Deblurring subject to nonnegativity constraints when known functions are present with application to object-constrained computerized tomography.

The reconstruction of tomographic images is often treated as a linear deblurring problem. When a high-density, man-made metal object is present somewhere in the image field, it is a deblurring problem in which the unknown function has a component that is known except for some location and orientation parameters. We first address general linear deblurring problems in which a known function having unknown parameters is present. We then show how the resulting iterative solution can be applied to tomographic imaging in the presence of man-made foreign objects, and we apply the result, in particular, to X-ray computed tomography imaging used in support of brachytherapy treatment of advanced cervical cancer.

Filter matrix estimation in automated DNA sequencing.

In four-color fluourescence-based automated DNA sequencing, a 4 x 4 filter matrix parameterizes the relationship between the dye-intensity signals of interest and the data collected by an optical imaging system. The filter matrix is important because the estimated DNA sequence is based on the dye intensities that can only be recovered via inversion of the matrix. In this paper, we present a calibration method for the estimation of the columns of this matrix, using data generated through a special experiment in which DNA samples are labeled with only one fluorescent dye at a time. Simulations and applications of the method to real data are provided, with promising results.

Corrections for accidental coincidences and attenuation in maximum-likelihood image reconstruction for positron-emission tomography.

Reconstruction procedures that account for attenuation in forming maximum-likelihood estimates of activity distributions in positron-emission tomography are extended to include regularization constraints and accidental coincidences. A mathematical model is used for these effects. The corrections are incorporated into the iterations of an expectation-maximization algorithm for numerically producing the maximum-likelihood estimate of the distribution of radioactivity within a patient. The images reconstructed with this procedure are unbiased and exhibit lower variance than those reconstructed from precorrected data.

Spatial normalization of one-dimensional electrophoretic gel images.

A strategy for using processed, digitized images of one-dimensional electrophoretic gels to facilitate the analysis of large sets of overlapping clones is described. The images are acquired from fluorescently stained gels or from transilluminated gel photographs using a cooled, solid-state charge-coupled device camera. By employing sets of bands in the size-standard lanes as reference points, all the gel images are spatially normalized to a common reference template. After normalization, lane images from different gels can be compared as though the gels had been electrophoresed under identical, uniform-field conditions. Applications of this procedure to the analysis of a large set of overlapping lambda clones from chromosome VII of Saccharomyces cerevisiae and to the estimation of fragment sizes are illustrated.

Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography.

Images produced in emission tomography with the expectation-maximization algorithm have been observed to become more noisy and to have large distortions near edges as iterations proceed and the images converge towards the maximum-likelihood estimate. It is our conclusion that these artifacts are fundamental to reconstructions based on maximum-likelihood estimation as it has been applied usually; they are not due to the use of the expectation-maximization algorithm, which is but one numerical approach for finding the maximum-likelihood estimate. In this paper, we develop a mathematical approach for suppressing both the noise and edge artifacts by modifying the maximum-likelihood approach to include constraints which the estimate must satisfy.