A nonlinear transform for subband image coding

In this paper, a new image transform, the so-called spherical subband (SSB) decomposition, is introduced and applied to image compression. After a phy sical motivation of this transform, we will show that it can be viewed as a classical wavelet transform followed by the transformation of the high-fre quency subbands into spherical coordinates. Based on this nonlinear transfo rm, image coding schemes can be designed that allow the exploitation of the intercorrelations between subbands at the same level of resolution. This w ill be shown theoretically by means of an analysis of the asymptotic rate-d istortion behaviour of the scheme. Hence, a net performance increase at unc hanged complexity for level-constrained quantization systems or a significa nt complexity reduction at unchanged performance for entropy constrained sy stems can be demonstrated. In conclusion, a practical coding scheme, with f eatures such as scalability, training freeness, low computational complexit y and the possibility of progressive transmission, is developed and success fully compared to established compression schemes. (C) 1999 Elsevier Scienc e B.V. All rights reserved.