Multiscale Variational Threshold SAR Image Denoising Based on Quad-tree Complex Wavelet Packets Transform

A new image transform, namely, the quad-tree complex wavelet packets transform (QCWPT) is introduced ,which both has shift invariance and good direction analysis ability and other merits of the dual-tree complex wavelet transform (DCWT), and has the ability of analyzing the high frequency detail signal carefully like the wavelet packet transform (WPT). Furthermore, a novel image denoising scheme based on QCWPT was presented via setting multiscale variational thresholding method,which accords with the characteristic that the high frequency coefficient modules and the variance of the noise attenuate rapidly along with the decomposition scale increasing, the best complex wavelet packets basis was determined and processed at the largest scale. In numerical comparison with various methods, the presented scheme outperforms the traditional Wiener filtering, DCWT and QCWPT in terms of the equivalent number of looks (ENL), the figure of merit (FOM) and visual effects. Experiments also show that the presented scheme could not only remove the noises effectively, but also reserve the SAR image texture and edge details better.