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Orthogonal signal decomposition with applications in wavelet denoising

In this paper, signal de-noising is achieved through searching for optimum orthogonal decomposition of the received noisy data. The proposed procedure is well suited for small length data. It is based on applying Gram-Schmidt orthogonalization scheme to a matrix constructed from the outputs of MA, AR or ARMA model representation of the noisy signal. It is shown that the rank of this matrix determines the order of the model under investigation. Next, this scheme is used in conjunction with wavelet de-noising applications. There, instead of zeroing noisy wavelet packet coefficients, these coefficients are orthogonally decomposed to construct new coefficients with reduced noise content. In this respect, an efficient scheme is devised to decide whether a specific wavelet packet should be processed by the orthogonalization scheme or not. Illustrative examples are given to show that the proposed method competes well with other adaptive-based techniques