L2 norm optimization of tone mapping for two layer lossless coding of HDR images

This paper optimizes a tone mapping function in a backward compatible lossless coding of high dynamic range (HDR) images. The mapping function is designed so that it maximizes quality of decoded low dynamic range (LDR) images. An optimization procedure for a lossy coding system is extended to a lossless system under the condition that a user can specify arbitrary tone mapping function to produce an LDR image from the original HDR image. Superiority of the proposed method on the rate distortion curves of the LDR image was confirmed to be up to 7.5 dB in PSNR improvement for an image sample.