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Biomedical subjects

R M Lewitt

Publications and source records attributed to R M Lewitt.

6 recordsLinked to original sources
PubMed1992

Alternatives to voxels for image representation in iterative reconstruction algorithms.

Spherically symmetric volume elements are alternatives to the more conventional voxels for the construction of volume images in the computer. The image representation, and the calculation of projections of it, are essential components of iterative algorithms for image reconstruction from projection data. A two-parameter family of spherical volume elements is described that allows control of the smoothness properties of the represented image, whereas conventional voxels are discontinuous. The rotational symmetry of the spherical elements leads to efficient calculation of projections of the represented image, as required in iterative reconstruction algorithms. For volume elements whose shape is ellipsoidal (rather than spherical) it is shown that efficient calculation of the projections is also possible by means of an image space transformation.

Algorithms↗
PubMed1990

Multidimensional digital image representations using generalized Kaiser-Bessel window functions.

Inverse problems that require the solution of integral equations are inherent in a number of indirect imaging applications, such as computerized tomography. Numerical solutions based on discretization of the mathematical model of the imaging process, or on discretization of analytic formulas for iterative inversion of the integral equations, require a discrete representation of an underlying continuous image. This paper describes discrete image representations, in n-dimensional space, that are constructed by the superposition of shifted copies of a rotationally symmetric basis function. The basis function is constructed using a generalization of the Kaiser-Bessel window function of digital signal processing. The generalization of the window function involves going from one dimension to a rotationally symmetric function in n dimensions and going from the zero-order modified Bessel function of the standard window to a function involving the modified Bessel function of order m. Three methods are given for the construction, in n-dimensional space, of basis functions having a specified (finite) number of continuous derivatives, and formulas are derived for the Fourier transform, the x-ray transform, the gradient, and the Laplacian of these basis functions. Properties of the new image representations using these basis functions are discussed, primarily in the context of two-dimensional and three-dimensional image reconstruction from line-integral data by iterative inversion of the x-ray transform. Potential applications to three-dimensional image display are also mentioned.

Fourier Analysis↗
PubMed1977

Computed tomography with fan beam geometry.

Data collection for computed tomography (CT), using a fan beam of radiation, is considered in detail. The manner in which the required projection data set is built up as scanning proceeds is demonstrated. It is shown that by offsetting the fan beam detector from its symmetrical position by a fraction of the element spacing, and by making measurements over 360 degrees, the spatial resolution of the detector may be increased by up to a factor of two. Results of simulations relating to an actual CT device under construction are presented.

Mathematics↗
PubMed1976

A possible conformation for double-stranded polynucleotides.

A model is presented for double-stranded polynucleotides which involves side-by-side meshing of the two strands rather than double helical intertwining. The sugar-phosphate backbone has a twisted strip-like character, yet base-pairing of the Watson-Crick type is still possible. Structural features of the basic model are described and coordinates are presented for a representative example. The structure has, on the whole, reasonable sterochemical contacts, and can be shown to produce a fiber diffraction pattern with x-rays not unlike that of the B form of DNA.

DNA↗
PubMedDate not supplied

Processing of incomplete measurement data in computed tomography.

Conventional approaches to computed tomography involve scanning the entire cross section and producing an image whose spatial and density resolution is uniform over its entire area. If the extent of each scan is restricted to the width of the lesion being investigated, then the x-ray dose is reduced, but a set of incomplete "truncated" projections is measured. Conversely, projections are "hollow" when their inner parts cannot be measured, e.g., when there is a metallic object within the body cross section. We present procedures for preprocessing incomplete projections so that images can be reconstructed from them using the convolution/back projection method.

Mathematics↗