JPEG XR is a draft international standard undergoing standardization within the JPEG committee, based on a Microsoft technology known as HD Photo. One of the key innovations in the draft JPEG XR standard is its integer-reversible hierarchical lapped transform. The transform can provide both bit-exact lossless and lossy compression in the same signal flow path. The transform requires only a small memory footprint while providing the compression benefits of a larger block transform. The hierarchical nature of the transform naturally provides three levels of multi-resolution signal representation. Its small dynamic range expansion, use of only integer arithmetic and its amenability to parallelized implementation lead to reduced computational complexity. This paper provides an overview of the key ideas behind the transform design in JPEG XR, and describes how the transform is constructed from simple building blocks.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.