A method and apparatus is provided to reconstruct a computed tomography image from projection data using windowed filtered back-projection (FBP) and using regularization constraints that can be quadratic or non-quadratic. The method emulates multiple Landweber iterations using a single windowed FBP operation and then iterates between imposing regularization constraints and a single windowed FBP operation. This windowed FBP operation is only performed once. The regularization constraints can be imposed using edge-preserving denoising methods, including, e.g., a Huber filter, a median filter, a bilateral filter, a guided filter, a non-local means filter, a total-variation minimization regularizer, other known regularizer, or an anisotropic diffusion filter. The entire procedure contains no forward projection and contains only one back-projection.