Non-decimated Complex Wavelet Spectral Tools with Applications
Taewoon Kong, Brani Vidaković · 2019 · 4 citationsRead the paper
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.
What the full text shows
Working prototype- NDWTc using both spectral slopes and phase averages achieved the highest overall accuracy for pupil diameter signal classification. — 0.8226 accuracy vs. 0.4458 for WT slope (1-D signal classification of visual acuity (pupil diameter))
- NDWTc using only phase-based features achieved the highest accuracy for mammogram image classification. — 0.7456 accuracy vs. 0.5306 for WT slope (2-D digital mammogram image classification)
- NDWTc outperformed CNN in both accuracy and computational efficiency for mammogram classification. — 0.7456 accuracy (NDWTc) vs. 0.6250 accuracy (CNN) (Mammogram image dataset)
- NDWTc processing time for mammogram images was significantly lower than CNN training/testing. — ~18 mins total vs. ~15 hours (1024x1024 images, Intel Core i7-6500U CPU)
- Phase information is more discriminatory than spectral slopes for both 1-D and 2-D datasets. (NDWTc transform)
- Setup
- 1-D pupil diameter signals (1024 length) and 2-D digital mammogram images (1024x1024).
- How
- The authors implemented a non-decimated complex wavelet transform (NDWTc) using a matrix formulation to handle non-dyadic signal and image dimensions. They extracted spectral slopes and phase averages as descriptors for classification using Gradient Boosting (1-D) and Random Forest (2-D) classifiers.
- Limitations
- Computational time increases with accuracy, especially in 2-D due to double matrix multiplication. · Performance of phase vs. slope may vary across different datasets.
Summarized by Gemma 4 from the open-access full text · 8 Oct 2026. Read it