algorithm is in the form of backprojection filtering, in which the backprojection is performed first by using a time-resolution profile function, and then a 3D filter is applied to the backprojected image. For the list-mode data, the backprojection is carried out in the event-by-event fashion, and the timing resolution determined weighting function is used along the projection LOR. Computer simulations are carried out to verify the feasibility of the proposed algorithm.

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.

Analytic time-of-flight positron emission tomography reconstruction: two-dimensional case

In a positron emission tomography (PET) scanner, the time-of-flight (TOF) information gives us rough event position along the line-of-response (LOR). Using the TOF information for PET image reconstruction is able to reduce image noise. The state-of-the-art TOF PET image reconstruction uses iterative algorithms. Analytical image reconstruction algorithm exits for TOF PET which emulates the iterative Landweber algorithm. This paper introduces such an algorithm, focusing on two-dimensional (2D) reconstruction. The proposed algorithm is in the form of backprojection filtering, in which the backprojection is performed first, and then a 2D filter is applied to the backprojected image. For the list-mode data, the backprojection is carried out in the event-by-event fashion, and a profile function may be used along the projection LOR. The 2D filter depends on the TOF timing resolution as well as the backprojection profile function. In order to emulate the iterative algorithm effects, a Fourier-domain window function is suggested. This window function has a parameter, k, which corresponds to the iteration number in an iterative algorithm.