Multiscale discrete wavelet transform of the finite spectrum digital images
Viktor P. Dvorkovich · 2016
Summary form only given. The main problem in using of multiscale algorithms of digital image coding and compression is the choice of the basis for wavelet decomposition. This complex problem has not got general solution yet. A number of criteria are known to be determined qualifying a wavelet basis, among them the most important are: smoothness, accuracy of image reconstruction and the frequency selectivity of the filters. Commonly used is the dual subband wavelet transform, in which the image is decomposed into 4 subband regions. The new approach consists in the application of multiband wavelet decomposition with the use of specially calculated and optimized wavelet basis. When using the three-, four- and five-band wavelet system the image is decomposed into 9, 16 or 25 subbands respectively. Each subband can be also divided using wavelet transforms. Improving of the efficiency of image conversion is possible by separating of signals using, for example, three-band filters and followed by further conversion of Hi-pass subbands by two-band wavelet filters. To describe the random variable distribution of pixel brightness in each of the high-frequency component of the wavelet transform a one-dimensional probability density of Laplace's form may be applied with the sufficient accuracy. The density distribution of high-frequency subbands data is split (quantized) in a new way that makes the amount of coefficients matching each split zone range to be equal (as in Lloyd-Max procedure).