A method, for generating (a) a forward reshaping function for compressing an input high-dynamic range (HDR) image into a reshaped standard-dynamic-range (SDR) image and (b) a backward reshaping function for decompressing the reshaped SDR image into a reconstructed HDR image, includes (i) optimizing the forward reshaping function to minimize a deviation between the reshaped SDR image and an input SDR image corresponding to the input HDR image, (ii) optimizing the backward reshaping function to minimize a deviation between the reconstructed HDR image and the input HDR image, and (iii) until a termination condition is met, applying a correction to the input SDR image and reiterating, based on the input SDR image as corrected, the steps of optimizing the forward and backward reshaping functions.