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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 …