Signal denoising based on parametric Haar-like transforms

Orthogonal transforms have found considerable interest in signal denoising applications. Recently Parametric Haar-like Transforms (PHTs) have been introduced and shown to be efficient in image denoising and compression applications. PHT is such that it may be computed with fast algorithm in structure a similar to that of classical fast Haar transform and such that its matrix contains a predefined basis vector, called generating vector, as its first row. PHT may be adapted to the characteristics of the input signal or to its parts by a proper selection of the generating vectors. Possibility of adaptation to the input signal may, in principle, be significant source for performance improvement of transform based signal processing algorithms. In this paper, the capability of parametric Haar-like transforms, in 1-D signal denoising application is explored. A new PHT based post-processing algorithm for 1-D signal denoising is proposed, which may be combined with another denoising method in order to improve the quality of the output signal. Experiments were conducted where the basic wavelet thresholding based signal denoising method was complemented with the proposed post-processing algorithm. Simulation results illustrate significant performance improvement due to the use of the proposed algorithm.