Image denoising via bivariate shrinkage function based on a new structure of dual contourlet transform

• A new image transform structure with the name of dual contourlet transform (DCT) is presented, which conducted with both dual LP and DFBS.
• A new image denoising method is developed with using bivariate shrinkage threshold on the coefficients of DCT. It is worth mentioning that it is the first time using bivariate shrinkage threshold on DCT domain.
• In evaluating process, we use a new measure that the difference between the original image and the denoised image to identify the denoised result, which is rarely used in other denoising literatures.

Image denoising is a basic procedure of image processing, and the purpose of image denoising is to remove noises entirely and well preserve image boundaries and texture information simultaneously. However, conventional filtering methods easily lead to the loss of texture and details information. This paper proposes a new image denoising method to improve this problem, first proposing a new structure called dual contourlet transform (DCT) which is improved from contourlet transform and dual tree complex wavelet transform (DTCWT). The DCT employs a dual tree Laplacian Pyramid (LP) transform to improve the shift invariance and adopts directional filter banks (DFB) to achieve higher directional selectivity. Compared to other existing structures of multiresolution analysis, the main advantage of the DCT is that it not only possesses the advantages of other structures, but also it has simple structure and easy to implement. The most noteworthy is the redundancy of DCT is 8/3 at most; it is the envy of other existing structures. Second, after studying the distribution of DCT coefficients and the correlation between the interscale and intrascale dependencies, we take this account into denoising and use bivariate threshold function on DCT coefficients. Simulation experiments show that the proposed method achieves better performance than those outstanding denoising algorithms in terms of peak signal-to-noise ratio (PSNR), as well as visual quality. In addition, to verify the validity of our method, we give the difference between the original image and the denoised image that rarely used in other denoising literatures.