Noise weighting with an exponent for transmission CT

It is widely believed that the correct weighting function is the reciprocal of the noise variance of the associated measurement. Many researchers are making great efforts to find the accurate variance for the measurements for imaging systems so that they can hopefully achieve an optimal reconstruction. An 'optimal' solution in the context of this paper is referred to as the image that reaches optimum according to a criterion or criteria among a group of candidates, regardless how the images in the group are obtained. This 'optimal' solution is not a theoretical concept, but is simply the ` best of the bunch'. The goal of the paper is to investigate how the weighting function affects the image noise when the image contrast is pre-specified in an iterative algorithm for x-ray CT. This paper makes some interesting observations: there is no universal optimal weighting function. The noise weighting function can introduce artifacts. The optimal noise weighting varies with the object to be reconstructed and targeted image contrast in an iterative image reconstruction algorithm and in a filtered backprojection algorithm that incorporates the projection noise. It is suggested that an exponent be used in the weighting function so that the artifacts caused by the weighting function can be reduced.