This paper offers an overall review of recent advances in the design of modern transforms for image and video coding
applications. Transforms have been an integral part of signal coding applications from the beginning, but emphasis had
been on true floating-point transforms for most of that history. Recently, with the proliferation of low-power handheld
multimedia devices, a new vision of integer-only transforms that provide high performance yet very low complexity has
quickly gained ascendency. We explore two key design approaches to creating integer transforms, and focus on a
systematic, universal method based on decomposition into lifting steps, and use of (dyadic) rational coefficients. This
method provides a wealth of solutions, many of which are already in use in leading media codecs today, such as H.264,
HD Photo/JPEG XR, and scalable audio. We give early indications in this paper, and more fully elsewhere.