Quantitative Statistical Methods for Image Quality Assessment

Quantitative measures of image quality and reliability are critical for both qualitative interpretation and quantitative analysis of medical images. While, in theory, it is possible to analyze reconstructed images by means of Monte Carlo simulations using a large number of noise realizations, the associated computational burden makes this approach impractical. Additionally, this approach is less meaningful in clinical scenarios, where multiple noise realizations are generally unavailable. The practical alternative is to compute closed-form analytical expressions for image quality measures. The objective of this paper is to review statistical analysis techniques that enable us to compute two key metrics: resolution (determined from the local impulse response) and covariance. The underlying methods include fixed-point approaches, which compute these metrics at a fixed point (the unique and stable solution) independent of the iterative algorithm employed, and iteration-based approaches, which yield results that are dependent on the algorithm, initialization, and number of iterations. We also explore extensions of some of these methods to a range of special contexts, including dynamic and motion-compensated image reconstruction. While most of the discussed techniques were developed for emission tomography, the general methods are extensible to other imaging modalities as well. In addition to enabling image characterization, these analysis techniques allow us to control and enhance imaging system performance. We review practical applications where performance improvement is achieved by applying these ideas to the contexts of both hardware (optimizing scanner design) and image reconstruction (designing regularization functions that produce uniform resolution or maximize task-specific figures of merit)

Efficient Resource Allocation Schemes for Search.

This thesis concerns the problem of efficient resource allocation under constraints. In many applications a finite budget is used and allocating it efficiently can improve performance. In the context of medical imaging the constraint is exposure to ionizing radiation, e.g., computed tomography (CT). In radar and target tracking time spent searching a particular region before pointing the radar to another location or transmitted energy level may be limited. In airport security screening the constraint is screeners' time. This work addresses both static and dynamic resource allocation policies where the question is: How a budget should be allocated to maximize a certain performance criterion. In addition, many of the above examples correspond to a needle-in-a-haystack scenario. The goal is to find a small number of details, namely `targets', spread out in a far greater domain. The set of `targets' is named a region of interest (ROI). For example, in airport security screening perhaps one in a hundred travelers carry prohibited item and maybe one in several millions is a terrorist or a real threat. Nevertheless, in most aforementioned applications the common resource allocation policy is exhaustive: all possible locations are searched with equal effort allocation to spread sensitivity. A novel framework to deal with the problem of efficient resource allocation is introduced. The framework consists of a cost function trading the proportion of efforts allocated to the ROI and to its complement. Optimal resource allocation policies minimizing the cost are derived. These policies result in superior estimation and detection performance compared to an exhaustive resource allocation policy. Moreover, minimizing the cost has a strong connection to minimizing both probability of error and the CR bound on estimation mean square error. Furthermore, it is shown that the allocation policies asymptotically converge to the omniscient allocation policy that knows the location of the ROI in advance. Finally, a multi-scale allocation policy suitable for scenarios where targets tend to cluster is introduced. For a sparse scenario exhibiting good contrast between targets and background this method achieves significant performance gain yet tremendously reduces the number of samples required compared to an exhaustive search.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60698/1/bashan_1.pd

Estimation of the Image Quality in Emission Tomography: Application to Optimization of SPECT System Design

In Emission Tomography the design of the Imaging System has a great influence on the quality of the output image. Optimisation of the system design is a difficult problem due to the computational complexity and to the challenges in its mathematical formulation. In order to compare different system designs, an efficient and effective method to calculate the Image Quality is needed. In this thesis the statistical and deterministic methods for the calculation of the uncertainty in the reconstruction are presented. In the deterministic case, the Fisher Information Matrix (FIM) formalism can be employed to characterize such uncertainty. Unfortunately, computing, storing and inverting the FIM is not feasible with 3D imaging systems. In order to tackle the problem of the computational load in calculating the inverse of the FIM a novel approximation, that relies on a sub-sampling of the FIM, is proposed. The FIM is calculated over a subset of voxels arranged in a grid that covers the whole volume. This formulation reduces the computational complexity in inverting the FIM but nevertheless accounts for the global interdependence between the variables, for the acquisition geometry and for the object dependency. Using this approach, the noise properties as a function of the system geometry parameterisation were investigated for three different cases. In the first study, the design of a parallel-hole collimator for SPECT is optimised. The new method can be applied to evaluating problems like trading-off collimator resolution and sensitivity. In the second study, the reconstructed image quality was evaluated in the case of truncated projection data; showing how the subsampling approach is very accurate for evaluating the effects of missing data. Finally, the noise properties of a D-SPECT system were studied for varying acquisition protocols; showing how the new method is well-suited to problems like optimising adaptive data sampling schemes

