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In this paper, a new image fusion algorithm based on non-subsampled contourlet transform (NSCT) is proposed for the fusion of multi-focus images. The selection of different subband coefficients obtained by the NSCT decomposition is critical to image fusion. So, in this paper, firstly, original images are decomposed into different frequency subband coefficients by NSCT. Secondly, the selection of the low-frequency subband coefficients and the bandpass directional subband coefficients is discussed in detail. For the selection of the low-frequency subband coefficients, the non-negative matrix factorization (NMF) method is adopted. For the selection of bandpass directional subband coefficients, a regional cross-gradient method that selects the coefficients according to the minimum of the regional cross-gradient is proposed. Finally, the fused image is obtained by performing the inverse NSCT on the combined coefficients. The experimental results show that the proposed fusion algorithm can achieve significant results in getting a new image where all parts are sharp. [ABSTRACT FROM PUBLISHER]