A computed tomography (CT) method and apparatus including a radiation source configured to produce radiation directed to an object space, and a plurality of detector elements configured to detect the radiation produced from the radiation source through the object space and generate projection data. A rotation mount is configured to rotate the radiation source around the object space. Processing circuitry is configured to cause the rotation mount to rotate the radiation source, and to receive the projection data. The projection data includes a plurality of projection data sets. The processing circuitry calculates a set of weights based on the projection data sets, calculates a set of pre-weights based on the weights, and minimizes a penalized weighted least-squares cost function to produce a reconstructed image. The cost function is a sum of a weighted least-squares term, weighted using the weights, and a penalty term weighted using the pre-weights.
