Research On Wavelet De-Noising And Application Of Wavelet Decomposition To K-L Transform

Research on Wavelet De-Noising and Application of Wavelet Decomposition to K-L TransformCandidate: Zhang Yiwei, Supervisor: Wang Qiao Department of Radio Engineering, Southeast University, ChinaEstimating the original signals from noise has always been an important part in the field of signal processing. Because of its fine time-frequency localization characteristic, multiscale wavelet transform can effectively discriminate signals from noise and achieves pretty good performance. However, the traditional discrete wavelet transform is shift-variant which affects the de-noising result. So we need to initiate a shift-invariant algorithm. Also the sparsity of the coefficient can be applied to the fast estimation of K-L transform. The main contents of this dissertation are expressed as follows: Firstly, the shift-invariant wavelet and wavelet packets algorithm based on some cost function and best shift are studied. Secondly, the above shift-invariant algorithm is combined with de-noising methods such as thresholding and Bayes estimation algorithm to overcome the limits of traditional methods. Also, the shift-invariant wavelet packets algorithm is applied to coherent bases extracting method to remove some non-gaussian noise which is hard for traditional thresholding method. Finally, the sparsity of the wavelet decomposition coefficients can be applied to construct a matrix with lower dimension to estimate original K-L eigenvectors. In this paper, this method is applied to the fast estimation of K-L eigenvectors for image data.