Wavelet thresholding

This research theme explores the development and evaluation of wavelet thresholding techniques focused on denoising signals and images, particularly in biomedical and remote sensing applications. It addresses the challenge of selecting optimal threshold values, thresholding functions (hard/soft), wavelet bases, decomposition levels, and adaptive criteria to maximize noise reduction while minimizing loss of important signal characteristics such as edges or cardiac signal features. The theme is crucial for enabling accurate diagnostics, efficient image processing, and robust signal interpretation in noisy environments.

This theme investigates the theoretical foundations and practical approaches to enhance wavelet-based function estimators through the combination of multiple thresholding rules. Specifically, it focuses on addressing cases where thresholding methods have non-nested maxisets (sets of functions reconstructible at a given convergence rate). By hybridizing complementary thresholding schemes, new estimators can be constructed with larger, unified maxisets, thereby improving their adaptability and performance across diverse signal classes. This approach advances wavelet denoising by overcoming limitations of any single thresholding technique.

This theme covers the application of wavelet transform combined with entropy measures or multi-resolution spatial analysis to detect edges and identify structural boundaries in complex image data sets, including geophysical potential fields and medical images. By decomposing data into multiple frequency subbands, entropy can quantify the complexity or structural presence at each scale, guiding adaptive thresholding or edge localization. These methods aim to achieve computationally efficient, noise-robust edge detection critical for segmentation and interpretation tasks in fields where accurate boundary delineation impacts decision-making.