A fusion estimation method based on fractional Fourier transform

Image denoising methods have different denoising performance in both spatial and transform domains, and each method has its relative advantages and inherent shortcomings compared with other methods. A very intuitive idea is to find that an effective fusion method that can combine with the advantages of different denoising methods. In this paper, we propose a novel fusion method based on the fractional Fourier transform and apply it to image denoising problem. Our method is mainly divided into three steps: Firstly, a pre-estimation is made by any two denoising method separately in the spatial domain. Secondly, using these two estimated results as well as their Fourier transform, twice Fourier transform and three times Fourier transform, we obtain a fused result in the fractional Fourier transform domain. Thirdly, the inverse fractional Fourier transform and the modulus operation are used to obtain the final fusion result. Obviously, this approach is the fusion method in four different domains. Experimental results on benchmark test images demonstrate that the proposed method outperforms state-of-the-art stand-alone methods as: BM3D, DDID, MLP, EPLL and also superior to the fusion methods such as classic wavelet fusion method, PCA fusion method and the state-of-the-art CIEM fusion method in terms of quantity value such as the peak signal to noise ratio (PSNR), the structural similarity (SSIM), and visual quality.