Image reconstruction algorithms implemented on existing CT scanners require the collection of line integrals that are evenly spaced over 360 degrees.1 In many practical situations requirements for high temporal resolution or the presence of an x-ray opaque structure prevent the measurement of all the line integrals. Attempts to use existing algorithms in this "limited data" situation result in images with severe streak artifacts.2 This paper formulates the limited data image reconstruction problem as an optimization problem. An estimate of the missing data is sought which is consistent with the measured data and any a priori knowledge about the object. An iterative procedure computes a set of error signals at each step and uses these errors to improve the missing data estimate. A variety of iterative algorithms can be derived using different methods of updating the estimate. These algorithms have been implemented on a commercial CT scanner. Examples of images with reduced streak artifact generated from limited data are presented.