Wavelet Transform in Signal and Image Restoration

The paper presents selected mathematical methods of digital signal and image processing based upon the use of wavelet transform and signal decomposition with applications in system identification, analysis and modelling. The main part of the paper is devoted to signal de-noising using hard and soft thresholding and to the recovery of degraded parts of signals and images. The wavelet transform approach has been adopted here and used for the recovery of the corrupted image regions as an alternative to probabilistic models. Proposed methods present results of the iterated wavelet transform interpolation of missing signal and image components both for simulated signals and biomedical magnetic resonance images. Resulting algorithms are closely related to signal segmentation, change points detection and prediction with the use in process control, computer vision, signal or image processing and computer intelligence.