  In this paper we propose spectral tools based on non-decimated complex
wavelet transforms implemented by their matrix formulation. This non-decimated
complex wavelet spectra utilizes both real and imaginary parts of
complex-valued wavelet coefficients via their modulus and phases. A structural
redundancy in non-decimated wavelets and a componential redundancy in complex
wavelets act in a synergy when extracting wavelet-based informative
descriptors. In particular, we suggest an improved way of separating signals
and images based on their scaling indices in terms of spectral slopes and
information contained in the phase in order to improve performance of
classification. We show that performance of the proposed method is
significantly improved when compared with procedures based on standard versions
of wavelet transforms or on real-valued wavelets. It is also worth mentioning
that the matrix-based non-decimated wavelet transform can handle signals of an
arbitrary size and in 2-D case, rectangular images of possibly different and
non-dyadic dimensions. This is in contrast to the standard wavelet transforms
where algorithms for handling objects of non-dyadic dimensions requires either
data preprocessing or customized algorithm adjustments. To demonstrate the use
of defined spectral methodology we provide two examples of application on
real-data problems: classification of visual acuity using scaling in pupil
diameter dynamic in time and diagnostic and classification of digital mammogram
images using the fractality of digitized images of the background tissue. The
proposed tools are contrasted with the traditional wavelet based counterparts.
