WAVELET-BASED MULTIRESOLUTION LOCAL TOMOGRAPHY

We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data, The proposed method uses the prop erties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almos t completely local data that significantly reduces the amount of expos ure and computations in X-ray tomography. The property that distinguis hes our algorithm from the previous algorithms is based on the observa tion that for some wavelet bases with sufficiently many vanishing mome nts, the ramp-filtered version of the scaling function as well as the wavelet function has extremely rapid decay, We show that the variance of the elements of the null-space is negligible in the locally reconst ructed image, Also, we find an upper bound for the reconstruction erro r in terms of the amount of data used in the algorithm, To reconstruct a local region 16 pixels in radius in a 256 x 256 image, we require 2 2% of full exposure data.