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)

Minimax Emission Computed Tomography using High-Resolution Anatomical Side Information and B-Spline Models

In this paper a minimax methodology is presented for combining information from two imaging modalities having different intrinsic spatial resolutions. The focus application is emission computed tomography (ECT), a low-resolution modality for reconstruction of radionuclide tracer density, when supplemented by high-resolution anatomical boundary information extracted from a magnetic resonance image (MRI) of the same imaging volume. The MRI boundary within the two-dimensional (2-D) slice of interest is parameterized by a closed planar curve. The Cramer-Rao (CR) lower bound is used to analyze estimation errors for different boundary shapes. Under a spatially inhomogeneous Gibbs field model for the tracer density a representation for the minimax MRI-enhanced tracer density estimator is obtained. It is shown that the estimator is asymptotically equivalent to a penalized maximum likelihood (PML) estimator with resolution-selective Gibbs penalty. Quantitative comparisons are presented using the iterative space alternating generalized expectation maximization (SAGE-FM) algorithm to implement the PML estimator with and without minimax weight averaging.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85822/1/Fessler86.pd

On regularization methods of EM-Kaczmarz type

We consider regularization methods of Kaczmarz type in connection with the expectation-maximization (EM) algorithm for solving ill-posed equations. For noisy data, our methods are stabilized extensions of the well established ordered-subsets expectation-maximization iteration (OS-EM). We show monotonicity properties of the methods and present a numerical experiment which indicates that the extended OS-EM methods we propose are much faster than the standard EM algorithm.Comment: 18 pages, 6 figures; On regularization methods of EM-Kaczmarz typ

Improving Quantification in Lung PET/CT for the Evaluation of Disease Progression and Treatment Effectiveness

Positron Emission Tomography (PET) allows imaging of functional processes in vivo by measuring the distribution of an administered radiotracer. Whilst one of its main uses is directed towards lung cancer, there is an increased interest in diffuse lung diseases, for which the incidences rise every year, mainly due to environmental reasons and population ageing. However, PET acquisitions in the lung are particularly challenging due to several effects, including the inevitable cardiac and respiratory motion and the loss of spatial resolution due to low density, causing increased positron range. This thesis will focus on Idiopathic Pulmonary Fibrosis (IPF), a disease whose aetiology is poorly understood while patient survival is limited to a few years only. Contrary to lung tumours, this diffuse lung disease modifies the lung architecture more globally. The changes result in small structures with varying densities. Previous work has developed data analysis techniques addressing some of the challenges of imaging patients with IPF. However, robust reconstruction techniques are still necessary to obtain quantitative measures for such data, where it should be beneficial to exploit recent advances in PET scanner hardware such as Time of Flight (TOF) and respiratory motion monitoring. Firstly, positron range in the lung will be discussed, evaluating its effect in density-varying media, such as fibrotic lung. Secondly, the general effect of using incorrect attenuation data in lung PET reconstructions will be assessed. The study will compare TOF and non-TOF reconstructions and quantify the local and global artefacts created by data inconsistencies and respiratory motion. Then, motion compensation will be addressed by proposing a method which takes into account the changes of density and activity in the lungs during the respiration, via the estimation of the volume changes using the deformation fields. The method is evaluated on late time frame PET acquisitions using ¹⁸F-FDG where the radiotracer distribution has stabilised. It is then used as the basis for a method for motion compensation of the early time frames (starting with the administration of the radiotracer), leading to a technique that could be used for motion compensation of kinetic measures. Preliminary results are provided for kinetic parameters extracted from short dynamic data using ¹⁸F-FDG