Nonlinear kernel backprojection for computed tomography

In this paper, we propose a kernel backprojection method for computed tomography. The classical backprojection method estimates an unknown pixel value by the summation of the projection values with linear weights, while our kernel backprojection is a generalized version of the classic approach, in which we compute the weights from a kernel (weight) function. The generalization reveals that the performance of the backprojection operation strongly depends on the choice of the kernel, and a good choice of the kernels effectively suppresses both noise and streak artifacts while preserving major structures of the unknown phantom. The proposed method is a two-step procedure where we first compute a preliminary estimate of the phantom (a “pilot”), from which we compute the kernel weights. From these kernel weights we then reestimate the phantom, arriving at a much improved result. The experimental results show that our approach significantly enhances the backprojection operation not only numerically but also visually.