Wikipedia
JPEG-HDR is a backwards-compatible extension to the standard JPEG image file format allowing it to store wide color gamut, high dynamic range images. JPEG-HDR was created by Greg Ward and Maryann Simmons as a way to store high dynamic range images inside a standard JPEG file. It was later modified by Ajit Ninan, Greg Ward, Arkady Ten, Wenhui Jia and William Rozzito to support the addition of other features such as wide color.
This format reduces the file size required to store HDR images compared to other HDR formats such as floating point TIFF and RGBE.
Reduction in filesize is achieved by first converting the image into a tone mapped version, then storing a reconstructive multiplier image in APP11 markers in the same JPEG file. Ordinary viewing software will ignore the multiplier image allowing anyone to see the tone mapped version of the image presented in a standard dynamic range and color gamut.