Wavelet transform filtering and nonlinear anisotropic diffusion assessed for signal reconstruction performance on multidimensional biomedical data

Computer tomography (CT) techniques are the most widely applicable noninvasive methods for obtaining two- and three-dimensional insights into biological objects. They comprise CT for medical applications, as well as electron tomography used for investigating macromolecular and cellular specimens. Recent advances in the recording schemes improve the speed and resolution frontiers and provide new insights into structural organizations of different objects. However, many data sets suffer from a poor signal-to-noise ratio, which severely hinders the application of methods for automated data analysis, such as feature extraction, segmentation, and visualization. We propose the multidimensional implementation of two powerful signal reconstruction techniques, namely invariant wavelet filtering and nonlinear anisotropic diffusion. We establish quantitative measures to assess the signal reconstruction performance on synthetic data and biomedical images. The appropriate multidimensional implementations of wavelet and diffusion techniques allow for a superior performance over conventional noise-reduction methods. We derive the conditions for the choice between wavelet and diffusion techniques with respect to an optimal signal reconstruction performance. Results of applying the proposed methods in two very different imaging domains-molecular biology and clinical research-are provided.