Image representation using mollified pixels for iterative reconstruction in x-ray CT

We introduce a new basis function, the mollified pixel, for image representation in x-ray computed tomography and other imaging modalities. The mollified pixel is defined as the convolution of a classical pixel with a smooth function that approximates the Dirac impulse. Since such a smooth function can be defined in an infinite number of ways, the mollified pixel defines a wide class of methods for image representation. For utilization of the mollified pixel in iterative reconstruction, it is needed to know the Radon transform of a mollified pixel. Using a link between classical pixels and B-splines, we suggest a computationally-efficient expression for this Radon transform. Preliminary iterative CT reconstruction results based on mollified pixels are provided along with our theoretical developments to demonstrate the potential benefits of mollified pixels.