Because the fusion method of traditional Shearlet transform may emerge pseudo Gibbs phenomenon and has a large amount of data,this paper puts forward an infrared and visible image fusio n method based on the improved Shearlet transform and the theory of compressed sensing.Shearlet transform can analyze im age in more directions,and the inverse transform is only Shearlet filter.First o f all,the pyramid filters are used to decomposite the images to get the high fre quency and low frequency in formation graphs with the same size as the original images.For the low frequency information graph,the local area information entrop y is used for fusion.For the high frequency information graph,the horizontal ver tical and diagonal Shearlet filters are utilized and then the Toeplitz matrix is adopted to observe the filter coefficients,which is more simple and with easy p hysical implementation and then the split Bergman iteration is used to get the Shearlet coefficient for fusion.Finally,the fused image is got by filter reconstr uction.The experimental results show that the proposed method effectively avoids the pseudo-Gibbs phenomenon and outperforms the conventional fusion method on the amount of data transmission and fusion,and shortens the fusion time to less than 50,enhancing the efficiency of image fusion.