Group-normalized processing of complex wavelet packets

Linear phase is not possible for real valued FIR QMF, while linear phase FIR biorthogonal wavelet filter banks make the mean squared error of the constructed signal exceed that of the quantization error. W Lawton’ s method for complex valued wavelets construction is extended to generate the complex valued compactly supported wavelet packets that are symmetrical and unitary orthogonal; then well-defined wavelet packets are chosen by the analysis remarks on their time-frequency characteristics. Since the traditional wavelel packets transform coefficients do not exactly represent the strength of signal components, a modified adaptive wavelets transform, group-normalized wavelet packet transform (GNWPT), is presented and utilized for target extraction from formidable clutter or noises with the time-frequency masking technique. The extended definition of lp-norm entropy improves the performance cf GNWPT. Similar method can also be applied to image enhancement, clutter and noise suppression, optimal detection