Study Of Multi-scale Domain Signal And Image Denoising Method

In recent years, wavelet has become a useful time-frequency analysis tool for investigation and analysis of many kind of problem, one reason that wavelets are popular is that they overcome some of the shortcomings of short-time Fourier decompositions. Wavelet has good local performance in time and frequency domain, simultaneity with time-frequency domain resolution variable performance. Wavelet de-noising is one of its important application aspects. So, it will be meaningful to propose the new de-noising method in multi-scale domain based on wavelet de-noising. In this paper, our work is focus on M-band wavelet domain and Ridgelet domain.M-band wavelet theory is proposed based on the traditional 2-band wavelet. It has advantages in following aspects: traditional wavelet has defect in decomposition rule (just the sequence with the integral power of 2), sometimes this isn't enough. M-band wavelet helps to zoom in onto narrow band high frequency components of a signal, it provides the fine describe. M-band wavelet can have linear phase, high regularity and compactly supported simultaneity, have better energy compaction. Moreover, the speed of the decomposition is increased because of the M-band. Ridgelet is presented to overcome the weakness of wavelets in higher dimensions, it is especially suitable for describing the signals which have linear singularities in 2-D.The main work includes:1. According to nonparametric adaptive estimation theory, the difference between parametric and nonparametric is depicted, and the advantage of nonparametric in de-noising domain is discussed. Based on Gaussian modeling, the model selection concept is introduced and the adaptive estimation presented to solve the problem on variable selection is discussed. As one of the adaptive estimation methods, the Birge-Massart method is imported, with the idea of contrast function, penalty function, and penalized projection estimator and so on. Combining these theories...