Image Noise Covariance Can be Adjusted by a Noise Weighted Filtered Backprojection Algorithm

It was believed that the noise covariance of an image reconstructed with the filtered backprojection (FBP) algorithm is anisotropic. This paper shows that the noise-weighted FBP algorithm is able to alter the noise covariance and make it approximately isotropic. For the noise-weighted FBP algorithm, this paper develops a closed-form expression for the noise variance image and a closed-form expression for the noise covariance image. Computer simulations are carried out to evaluate the noise covariance with and without the noise weighting in the FBP algorithm. Transmission and emission noise models are used in computer simulations. The noise weighted FBP algorithm has a parameter that emulates the iteration number in the iterative Landweber algorithm. It is observed that the noise covariance can be altered by this emulated iteration number when noise weighting is used. The noise weighting in the noise-weighted FBP algorithm is able to change the noise covariance and a proper selection of the emulated iteration number may be able to give an approximately isotropic image noise covariance function.