Abstract:

When images are denoised by means of nonlinear filtering algorithms,the selections of the threshold pa-rameter and the filter function tend to have great effects on the quality of the denoised images.In order to overcome this difficulty,a family of piecewise n-degree filter functions of wavelet threshold parameter are constructed.which can be used to nonlinear filtering algorithms.It is then proved that the wavelet approximation is a near.minimizer of the functional which has to be minimized to solve the denoising problem,and that the near.minimizer can be used to substitute the soft threshold filter of Donoho. Moreover,the bigger the degree n is,the better the approximation
quality is.It is finally proved that the limit of the n-degree filter is an ideal lowpass filter.

Key words: image denoising, variational problem, wavelet threshold, Rear-minimizer