An adaptive optimization of the polynomial wavelet threshold

In this thesis parametrically defined polynomial thresholding operators are proposed. Prior work has shown that the optimal choice of the polynomial coefficients can be formulated as a least squares (LS) problem if the training sequences are available. An adaptive LMS approach for the optimization of wavelet coefficients is proposed and studied as an approach to reduce computational costs. This thesis presents a new class of polynomial threshold operators for denoising signals using wavelet transforms. The operators are parameterized to include classical soft- and hard-thresholding operators and have many degrees of freedom to optimally suppress undesired noise and preserve signal details. To avoid the complicated process of signal model identification for specific type of signals, an adaptive least mean squares (LMS) optimization method is proposed for the polynomial coefficients.

This approach optimizes coefficients without matrix inversion and if needed allows to optimally adapt the threshold polynomials for different sub bands without relative significant computational overheads. The approach is applied to 1D, 2D and 3D signals, and the results are compared to the conventional methods. High potential of the proposed approach is demonstrated through the simulations.