Time-Encoded Thermal Neutron Imaging using Large-Volume Pixelated CdZnTe Detectors

CdZnTe detectors are commonly used for room-temperature gamma-ray spectroscopy and imaging in a variety of applications including nuclear security, nuclear medicine, and space science. The material's long-established sensitivity to thermal neutrons, however, is less utilized. Generally speaking, the performance of neutron detectors based on the Cd capture reaction is limited by the physical nature of the reaction itself. Multiple gamma rays are emitted promptly following each capture event, which consists of one realization of many possible combinations of gamma-ray lines. Although the gamma-ray cascade can reduce photopeak efficiency in conventional devices, this work demonstrates that pixelated CdZnTe can recover losses by reading out each gamma-ray interaction separately. Including coincident events, the measured 558-keV photopeak efficiency for a 3 by 3 array of 2 cm by 2 cm by 1.5 cm pixelated CdZnTe detectors was about 10%, i.e., ten 558 keV photopeak events per 100 incident thermal neutrons. This was in good agreement with its calculated value. Initial measurements also show that neutron-gamma discrimination beyond simple energy windowing is possible when incorporating the 3-D interaction locations of gamma rays provided by the pixelated readout. In this work, we developed and successfully demonstrated a proof-of-principle time-encoding system for thermal neutron imaging using pixelated CdZnTe. Time encoding was chosen because it is not limited by the detector's position resolution or spatial extent. These issues are exacerbated by Cd capture due to the dispersal of cascade gamma rays throughout the device. The system was first tested using a MURA-based, W-metal mask with both Co-57 and U-metal gamma-ray sources. About 0.3-degree angular resolution within a 22-degree field of view was achieved for gamma rays, and good image uniformity was observed for objects of moderate spatial extent. A MURA-based thermal neutron mask was then constructed using 1-mm-thick BN tiles, which attained roughly 4-degree angular resolution within a 50-degree field of view when measuring HDPE-moderated Cf-252. Two different thermal neutron imaging measurements were taken, with one and two moderators within the field of view. Reconstructed images corresponded well with the 3-D locations and sizes of moderators, and had predictable signal-to-noise ratio. We believe the experimental imaging results provided here warrant further studies on the use of CdZnTe for other thermal neutron imaging scenarios.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137131/1/stbrow_1.pd

Statistical Performance Evaluation, System Modeling, Distributed Computation, and Signal Pattern Matching for a Compton Medical Imaging System.

Radionuclide cancer therapy requires imaging radiotracers that concentrate in tumors and emit high energy charged particles that kill tumor cells. These tracers, such as 131I, generally emit high energy photons that need to be imaged to estimate tumor dose and changes in size during treatment. This research describes the performance of a dual-planar silicon-based Compton imaging system and compares it to a conventional parallel-hole collimated Anger camera with high energy general purpose lead collimator for imaging photons emitted from 131I. The collimated Anger camera imposes a tradeoff between resolution and sensitivity due to the mechanical collimation. As the energy of photons exceed 364keV, increased septal penetration and scattering further degrade the imaging performance. Simulations of the Anger camera and the Compton imaging system demonstrate a 20-fold advantage in detection efficiency and higher spatial resolution for detecting high energy photons by the Compton camera since it decouples the tradeoff. The system performance and comparision are analyzed using the modified uniform Cramer-Rao bound algorithms we developed along with the Monte Carlo calculations and system modeling. The bound show that the effect of Doppler broadening is the limiting factor for Compton camera performance for imaging 364keV photons. Performance of the two systems was compared and analyzed by simulating a 2D disk with uniform activities. For the case in which the two imaging systems detected the same number of events, the proposed Compton imaging system has lower image variance than the Anger camera with HEGP when the FWHM of the desired point source response is less than 1.2 cm. This advantage was also demonstrated by imaging and reconstructing a 2D hot spot phantom. In addition to the performance analysis, the distributed Maximum Likelihood Maximization Expectation algorithm with chessboard data partition was evaluated for speeding up image reconstruction for the Compton imaging system. A 1 x 64 distributed computing system speeded computation by about a factor of 22 compared to a single processor. Finally, a real-time signal processing and pattern matching system employing state-of-the-art digital electronics is described for solving problems of event pile-up raised by high photon count rate in the second detector.Ph.D.Biomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60851/1/lhan_1.pd