WAVELET LOCALIZATION OF THE RADON-TRANSFORM

In this paper we develop an algorithm which significantly reduces radiation exposure in x-ray tomography, when a local region of the body is to be imaged. The algorithm uses the properties of wavelets to essentially localize the Radon transform. This algorithm differs from previous algorithms for doing local tomography because it recovers an approximation to the original image, not the image modulo the nullspace of the local tomography operator, or the Lambda transform of the image. This is possible because we do not truly invert the interior Radon transform, but rather sample the Radon transform sparsely away from the local region of interest. Much attention in the field has been directed towards localized tomography. We believe that this technique represents a significant contribution towards this effort.