Multi-focus Image Fusion Based On Four-channel Non-separable Lifting Wavelet

In image fusion processing,tensor product wavelet and its lifting wavelet only emphasize the horizontal and vertical edges of images,resulting in the low spatial resolution of the fused image when applied to multi-focus image fusion.The image fusion method based on two-dimensional four-channel non-separable wavelet has high spatial resolution,but the computation amount of this fusion method is higher since the convolution operations is adopted while the images are decomposed and reconstructed.To solve these problems,this paper lifts two-dimensional four-channel non-separable wavelet filter banks and proposes a new method of multi-focus image fusion based on this lifting schema.The main research work of this paper are as follows:Using the Euclidean division of the one-dimensional polynomials,Daubechies et al.successfully decomposed the one-dimensional wavelet polyphase matrix into the unit product of the lower left triangular matrix,the right upper triangular matrix,and the diagonal matrix,thus lifted the one-dimensional wavelet transform.However,because the two-dimensional polynomials do not contain Euclidean division,the polyphase matrix of two-dimensional non-separable wavelets cannot be decomposed while one-dimensional wavelet can.To solve this problem,this paper successfully designs the two-dimensional four-channel non-separable filter banks,decomposes the polyphase matrix of it,and gets the lifting method.A multi-focus image fusion based on four-channel non-separable lifting wavelet is proposed in this paper.Firstly,the polyphase matrix of two-dimensional four-channel non-separable filter banks is lifted and decomposed,and the source image is decomposed by the proposed lifting scheme.Secondly,the low frequency sub-images and high frequency sub-images are fused respectively.Finally,the inverse transform of the lifting wavelet is implemented and the fused image is obtained.The fusion performance is evaluated by entropy,average gradient and image definition.The experimental results show that the proposed fusion method has higher definition and spatial resolution than that of the tensor product wavelet method,tensor product lifting wavelet method,and contourlet fusion method,respectively.The speed of the proposed fusion method has been greatly improved than that of its original two-dimensional four-channel non-separable wavelet fusion method.