A relaxation algorithm for minimizing the L/sup 2/ reconstruction error in 2-D nonorthogonal subband coding
Pierre Moulin · 2002
We present a technique for improving the applicability of complete, nonorthogonal, multiresolution transforms to image coding. As is well known, the L/sup 2/ norm of the quantization error is not preserved by nonorthogonal transforms, so the L/sup 2/ 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 L/sup 2/ 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.>