Reconstruction from projections under time-frequency constraints

Low-pass filtering computed tomography (CT) images to reduce noise may smooth or modify image features which are very important to the physician. Image features are often more easily identified and processed in the time-frequency plane. The authors use time-frequency distributions for spatially varying filtering of noisy CT images, constraining time-frequency representation coefficients of the projection data or of the reconstructed image to be zero in certain regions of the time-frequency plane. The authors consider two different applications: 1) filtering the projection data and then performing image reconstruction; and 2) filtering the reconstructed image directly. Criteria minimized, subject to constraints, may be either a deterministic minimum weighted perturbation of the given projection data or a stochastic minimum mean-square error in colored Gaussian noise. Results show improvement over processing the image with a linear spatially invariant filter.