Recent years

decomposing an image into cartoon component (bounded variation component) and oscillating component (texture component) is an important problem in the field of image processing.The cartoon component of an image is modeled by a bounded variation (BV) function;the corresponding incorporation of BV penalty terms in the variational functional leads to solve PDE equations.Daubechies replaced the BV penalty term by a Besov term and wrote the problem in a wavelet framework.Following her ideas

we propose a new image decomposition algorithm based on the digital curvelet transform.By designing a digital curvelet transform algorithm and a scale-dependent thresholding rule

elegant and numerically efficient schemes are obtained.We can see that this approach is very robust to additive noise and can keep the image edges stable.