Image representation by blob and its application in CT reconstruction from few projections

Abstract: The localized radial symmetric function, or blob, is an ideal alternative to the pixel basis for X-ray computed tomography (CT) image reconstruction. In this paper we develop image representation models using blob, and propose reconstruction methods for few projections data. The image is represented in a shift invariant space generated by a Gaussian blob or a multiscale blob system of different frequency selectivity, and the reconstruction is done through minimizing the Total Variation or the 1 norm of blob coefficients. Some 2D numerical results are presented, where we use GPU platform for accelerating the X-ray projection and back-projection, the interpolation and the gradient computations.