Abstract: A method and apparatus are provided for reconstructing a tomographic image from a halfscan fan-beam sinogram using the parallel beam reconstruction algorithms. The method includes the steps of weighting at least some elements of the halfscan fan-beam sinogram to forming a weighted fan-beam sinogram and expanding the weighted fan-beam sinogram into a Fourier series. The method further includes the steps of linearly interpolating at least some elements of the Fourier series to form a parallel beam sinogram of linearly interpolated data and reconstructing the image from the parallel beam sinogram using the parallel beam reconstruction algorithms.

Abstract: A method and apparatus are provided for reconstructing a set of CT images from helical CT data. The method includes the steps of receiving the helical CT data and generating a set of fan-beam sinograms at equally spaced longitudinal positions. The method further includes the steps of estimating a set of parallel-beam sinograms from the generated set of fan-beam sinograms and reconstructing the CT images using a parallel beam reconstruction algorithm.

Abstract: A method and apparatus are provided for interpolating a first set of multi-dimensional sample values from a second set of multi-dimensional sample values. The method includes the steps of determining a set of relationships between a second sampling space from which the second set of samples are obtained and a first sampling space into which the first set of samples are interpolated and calculating a partial Fourier transform of the second set of samples. The method further includes the steps of obtaining a partial Fourier transform of the first set of samples using the calculated partial Fourier transform of the second set of samples based upon the determined relationship between the first and second space and performing an inverse partial Fourier transform on the obtained partial Fourier transform of the first set of sample values to recover the first set of sample values.