Maximum Likelihood Event Estimation and List-mode Image Reconstruction on GPU Hardware

Null functions in three-dimensional imaging of alpha and beta particles

Null functions of an imaging system are functions in the object space that give exactly zero data. Hence, they represent the intrinsic limitations of the imaging system. Null functions exist in all digital imaging systems, because these systems map continuous objects to discrete data. However, the emergence of detectors that measure continuous data, e.g. particle-processing (PP) detectors, has the potential to eliminate null functions. PP detectors process signals produced by each particle and estimate particle attributes, which include two position coordinates and three components of momentum, as continuous variables. We consider Charged-Particle Emission Tomography (CPET), which relies on data collected by a PP detector to reconstruct the 3D distribution of a radioisotope that emits alpha or beta particles, and show empirically that the null functions are significantly reduced for alpha particles if ≥3 attributes are measured or for beta particles with five attributes measured.

Charged-particle emission tomography

Purpose

Conventional charged‐particle imaging techniques — such as autoradiography — provide only two‐dimensional (2D) black ex vivo images of thin tissue slices. In order to get volumetric information, images of multiple thin slices are stacked. This process is time consuming and prone to distortions, as registration of 2D images is required. We propose a direct three‐dimensional (3D) autoradiography technique, which we call charged‐particle emission tomography (CPET). This 3D imaging technique enables imaging of thick tissue sections, thus increasing laboratory throughput and eliminating distortions due to registration. CPET also has the potential to enable in vivo charged‐particle imaging with a window chamber or an endoscope.

Methods

Our approach to charged‐particle emission tomography uses particle‐processing detectors (PPDs) to estimate attributes of each detected particle. The attributes we estimate include location, direction of propagation, and/or the energy deposited in the detector. Estimated attributes are then fed into a reconstruction algorithm to reconstruct the 3D distribution of charged‐particle‐emitting radionuclides. Several setups to realize PPDs are designed. Reconstruction algorithms for CPET are developed.

Results

Reconstruction results from simulated data showed that a PPD enables CPET if the PPD measures more attributes than just the position from each detected particle. Experiments showed that a two‐foil charged‐particle detector is able to measure the position and direction of incident alpha particles.

Conclusions

We proposed a new volumetric imaging technique for charged‐particle‐emitting radionuclides, which we have called charged‐particle emission tomography (CPET). We also proposed a new class of charged‐particle detectors, which we have called particle‐processing detectors (PPDs). When a PPD is used to measure the direction and/or energy attributes along with the position attributes, CPET is feasible.

Joint reconstruction of activity and attenuation map using LM SPECT emission data

Attenuation and scatter correction in single photon emission computed tomography (SPECT) imaging often requires a computed tomography (CT) scan to compute the attenuation map of the patient. This results in increased radiation dose for the patient, and also has other disadvantages such as increased costs and hardware complexity. Attenuation in SPECT is a direct consequence of Compton scattering, and therefore, if the scattered photon data can give information about the attenuation map, then the CT scan may not be required. In this paper, we investigate the possibility of joint reconstruction of the activity and attenuation map using list-mode (LM) SPECT emission data, including the scattered-photon data. We propose a path-based formalism to process scattered-photon data. Following this, we derive analytic expressions to compute the Cramér-Rao bound (CRB) of the activity and attenuation map estimates, using which, we can explore the fundamental limit of information-retrieval capacity from LM SPECT emission data. We then suggest a maximum-likelihood (ML) scheme that uses the LM emission data to jointly reconstruct the activity and attenuation map. We also propose an expectation-maximization (EM) algorithm to compute the ML solution.

List-mode MLEM Image Reconstruction from 3D ML Position Estimates

Current thick detectors used in medical imaging allow recording many attributes, such as the 3D location of interaction within the scintillation crystal and the amount of energy deposited. An efficient way of dealing with these data is by storing them in list-mode (LM). To reconstruct the data, maximum-likelihood expectation-maximization (MLEM) is efficiently applied to the list-mode data, resulting in the list-mode maximum-likelihood expectation-maximization (LMMLEM) reconstruction algorithm.In this work, we consider a PET system consisting of two thick detectors facing each other. PMT outputs are collected for each coincidence event and are used to perform 3D maximum-likelihood (ML) position estimation of location of interaction. The mathematical properties of the ML estimation allow accurate modeling of the detector blur and provide a theoretical framework for the subsequent estimation step, namely the LMMLEM reconstruction. Indeed, a rigorous statistical model for the detector output can be obtained from calibration data and used in the calculation of the conditional probability density functions for the interaction location estimates.Our implementation of the 3D ML position estimation takes advantage of graphics processing unit (GPU) hardware and permits accurate real-time estimates of position of interaction. The LMMLEM algorithm is then applied to the list of position estimates, and the 3D radiotracer distribution is reconstructed on a voxel grid.

Maximum-Likelihood Estimation With a Contracting-Grid Search Algorithm

A fast search algorithm capable of operating in multi-dimensional spaces is introduced. As a sample application, we demonstrate its utility in the 2D and 3D maximum-likelihood position-estimation problem that arises in the processing of PMT signals to derive interaction locations in compact gamma cameras. We demonstrate that the algorithm can be parallelized in pipelines, and thereby efficiently implemented in specialized hardware, such as field-programmable gate arrays (FPGAs). A 2D implementation of the algorithm is achieved in Cell/BE processors, resulting in processing speeds above one million events per second, which is a 20× increase in speed over a conventional desktop machine. Graphics processing units (GPUs) are used for a 3D application of the algorithm, resulting in processing speeds of nearly 250,000 events per second which is a 250× increase in speed over a conventional desktop machine. These implementations indicate the viability of the algorithm for use in real-time imaging applications.