Signal denoising in tree-structured Haar basis

Signal denoising is one of the essential areas of Haar transform application due to its wavelet-like structure and low computing requirements. Recently the Haar transform has been generalized to the case of arbitrary time and scale splitting, thereby providing an opportunity of adapting the basis functions to the signal on hand, and, at the same time, being computationally as efficient as the classical Haar transform. In this paper, an application of such a transform, called the tree-structured Haar transform, for denoising stepwise signals is combined with the idea of averaging estimates from overlapping windows. For other type of signals a possibility of selecting either of two different transforms for each sliding window-the tree-structured Haar transform and the discrete cosine transform-is explored.