Multi-Dimensional Biomedical Image De-Noising using Haar Transform

Image de-noising and enhancement form two fundamental problems in many engineering and biomedical applications. The paper is devoted to the study of the multi-resolution approach to this topic employing the Haar wavelet transform and its application to processing of volumetric magnetic resonance image sets corrupted with additional noise. The resulting coefficients are thresholded and exploited for subsequent reconstruction. The Haar transform is evaluated using both the two-dimensional approach applied individually to each image layer, and the three-dimensional technique performed on the image volume as a whole. In noise reduction, the latter approach profits from similarities between the neighbouring image layers and shows a considerable improvement over the former method. Results are presented in numerical and graphical forms using three-dimensional visualization tools.