Reversible FFT and MDCT via matrix lifting

A reversible transform not only converts integer input to integer output, but also reconstructs the exact input from the output. It is one of the key modules for lossless and progressive-to-lossless media codecs. We have established that the closer the reversible transform is to its float counterpart, the better the compression performance of the lossless and progressive-to-lossless codecs that utilize the transform. In this work, a new design of the reversible transform based on matrix lifting is proposed. With matrix lifting, we can design a transform that is reversible, is close in transform value to its float counterpart, and can be computed via fast algorithms. A progressive-to-lossless embedded audio codec employing the reversible MDCT with matrix lifting is implemented. Superior results on lossless and lossy audio compression are demonstrated.