Print

Ge, Jun

Chemistry

2004

Ph. D.

The recovery of a signal from observed noisy data, while still preserving its important features, continues to remain a fundamentally elusive and challenging problem in signal analysis. Multiscale product method (MPM) is an efficient and effective denoising technique method. We justify the use of spline wavelets in MPM and examine the properties of MPM. By combining the capture of singularities and characterization of noisy residual, we "soften" the traditional MPM to achieve better visual quality and better qualitative performance. A fixed-pointed algorithm is then used to reduce the computation burden. The extension of MPM to two dimensions is not trivial. The tensor-product based wavelet representation cannot capture the 1D singularities (edges) and 2D singularities (corners) very efficiently. Specific techniques are needed to capture the intrascale correlation caused by those high-dimensional singularities. To this end, we introduce a new weight function based on local covariance analysis (LCA) of geometrical features to generate a data-driven adaptive shrinkage function for two-dimensional images. Our new MPM-LCA denoising algorithm has simple implementation, and its performance is comparable to the sophisticated state-of-art statistical methods.