The Application Of A New Threshold Function In Wavelet Denoising

Original signal is often polluted in the process of collection,convertion and tansmission because of equipments and enviroment. So denoising has become a very import issue. The traditional denoising method tends to make a Fourier transform to make a filteration.But this method often causes some useful information disappear.Wavelet transform has some good quality like local time-frequency,MRA and electoral base and so on,This method makes the separation of noise from signal much easier,and it is more widely used.In the history of math,wavelet analysis is a milestone which expands the appalication of pure math. As for the time-frequency localization and MRA,wavelet transform became a very useful tool for signal processing.Denoising is very important field in image processing.This paper is mainly about wavelet denoising.There are three method in wavelet denoising:namely, maxima modulus denoising method,spatially selective noise filtrantion method and wavelet threshold denoising method.These method have diffrent appalications and many useful properties.Among these method,the theory of wavelet threshold denoising is not complacated,and implentation of this method is available and stable.The key of this method is threshold function. Although the soft and hard threshold function are useful somehow,there are a few shortcomings,like the discontinuty of hard threshold function and not infinitely diffrentiable of soft threshold function also,there is constant gap in hard threshold method which can make negative effect.To improve the denoising qualaty,I invent a brand new threshold function.It inherit the good properties of conventional threshold function and is infinitely diffrential.During the parameter changes,it changes between soft threshold function and hard threshold function.It is available to programm and computate for its structure.Finally,I denoise a picture added with white noise.I programms and computates under MATLAB R2010a.Judging from the index of MSE and PSNR,I came to a conculusion that the threshold function is better than two conventional threshold functions.