Maximum-likelihood estimation methods offer many advantages for processing experimental data to extract information, especially when combined with carefully measured calibration data. There are many tasks relevant to x-ray and gamma-ray detection that can be addressed with a new, fast ML-search algorithm that can be implemented in hardware or software. Example applications include gamma-ray event position, energy, and timing estimation, as well as general applications in optical testing and wave-front sensing.
Evaluation of imaging hardware represents a vital component of system design. In small-animal SPECT
imaging, this evaluation has become increasingly diffcult with the emergence of multi-pinhole apertures
and adaptive, or patient-specific, imaging. This paper will describe two methods for hardware evaluation
using reconstructed images. The first method is a rapid technique incorporating a system-specific non-linear,
three-dimensional point response. This point response is easily computed and offers qualitative insight into
an aperture's resolution and artifact characteristics. The second method is an objective assessment of signal
detection in lumpy backgrounds using the channelized Hotelling observer (CHO) with 3D Laguerre-Gauss and
difference-of-Gaussian channels to calculate area under the receiver-operating characteristic curve (AUC).
Previous work presented at this meeting described a unique, small-animal SPECT system (M3R) capable of
operating under a myriad of hardware configurations and ideally suited for image quality studies. Measured
system matrices were collected for several hardware configurations of M3R. The data used to implement
these two methods was then generated by taking simulated objects through the measured system matrices.
The results of these two methods comprise a combination of qualitative and quantitative analysis that is
well-suited for hardware assessment.
An observer performing a detection task analyzes an image and produces a single number, a test statistic, for
that image. This test statistic represents the observers "confidence" that a signal (e.g., a tumor) is present. The
linear observer that maximizes the test-statistic SNR is known as the Hotelling observer. Generally, computation
of the Hotelling SNR, or Hotelling trace, requires the inverse of a large covariance matrix. Recent developments
have resulted in methods for the estimation and inversion of these large covariance matrices with relatively
small numbers of images. The estimation and inversion of these matrices is made possible by a covariance matrix
decomposition that splits the full covariance matrix into an average detector-noise component and a
background-variability component. Because the average detector-noise component is often diagonal and/or
easily estimated, a full-rank, invertible covariance matrix can be produced with few images. We have studied
the bias of estimates of the Hotelling trace using this decomposition for high-detector-noise and low-detector noise
situations. In extremely low-noise situations, this covariance decomposition may result in a significant
bias. We will present a theoretical evaluation of the Hotelling-trace bias, as well as extensive simulation studies.
Proc. SPIE. 5749, Medical Imaging 2005: Image Perception, Observer Performance, and Technology Assessment
KEYWORDS: Imaging systems, Cameras, Sensors, Image processing, Computer simulations, 3D modeling, Monte Carlo methods, Single photon emission computed tomography, Systems modeling, Information operations
The Center for Gamma-Ray Imaging is developing a number of small-animal SPECT imaging systems. These systems consist of multiple stationary detectors, each of which has its own multiple-pinhole collimator. The location of the pinhole plates (i.e., magnification), the number of pinholes within each plate, as well the pinhole locations are all adjustable. The performance of the Bayesian ideal observer sets the upper limit on task performance and can be used to optimize imaging hardware, such as pinhole configurations. Markov-chain Monte Carlo techniques have been developed to compute the ideal observer but require complete knowledge of the statistics of both the imaging system (such as the noise) and the class of random objects being imaged, in addition to an accurate forward model connecting the object to the image. Ideal observer computations using Monte Carlo techniques are burdensome because the forward model must be simulated millions of times for each imaging system. We present an efficient technique for computing the Bayesian ideal observer for multiple-pinhole, small-animal SPECT systems that accounts for both the finite-size of the pinholes and the stochastic nature of the objects being imaged. This technique relies on an efficient, radiometrically correct forward model that maps an object to an image in less than 20 milliseconds. An analysis of the error of the forward model, as well as the results of a ROC study using the ideal observer test statistic is presented.
We have previously utilized lumpy object models and simulated imaging systems in conjunction with the ideal observer to compute figures of merit for hardware optimization. In this paper, we describe the development of methods and phantoms necessary to validate or experimentally carry out these optimizations. Our study was conducted on a four-camera small-animal SPECT system that employs interchangeable pinhole plates to operate under a variety of pinhole configurations and magnifications (representing optimizable system parameters). We developed a small-animal phantom capable of producing random backgrounds for each image sequence. The task chosen for the study was the detection of a 2mm diameter sphere within the phantom-generated random background. A total of 138 projection images were used, half of which included the signal. As our observer, we employed the channelized Hotelling observer (CHO) with Laguerre-Gauss channels. The signal-to-noise (SNR) of this observer was used to compare different system configurations. Results indicate agreement between experimental and simulated data with higher detectability rates found for multiple-camera, multiple-pinhole, and high-magnification systems, although it was found that mixtures of magnifications often outperform systems employing a single magnification. This work will serve as a basis for future studies pertaining to system hardware optimization.