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An inverse problem: Histogram equalization

The well-known histogram equalization algorithm is not reversible, namely, given an equalized image and its initial histogram, the original image cannot be recovered. The paper proposes a solution to histogram inversion problem. An ordering on images, closely related to the human perception of brightness, is defined. The proposed ordering refines the normal ordering on graylevels up to a strict ordering. Based on the assumption that the ordering is conserved by histogram equalization algorithm, the inverse problem is further solved. The experimental results show a very good recovery of the original.