In this paper, we propose a high dynamic range image coding method based on wavelet compression. In our method, we employ a pre-processing function to minimize errors between rendered (i.e. tone mapped) version of an original and compressed images. To enhance efficiency of the coding, we introduce the Hill function as the pre-processing. This function partially compresses the dynamic range of the HDR images based on the Human Visual System. The method implicitly assigns more bits to visually important luminance regions. We show the validity of our pre-processing by some experimental results.