Application of a discrete tomography algorithm to computerized tomography

Linear programming is used in discrete tomography for solving the relaxed problem of reconstructing a function f with values in interval [0, 1]. The linear program minimizes the uniform norm ‖Ax−b‖∞ or the 1-norm ‖Ax−b‖1 of the error on the projections. We can add to this objective function a linear penalty function p(x) for trying to obtain smooth solutions. The same approach can be used in computerized tomography. Due to the size of the linear program this method has the disadvantage to be slow but it remains the question to know if it can provide better images than classical methods of computerized tomography. The aim of the paper is to provide a beginning of answer.