Construction of Nonseparable Multiwavelets for Nonlinear Image Compression

A procedure for the construction of balanced orthogonal nonseparable quincunx multiwavelets, having filters with good lowpass properties, is introduced. Thematrix filter bank is viewed as the polyphasematrix of other filters, uponwhich the lowpass condition is imposed. The multiscaling functions obtained are plotted by means of the cascade algorithm. The process of transforming an image with these wavelets is outlined: formulae for analysis and synthesis are given, the first steps are illustrated with images, and the decomposition of the original image into two input images is addressed. Compression is achieved in a nonlinear process. Experimental results show that (i) the constructedmultiwavelets having lowpass properties performbetter than other nonseparable multiwavelets, (ii) the energy compaction in the fine detail subbands is greater for the multiwavelets than for the one-dimensional wavelets tried.