Abstract: An improved computerized tomography method and an apparatus for performing the method are used for construction of visual images of a subject utilizing a Radon transform inversion scheme of lower computational complexity. A multiscale backprojection with a postprocessing step is utilized instead of a conventional backprojection algorithm or direct Fourier method to obtain improved images. Multilevel methods can be applied under weaker regularity requirements than Fourier methods, so the present algorithm can be adjusted to provide different resolutions for different parts of the reconstruction, whether or not the Radon data are equally spaced.