Ray-by-ray noise weighting in a Filtered Backprojection (FBP) algorithm

This paper is an extension of our recently developed FBP-MAP (Filtered Backprojection Maximum a Posteriori) algorithm, which has view-by-view noise weighting and a quadratic smoothing prior. The current method has ray-by-ray noise weighting and can encourage edge-preserving smoothing. An objective function is set up for the image reconstruction problem. The projection data are weighted according to their noise variances. An edge-preserving strategy is used to regulate the image noise while maintaining the sharp edges. The objective function leads to an iterative algorithm, and an FBP-type algorithm is developed in an ad hoc manner to emulate the iterative algorithm. The proposed algorithm has been implemented for the circular-orbit cone-beam geometry based on Feldkamp's algorithm. Image reconstructions with computer simulations and real cadaver data are presented to illustrate the effectiveness and feasibility of the proposed algorithm. The new FBP-type algorithm is able to significantly reduce or remove the noise texture, which the conventional FBP is unable to do. A ray-based noise weighting scheme is introduced to the FBP algorithm for the first time. The new FBP algorithm is also able to incorporate an edge-reserving prior. This new FBP-type algorithm significantly reduces or removes the streaking artifacts in low-dose CT.