Reversible FFT And MDCT Via Matrix Lifting

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 [1] that the closer the reversible transform is to its float counter part, 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 transform that is reversible, is close in transform value to its float counter part, 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.