Image reconstruction from limited or incomplete data

A system and method are provided for reconstructing images from limited or incomplete data, such as few view data or limited angle data or truncated data (including exterior and interior data) generated from divergent beams. In one aspect of the invention, the method and apparatus iteratively constrains the variation of an estimated image in order to reconstruct the image. As one example, a divergent beam maybe used to generate data ("actual data"). As discussed above, the actual data may be less than sufficient to exactly reconstruct the image by conventional techniques, such as FBP. In order to reconstruct an image, a first estimated image may be generated. Estimated data may be generated from the first estimated image, and compared with the actual data. The comparison of the estimated data with the actual data may include determining a difference between the estimated and actual data. The comparison may then be used to generate a new estimated image. For example, the first estimated image may be combined with an image generated from the difference data to generate a new estimated image. In order to generate the image for the next iteration, the variation of the new estimated image may be constrained. For example, the variation of the new estimated image may be at least partly constrained in order to lessen or reducing the total variation of the image.