To encode High Dynamic Range (HDR) images, the HDR images can be converted to Low Dynamic Range (LDR) images through tone mapping operation, and the LDR images can be encoded with an LDR encoder. The present principles formulates a rate distortion minimization problem when designing the tone mapping curve. In particular, the tone mapping curve is formulated as a function of the probability distribution function of the HDR images to be encoded and a Lagrangian multiplier that depends on encoding parameters. At the decoder, based on the parameters indicative of the tone mapping function, an inverse tone mapping function can be derived to reconstruct HDR images from decoded LDR images.