ecause cosh(x ) for x [0; 1], so we know that , which is the Fourier transform of exact data function g(t), must decay rapidly as . Small errors in high frequency components can blow up and completely destroy the solution for 0 x . Such a decay is not likely to occur in the Fourier transform of the measured data at x = 0, its Fourier transform is merely in The Meyer wavelet has a very good local property in frequency domain, i.e., for fixed index J, the Fourier transform of the scaling functions in and the wavelet functions in have common compact support, respectively. And so that, Problem ( 1 ) becomes a well-posed approximation problem in the scale space .
