An algorithm is created and applied to reconstruct the wavelet coefficients of an image from the Radon transform data for use in computed tomography, with a disclosed method that uses the properties of wavelets to localize the Radon transform such that a local region of the cross section of a body can be reconstructed using almost completely local data to significantly reduce the amount of exposure and computations in X-ray tomography. The described algorithm is based on the observation that for some wavelet bases with sufficiently many vanishing moments, the ramp-filtered version of the scaling function as well as the wavelet function has extremely rapid decay, with the variance of the elements of the nullspace is being negligible in the locally reconstructed image.
U.S. Patent and Trademark Office DescriptionPTO
David Walnut, Carlos Berenstein, K.J. Ray Liu, Farrokh Rashid-Farrokhi