To reduce the psudo-Gibbs effects and the"curvelet like"aliased curves resulted from using curvelet transform for image denoising

a noise removal method which combines computational harmonic analysis and variation is presented.Firstly

the nonlinear thresholding strategy is applied to the coefficients of the second generation curvelet transform of noisy image.And then

a total variation regularization model with constraint condition on curvelet transform domain is established

whose feasible domain is determined by the coefficients remained.Finally

the projected gradient algorithm is used to solve the model.Experiments show that the method can remove noisy and remain edges

while the distortions are suppressed efficiently

and that the vision effect has an advantage of improving.