Feasibility Study of Compton Scattering Enhanced Multiple Pinhole Imager for Nuclear Medicine

SPECT system optimization against a discrete parameter space

In this paper, we present an analytical approach for optimizing the design of a static SPECT system or optimizing the sampling strategy with a variable/adaptive SPECT imaging hardware against an arbitrarily given set of system parameters. This approach has three key aspects. First, it is designed to operate over a discretized system parameter space. Second, we have introduced an artificial concept of virtual detector as the basic building block of an imaging system. With a SPECT system described as a collection of the virtual detectors, one can convert the task of system optimization into a process of finding the optimum imaging time distribution (ITD) across all virtual detectors. Thirdly, the optimization problem (finding the optimum ITD) could be solved with a block-iterative approach or other nonlinear optimization algorithms. In essence, the resultant optimum ITD could provide a quantitative measure of the relative importance (or effectiveness) of the virtual detectors and help to identify the system configuration or sampling strategy that leads to an optimum imaging performance. Although we are using SPECT imaging as a platform to demonstrate the system optimization strategy, this development also provides a useful framework for system optimization problems in other modalities, such as positron emission tomography and x-ray computed tomography (Moore et al (2009 IEEE Nucl. Sci. Symp. Conf. Rec. pp 4154-7), Freed et al (2008 Med. Phys. 35 1912-25)).

Adaptive Angular Sampling for SPECT Imaging

This paper presents an analytical approach for performing adaptive angular sampling in single photon emission computed tomography (SPECT) imaging. It allows for a rapid determination of the optimum sampling strategy that minimizes image variance in regions-of-interest (ROIs). The proposed method consists of three key components: (a) a set of close-form equations for evaluating image variance and resolution attainable with a given sampling strategy, (b) a gradient-based algorithm for searching through the parameter space to find the optimum sampling strategy and (c) an efficient computation approach for speeding up the search process. In this paper, we have demonstrated the use of the proposed analytical approach with a single-head SPECT system for finding the optimum distribution of imaging time across all possible sampling angles. Compared to the conventional uniform angular sampling approach, adaptive angular sampling allows the camera to spend larger fractions of imaging time at angles that are more efficient in acquiring useful imaging information. This leads to a significantly lowered image variance. In general, the analytical approach developed in this study could be used with many nuclear imaging systems (such as SPECT, PET and X-ray CT) equipped with adaptive hardware. This strategy could provide an optimized sampling efficiency and therefore an improved image quality.

Illumination pattern optimization for fluorescence tomography: theory and simulation studies

Fluorescence molecular tomography is a powerful tool for 3D visualization of molecular targets and pathways in vivo in small animals. Owing to the high degrees of absorption and scattering of light through tissue, the fluorescence tomographic inverse problem is inherently ill-posed. In order to improve source localization and the conditioning of the light propagation model, multiple sets of data are acquired by illuminating the animal surface with different spatial patterns of near-infrared light. However, the choice of these patterns in most experimental setups is ad hoc and suboptimal. This paper presents a systematic approach for designing efficient illumination patterns for fluorescence tomography. Our objective here is to determine how to optimally illuminate the animal surface so as to maximize the information content in the acquired data. We achieve this by improving the conditioning of the Fisher information matrix. We parameterize the spatial illumination patterns and formulate our problem as a constrained optimization problem that, for a fixed number of illumination patterns, yields the optimal set of patterns. For geometric insight, we used our method to generate a set of three optimal patterns for an optically homogeneous, regular geometrical shape and observed expected symmetries in the result. We also generated a set of six optimal patterns for an optically homogeneous cuboidal phantom set up in the transillumination mode. Finally, we computed optimal illumination patterns for an optically inhomogeneous realistically shaped mouse atlas for different given numbers of patterns. The regularized pseudoinverse matrix, generated using the singular value decomposition, was employed to reconstruct the point spread function for each set of patterns in the presence of a sample fluorescent point source deep inside the mouse atlas. We have evaluated the performance of our method by examining the singular value spectra as well as plots of average spatial resolution versus estimator variance corresponding to different illumination schemes.

Non-Uniform Object-Space Pixelation (NUOP) for Penalized Maximum-Likelihood Image Reconstruction for a Single Photon Emission Microscope System

This paper presents a non-uniform object-space pixelation (NUOP) approach for image reconstruction using the penalized maximum likelihood methods. This method was developed for use with a single photon emission microscope (SPEM) system that offers an ultrahigh spatial resolution for a targeted local region inside mouse brain. In this approach, the object-space is divided with non-uniform pixel sizes, which are chosen adaptively based on object-dependent criteria. These include (a) some known characteristics of a target-region, (b) the associated Fisher Information that measures the weighted correlation between the responses of the system to gamma ray emissions occurred at different spatial locations, and (c) the linear distance from a given location to the target-region. In order to quantify the impact of this non-uniform pixelation approach on image quality, we used the Modified Uniform Cramer-Rao bound (MUCRB) to evaluate the local resolution-variance and bias-variance tradeoffs achievable with different pixelation strategies. As demonstrated in this paper, an efficient object-space pixelation could improve the speed of computation by 1-2 orders of magnitude, whilst maintaining an excellent reconstruction for the target-region. This improvement is crucial for making the SPEM system a practical imaging tool for mouse brain studies. The proposed method also allows rapid computation of the first and second order statistics of reconstructed images using analytical approximations, which is the key for the evaluation of several analytical system performance indices for system design and optimization.

Design and Feasibility Study of a Single Photon Emission Microscope System for Small Animal I-125 Imaging

This paper presents a design study of a single photon emission microscope (SPEM) system for small animal imaging using I-125 labelled radiotracers. This system is based on the use of a very-high resolution gamma camera coupled to a converging non-multiplexing multiple pinhole collimator. This enables one to "zoom" into a small local region inside the object to extract imaging information with a very high spatial resolution and a reasonable sensitivity for gamma rays emitted from this local region. The SPEM system also includes a pinhole (or multiple pinhole) gamma camera that has a full angular coverage of the entire object. The designed imaging spatial resolution for the SPEM system is between 250 μm to 500 μm FWHM.

A modified uniform Cramer-Rao bound for multiple pinhole aperture design

This paper presents a modified Uniform Cramer-Rao bound (UCRB) for studying estimator spatial resolution and variance tradeoffs. We proposed to use a resolution constraint that is imposed on mean gradient vectors of achieved estimators and derived the minimum achievable variance for any estimator satisfies this resolution constraint. This approach partially overcomes the limitations of the former UCRB approach based on a bias-gradient norm constraint. We applied this method in a feasibility study of using multiple pinhole apertures for small animal SPECT imaging applications. The SPECT system studied was based on an existing gamma camera. The achievable spatial resolution and variance tradeoffs for systems with different design parameters, such as number of pinholes and pinhole size, were studied.