A method of reducing ring artifacts in tomographic images including providing an original digitized projection measurement comprising a plurality of intensities corresponding to a domain of points on an 2-dimensional grid, operating on said original projection measurement with a filter wherein features of high radial frequency and low angular frequency are attenuated, forming a weighted mixture of said filtered projection measurement and said original projection measurement wherein ring artifacts in said original tomographic image are substantially reduced, and reconstructing the projection measurement to form a tomographic image. Alternatively, a first tomographic image is reconstructed from said original projection measurement, a second tomographic image is reconstructed from said filtered projection measurement, and a weighted mixture is formed from said first tomographic image and said second tomographic image.