A high dynamic range (HDR) video can be compressed using inter-frame or intra-frame compression. The compression results in multiple encoded macroblocks and associated residual images. The residual images can be lossy compressed by mapping floating point image data values of the residual image from a light linear space to a perceptually linear space using a first non-linear mapping function. A value in the light linear space is proportionate to the power of a light source, and a value in the perceptually linear space is proportionate to a visual perceived brightness. Floating point discrete cosine transform (DCT) frequency coefficients of the floating point image data values of the residual image are determined. The floating point DCT frequency coefficients are quantized. The quantized floating point DCT frequency coefficients are compressed. The compression of the quantized floating point DCT frequency coefficients is lossless. The compressed quantized floating point DCT frequency coefficients are stored.