Optimal histogram modification with MSE metric

We propose a method to modify the histogram of a signal to a desired specific histogram. Traditionally, points having the same value in the input signal are all mapped to same value in the output signal. Hence, the desired histogram can only be approximated. Here we formulate our problem as finding a transformation such that the error between the input and output signal is minimized and the output signal has the desired histogram. It turns out that this problem is equivalent to an integer linear programming problem. This method might be specifically useful for histogram-based watermarking and compression.