A data structure defining a high dynamic range image comprises a tone map having a reduced dynamic range and HDR information. The high dynamic range image can be reconstructed from the tone map and the HDR information. The data structure can be backwards compatible with legacy hardware or software viewers. The data structure may comprise a JFIF file having the tone map encoded as a JPEG image with the HDR information in an application extension or comment field of the JFIF file, or a MPEG file having the tone map encoded as a MPEG image with the HDR information in a video or audio channel of the MPEG file. Apparatus and methods for encoding or decoding the data structure may apply pre- or post correction to compensate for lossy encoding of the high dynamic range information.