Iterative inversion of the Radon transform using image-adaptive wavelet constraints

Sahiner and Yagle (1992, 1993, 1995) developed a procedure for image reconstruction from projections under wavelet-domain image constraints (WC). We constrain the wavelet transform (WT) of the noisy image to zero in WT regions determined by thresholding the WT of the noisy image. The least-squares image satisfying these constraints shows improved reconstruction not just in the constrained region, but over the entire image. This amounts to image-constrained localized low pass filtering. We now present new results on iterative implementation of this technique. At each iteration we use the image from the previous iteration as the source of WC for the next iteration. This can be viewed as iterative spatially-varying image-constrained Wiener filtering. At the third iteration the RMS error is reduced by more than twice as much as in our previous results, while preserving high-resolution image features