Signal Denoising by Better Multiwavelet Basis using Fuzzy Logic

A multiwavelet based signal denoising algorithm is proposed in this paper. The number of decomposition stages, L, in conventional signal denoising algorithms is fixed for different types and properties of noisy signals. The performance of these systems is enhanced by optimizing other parameters, like the thresholding. It is shown in this work that the fixed L is not always suitable for different signals. Therefore, the proposed algorithm performs the denoising under the supervision of a Fuzzy controller to find and use the suitable L, and hence the multiwavelet basis, to denoised an unknown noisy signal, subject to requirements on the maximum L, denoised signal smoothness, and MSE. This value of L is found by observing a both signal smoothness and MSE related parameter teach decomposition stage of the noisy signal. Then, the controller decides whether to continue or stop at the L level. The proposed algorithm does not involve noise power estimation. Computer simulation show that the proposed algorithm is more flexible than fixed L algorithms, since it provides the ability to have a trade-off among system complexity, signal smoothness and MSE to better suit the requirements of different application conditions.