Thomas J. Hebert

Adaptive optics scanning laser ophthalmoscopy.

We present the first scanning laser ophthalmoscope that uses adaptive optics to measure and correct the high order aberrations of the human eye. Adaptive optics increases both lateral and axial resolution, permitting axial sectioning of retinal tissue in vivo. The instrument is used to visualize photoreceptors, nerve fibers and flow of white blood cells in retinal capillaries.

Bayesian pixel classification using spatially variant finite mixtures and the generalized EM algorithm

A spatially variant finite mixture model is proposed for pixel labeling and image segmentation. For the case of spatially varying mixtures of Gaussian density functions with unknown means and variances, an expectation-maximization (EM) algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities, An a priori density function is formulated for the spatially variant mixture weights. A generalized EM algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived. This algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent. Gaussian densities have been used for simplicity, but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities. The accuracy of the algorithm is quantitatively evaluated through Monte Carlo simulation, and its performance is qualitatively assessed via experimental images from computerized tomography (CT) and magnetic resonance imaging (MRI).

Statistic-based MAP image-reconstruction from Poisson data using Gibbs priors

A statistical method for selecting the Gibbs parameter in MAP image restoration from Poisson data using Gibbs priors is presented. The Gibbs parameter determines the degree to which the prior influences the restoration. The presented method yields a MAP restored image, minimally influenced by the prior, for which a statistic falls within an appropriate confidence interval. The method assumes that a close approximation to the blurring function is known. A simple iterative feedback algorithm is presented to statistically select the parameter as the MAP image restoration is being performed. This algorithm is heuristically based on a model reference control formulation, but it requires only a minimal number of iterations for the parameter to settle to its statistically specified value. The performance of the statistical method for selecting the prior parameter and that of the iterative feedback algorithm are demonstrated using both 2-D and 3-D images. >

Numerical evaluation of methods for computing tomographic projections

Methods for computing forward/back projections of 2D images can be viewed as numerical integration techniques. The accuracy of any ray-driven projection method can be improved by increasing the number of ray-paths that are traced per projection bin. The accuracy of pixel-driven projection methods can be increased by dividing each pixel into a number of smaller sub-pixels and projecting each sub-pixel. The authors compare 4 competing methods of computing forward/back projections: bilinear interpolation, ray-tracing, pixel-driven projection based upon sub-pixels, and pixel-driven projection based upon circular, rather than square, pixels. This latter method is equivalent to a fast, bi-nonlinear interpolation. These methods and the choice of the number of ray-paths per projection bin or the number of sub-pixels per pixel present a trade-off between computational speed and accuracy. To solve the problem of assessing backprojection accuracy, the analytical inverse Fourier transform of the ramp filtered forward projection of the Shepp and Logan head phantom is derived. >

Optical slicing of human retinal tissue in vivo with the adaptive optics scanning laser ophthalmoscope

We present imaging results in human retinal tissue in vivo that allowed us to determine the axial resolution of the adaptive optics scanning laser ophthalmoscope (AOSLO). The instrument is briefly described, and the imaging results from human subjects are compared with (a) the estimated axial resolution values for a diffraction-limited, double-pass instrument and (b) the measured one for a calibrated diffuse retinal model. The comparison showed that the measured axial resolution, as obtained from optical sectioning of human retinas in vivo, can be as low as 71 microm for a 50 microm confocal pinhole after focusing a 3.5 mm beam with a 100 mm focal-length lens. The axial resolution values typically fall between the predictions from numerical models for diffuse and specular reflectors. This suggests that the reflection from the retinal blood vessel combines diffuse and specular components. This conclusion is supported by the almost universal interpretation that the image of a cylindrical blood vessel exhibits a bright reflection along its apex that is considered specular. The enhanced axial resolution achieved through use of adaptive optics leads to an improvement in the volume resolution of almost 2 orders of magnitude when compared with a conventional scanning laser ophthalmoscope and almost a factor of 3 better than commercially available optical coherence tomographic instruments.

Fast methods for including attenuation in the EM algorithm

A fast approach to including attenuation in iterative maximum-likelihood and least-squares algorithms for single-photon-emission computed tomography (SPECT) is presented. Ray-tracing and summing of attenuation coefficients are replaced by the use of two lookup tables, one to compute attenuated ray path integrals based on a set of polar grid points and one to perform polar-to-rectangular transformations. The resulting algorithm implements a spatial average which is comparable in accuracy to ray-tracing with rectangular pixels, yet requires less than one sixteenth the CPU time. >

A union of deterministic and stochastic methods for image reconstruction

A reconstruction approach which combines the optimality of the EM (expectation maximization) maximum likelihood algorithm with the robustness of the FBP (filtered backprojection) algorithm has been formulated. This approach produces high-resolution reconstructions and requires only fractional computation time as compared to maximum likelihood reconstruction. Reconstructions from a patient study are presented.<<ETX>>

The GEM MAP algorithm with 3-D SPECT system response

In single photon emission computed tomography (SPECT), every reconstruction algorithm must use some model for the response of the gamma camera to emitted gamma-rays. The true camera response is both spatially variant and object dependent. These two properties result from the effects of scatter, septal penetration, and attenuation, and they forestall determination of the true response with any precision. This motivates the investigation of the performance of reconstruction algorithms when there are errors between the camera response used in the reconstruction algorithm and the true response of the gamma camera. In this regard, the authors compare the filtered backprojection algorithm, the expectation-maximization maximum likelihood algorithm, and the generalized expectation maximization (GEM) maximum a posteriori (MAP) algorithm, a Bayesian algorithm which uses a Markov random field prior.

An improved filtered back-projection algorithm using pre-processing

The theoretical basis for the filtered backprojection (FBP) algorithm is analyzed, and the underlying assumptions inherent in its use in single photon emission computed tomography (SPECT) are examined. Using both theoretical considerations and experimental investigation, the authors propose an improvement to the FBP algorithm for application to SPECT imaging. In the proposed modification to the filtered backprojection algorithm, the projection images are preprocessed so that the SPECT projection images more closely fit the model by which the FBP algorithm is formulated. The authors compare this approach with standard FBP in SPECT phantom and patient studies.<<ETX>>

Experimentally determining a parametric model for the point source response of a gamma camera (SPECT)

The authors experimentally investigate the response of a gamma camera to a source as a function of depth of the source in water and of distance from the gamma camera. They compute a least-squares estimate of the FWHM (full width at half maximum) of the camera line spread function as an affine function of these two parameters. They demonstrate a method for experimentally estimating the parameters of a camera response model and use this approach to estimate the parameters of a 2-D Gaussian model for the camera point source response in a true 3-D formulation. The 2-D Gaussian model was shown to yield good agreement with experimental data.<<ETX>>