Wavelet Based Variational Approach to Adaptive Regularization Parameter for Noisy Image Restoration

In noise removal the regularization parameter is traditionally global. In the new approach a variational model \min _g\|f-g\|_L_2(R)^2+\alpha R(g) is constructed, where g is in some wavelets space. Through wavelets pyramidal decomposition and relying on the different time-frequency properties of noise and signal, a certain regularization parameter is chosen adaptively, and different parameters are chosen in different levels for adaptive noise removal.