A novel multi-focus image fusion algorithm based on NSST-FRFT

Non-subsampled Shearlet transform (NSST) has good properties such as multi-scale, multi-direction and shift invariance, but limits the signal analysis to the time frequency domain. Fractional Fourier transform (FRFT) extend the signal analysis to fractional domain, but it is unable to analysis the partial characteristic of signal. Combine the advantages of NSST and FRFT, a novel image fusion algorithm is proposed. Firstly, NSST is applied to the two source images. Secondly, the FRFT is applied to the low-frequency sub-bands coefficients of NSST to acquire image description in fractional domain. Thirdly, fusion rule selecting maximizes of sum-modified-Laplacian is applied to fuse high-frequency sub-bands coefficients and fusion rule of the simple averaging operation is applied to fuse low-frequency coefficients. Finally, the fused image is obtained by the inverse FRFT and inverse NSST. Experimental results show that the proposed method can not only obtain good visual effect, but also improve its objective evaluation criteria.