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This paper proposes a novel algorithmic approach of image enhancement via optimal contrast-tone mapping. In a fundamental departure from the current practice of histogram equalization for contrast enhancement, the proposed approach maximizes expected contrast gain subject to an upper limit on tone distortion and optionally to other constraints that suppress artifacts. The underlying contrast-tone optimization problem can be solved efficiently by linear programming. This new constrained optimization approach for image enhancement is general, and the user can add and fine tune the constraints to achieve desired visual effects. Experimental results demonstrate clearly superior performance of the new approach over histogram equalization and its variants.