Unlike MENT (maximum entropy algorithm), the extended MENT algorithm can process prior information and deal with incomplete projections or limited angle data. The reconstruction problem is formulated for solving linear systems involving the Fredholm integral equation. To develop the extended MENT algorithm, maximum entropy is substituted by a more general optimization criterion, that of minimizing the discriminatory function. The a priori knowledge of the shape of the object is easily incorporated in the algorithm by using the discriminatory function. Useful mathematical properties that make the discriminatory function attractive are derived. The sensitivity of the minimum discriminatory solution is derived to determine the characteristics of the noise in the reconstructed images. The extended MENT algorithm is developed for a parallel geometry, and its convergence properties are given. Its image processing performance is better than that for other maximum entropy algorithms such as multiplicative algebraic reconstruction techniques (MART) or more standard methods such as ART and the convolution backprojection.
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