Kenneth M. Hanson

Gradient-based iterative image reconstruction scheme for time-resolved optical tomography

Currently available tomographic image reconstruction schemes for optical tomography (OT) are mostly based on the limiting assumptions of small perturbations and a priori knowledge of the optical properties of a reference medium. Furthermore, these algorithms usually require the inversion of large, full, ill-conditioned Jacobian matrixes. In this work a gradient-based iterative image reconstruction (GIIR) method is presented that promises to overcome current limitations. The code consists of three major parts: (1) A finite-difference, time-resolved, diffusion forward model is used to predict detector readings based on the spatial distribution of optical properties; (2) An objective function that describes the difference between predicted and measured data; (3) An updating method that uses the gradient of the objective function in a line minimization scheme to provide subsequent guesses of the spatial distribution of the optical properties for the forward model. The reconstruction of these properties is completed, once a minimum of this objective function is found. After a presentation of the mathematical background, two- and three-dimensional reconstruction of simple heterogeneous media as well as the clinically relevant example of ventricular bleeding in the brain are discussed. Numerical studies suggest that intraventricular hemorrhages can be detected using the GIIR technique, even in the presence of a heterogeneous background.

Detectability in computed tomographic images

The detection limitations inherent in statistically limited computed tomographic (CT) images are described through the application of signal detection theory. The detectability of large-area, low-contrast objects is shown to be chiefly dependent upon the low-frequency content of the noise power spectral density. For projection data containg uncorrelated noise, the resulting ramplike, low-frequency behavior of the noise power spectrum of CT reconstructions may be conveniently characterized by the number of noise-equivalent x-ray quanta (NEQ) detected in the projection measurements. The NEQ for a given image may be determined either from a measurement of the noise power spectrum or from the noise granularity computed with an appropriate weighting function. A measure of the efficiency of scanner dose utilization is proposed which compares the average dose to that required by an ideal scanner to obtain the same NEQ.

Bayesian approach to limited-angle reconstruction in computed tomography

An arbitrary source function cannot be determined fully from projection data that are limited in number and range of viewing angle. There exists a null subspace in the Hilbert space of possible source functions about which the available projection measurements provide no information. The null-space components of deterministic solutions are usually zero, giving rise to unavoidable artifacts. It is demonstrated that these artifacts may be reduced by a Bayesian maximum a posteriori (MAP) reconstruction method that permits the use of significant a priori information. Since normal distributions are assumed for the a priori and measurement-error probability densities, the MAP reconstruction method presented here is equivalent to the minimum-variance linear estimator with nonstationary mean and covariance ensemble characterizations. A more comprehensive Bayesian approach is suggested in which the ensemble mean and covariance specifications are adjusted on the basis of the measurements.

Local basis-function approach to computed tomography

In the local basis-function approach, a reconstruction is represented as a linear expansion of basis functions, which are arranged on a rectangular grid and possess a local region of support. The basis functions considered here are positive and may overlap. It is found that basis functions based on cubic B-splines offer significant improvements in the calculational accuracy that can be achieved with iterative tomographic reconstruction algorithms. By employing repetitive basis functions, the computational effort involved in these algorithms can be minimized through the use of tabulated values for the line or strip integrals over a single-basis function. The local nature of the basis functions reduces the difficulties associated with applying local constraints on reconstruction values, such as upper and lower limits. Since a reconstruction is specified everywhere by a set of coefficients, display of a coarsely represented image does not require an arbitrary choice of an interpolation function.

Computed tomography using proton energy loss

An experiment has been performed to demonstrate the feasibility of proton computed tomography. The proton energy loss was used to measure the projections of the relative stopping power of the phantom. High quality reconstructions were obtained from scans of 19 cm and 30 cm diameter performance phantoms. Comparison with reconstructions from an EMI CT-5005 X-ray scanner showed the proton technique is more dose efficient by a large factor.

Method of evaluating image-recovery algorithms based on task performance

A method of evaluating image-recovery algorithms is presented that is based on the numerical computation of how well a specified visual task can be performed on the basis of the reconstructed images. A Monte Carlo technique is used to simulate the complete imaging process including generation of scenes appropriate to the desired application, subsequent data taking, image recovery, and performance of the stated task based on the final image. The pseudorandom-simulation process permits one to assess the response of an image-recovery algorithm to many different realizations of the same type of scene. The usefulness of this method is demonstrated through a study of the algebraic reconstruction technique (ART), a tomographic reconstruction algorithm that reconstructs images from their projections. The task chosen for this study is the detection of disks of known size and position. Task performance is rated on the basis of the detectability index derived from the area under the receiver operating characteristic curve. In the imaging situations explored, the use of the nonnegativity constraint in the ART dramatically increases the detectability of objects in some instances, particularly when the data consist of a limited number of noiseless projections. Conversely, the nonnegativity constraint does not improve detectability when the data are complete but noisy.

Proton computed tomography of human specimens

The experimental procedure and results of a comparative study of the imaging characteristics of proton and X-ray CT scans are presented. Scans of a human brain and heart are discussed. The proton produced images are found to be similar in information content while providing a decided dose advantage.

A framework for assessing uncertainties in simulation predictions

Abstract A probabilistic framework is presented for assessing the uncertainties in simulation predictions that arise from model parameters derived from uncertain measurements. A probabilistic network facilitates both conceptualizing and computationally implementing an analysis of a large number of experiments in terms of many intrinsic models in a logically consistent manner. This approach permits one to improve one’s knowledge about the underlying models at every level of the hierarchy of validation experiments.

Model-based image reconstruction from time-resolved diffusion data

This paper addresses the issue of reconstructing the unknown field of absorption and scattering coefficients from time- resolved measurements of diffused light in a computationally efficient manner. The intended application is optical tomography, which has generated considerable interest in recent times. The inverse problem is posed in the Bayesian framework. The maximum a posteriori (MAP) estimate is used to compute the reconstruction. We use an edge-preserving generalized Gaussian Markov random field to model the unknown image. The diffusion model used for the measurements is solved forward in time using a finite-difference approach known as the alternating-directions implicit method. This method requires the inversion of a tridiagonal matrix at each time step and is therefore of O(N) complexity, where N is the dimensionality of the image. Adjoint differentiation is used to compute the sensitivity of the measurements with respect to the unknown image. The novelty of our method lies in the computation of the sensitivity since we can achieve it in O(N) time as opposed to O(N2) time required by the perturbation approach. We present results using simulated data to show that the proposed method yields superior quality reconstructions with substantial savings in computation.

Introduction to Bayesian image analysis

The basic concepts in the application of Bayesian methods to image analysis are introduced. The Bayesian approach has benefits in image analysis and interpretation because it permits the use of prior knowledge concerning the situation under study. The fundamental ideas are illustrated with a number of examples ranging from a problem in one and two dimensions to large problems in image reconstruction that make use of sophisticated prior information.