An Algorithm for Removing Artifacts in Wavelet Expansions

In the past of two decades, wavelet methods have been adopted enthusiastically in many engineering applications such as signal and image processing. However, like most of the classic orthogonal expansions, wavelet expansions also exhibit Gibbs phenomenon around discontinuities of the original signals. Therefore, the recovered signals using wavelet expansions could be corrupted by the overshoot (or undershoot) around the jump discontinuities. This is also true in the case of wavelet denoising and wavelet thresholding. In order to remove the artifacts, summability methods for orthogonal wavelet expansions were introduced in previous papers. These summability methods are based on replacing the conventional wavelet basis by its associated biorthogonal basis. This paper is devoted to the discussion of an algorithm used to construct the biorthogonal wavelet basis numerically.