Variable Filter Length Local Tomography

In Computed Tomography (CT) the goal is to reconstruct the distribution µ of the x-ray attenuation coefficient inside the object being scanned. Local Tomography (LT) computes not µ, but Bµ, where B is some operator that enhances singularities. Suppose one is interested in reconstructing a region of interest (ROI) inside a patient. For example, the ROI could be the cardiac region. Conventional (also known as global) reconstruction requires that the entire cross-section of the patient be irradiated. This means that during the scan one has to transmit x-rays through parts of the patient located far from the ROI. The main advantage of LT compared to global reconstruction is that it requires only the x-rays passing through the ROI, thereby allowing to reduce the x-ray dose to the patient. In classical cone beam LT the convolution kernel is very short, because it is equivalent to computing some kind of derivative on the detector. (See Disclosure