Total variation based band-limited sheralets transform for image denoising

Noise reduction is an important image pre-processing for improving the quality of image. Shearlet transform, as a method of multiscale geometric analysis, is more suitable for image processing because of better approximation precision and sparsity description. A novel approach based on the band-limited shearlet transform and total variation for image denoising was proposed. Unlike traditional hard threshold method, different thresholdings were used at each scale to obtain good estimate. The reconstruction image was used as initial image of total variation minimum method. Numerical examples demonstrated that the approach is highly effective at denoising complex images. Compared with other methods in multiscale geometric analysis domain, such as nonsubsampled contourlet transform, curvelet transform and hard-threshod method of shearlet transform, the denoised image in this paper removed the noise while retaining as much as possible the important signal features and details such as edges and texture information.