A relaxation algorithm for minimizing the L² reconstruction error in 2-D nonorthogonal subband coding

We present a technique for improving the applicability of complete, nonorthogonal, multiresolution transforms to image coding. As is well known, the L² norm of the quantization error is not preserved by nonorthogonal transforms, so the L² reconstruction error may be unacceptably large. However, given the quantizers and synthesis filters, we show that this artifact can be eliminated by formulating the coding problem as that of minimizing the L² reconstruction error over the set of possible encoded images. This high-dimensional, discrete optimization problem is solved using a multiscale relaxation algorithm. Bounds on the coding gain over the standard coding technique are derived. Experiments using biorthogonal spline filters demonstrate appreciable SNR gains over the standard coding technique, and comparable visual improvements.