1 Introduction
Due to the light optical imaging system's focusing scope is limited, it is hard to image clearly for all objects in the scene. It will be formed a clear image at the image plane when an object is located at the focal plane, while the objects will be formed the image with a different degree of blur at the other locations. In real life, people hope to get a image that all of objects in the image are clear. Usually, this problem can be solved by fusion multi-focus image. Currently, multi-focus image fusion method is generally divided into two categories: one is the multi-scale analysis method which include the pyramid, discrete wavelet transform and wavelet fusion algorithm commonly; The other is that the source image is divided into blocks and selected the clear image block to reconstruct the fused image[1], Most research currently focus on the fusion method of based on multi-scale, such as DWT (Discrete Wavelet Transform), but it is only to tell the limited direction and can't represent the texture feature in all directions. In 2002, Do et al. proposed the Contourlet transform which not only has the wavelet multi-resolution and time-frequency characteristics of the locality, but also has a high degree of directionality and anisotropy. Although using Contourlet fusion method can get better results, but the Contouriet doesn't have the shift-invariant[2] and leads to Gibbs effect easily. In 2006, Cunha et al. proposed a Contourlet transform with translation invariance completely and without downsampling Non-subsampled Contourlet Transform (NSCT)[3], which improves the limitation of Contourlet transform. NSCT solves the inadequate of Contourlet without shift-invariant. NSCT is an over-complete transformation with shift-invariant, multi-scale and multidirectional[4], which widely used in the field of image fusion. However, due to the NSCT is an over-complete transformation, it will generate a lot of data redundancy in the process of decomposing images and the algorithm is very complex. All of methods are based on multi-resolution analysis in the process of fusing and need to multi-resolution decomposition and reconstruction for the source image, thus it causes a greater change for the source image information and affects the quality of fusion image.