## 1 Introduction  
With the excellent propagation characteristics of sound waves in the water, side-scan sonar provides high-resolution and high-accuracy image information for underwater operations. Full sea area survey is general carried out by means of strip measurement, which requires the adjacent strip to have a certain width of overlapping area [1]. However, owing to the effect of imaging time, hull attitude, and ocean reverberation [2], underwater target and terrain texture in the overlapping area have a certain degree of distortion. The overlapping area of a single strip image has incomplete information detection, and the contours of underwater targets do not match. Therefore, the information fusion of overlapping area between adjacent strips is of great significance, which lays a foundation for the research of underwater target detection and distribution in public areas and classification of sediment types [3; 4; 5]. In recent years, the effective combination of multi-scale transform domain and other intelligent optimization methods has become a research hotspot of image fusion, especially the domain of nonsubsampled contourlet transform (NSCT) [6]. [PERSON] used NSCT and statistical fusion rules for the information fusion of a multi-sensor image, which effectively preserved texture and image edge information [7]. [PERSON] et al. combined NSCT and texture information for forward-looking sonar image fusion, which weakened the effect of the registration error [8]. The image characteristics of side-scan sonar are similar to forward-looking sonar, and NSCT can be applied to the side-scan sonar image fusion of adjacent strips. Generally, NSCT serves as a basis for multi-scale image fusion to decompose into low and high frequency sub-band images [9]. After that, it is very important for image fusion to make a reasonable fusion criterion for a low and high frequency image, respectively. For the sub-band coefficients of a low frequency image, the weighted average strategy was a conventional fusion criterion, which resulted in partial energy loss of the source image [10]. As for the fusion criterion of modified weighted saliency, the threshold selection of matching degree in this model is more skillful [11]. Moreover, sparse representation and its combination with dictionary learning were applied to select low frequency sub-band coefficients [12; 13]. Their scheme effectively avoided smoothing the texture, edge, and other details of the original image, but the processing of the sliding window might interfere with the correlation between the images, and the latter model involved a lot of training images in the process of iterative learning. Hence, sum-modified Laplacian (SML) energy can be used to characterize the clarity of the sub-band image, and it also reflects the gradient information to a certain extent. [PERSON] and [PERSON] [14] introduced SML energy into the coefficient selection of a low frequency sub-band, which eliminated the interference of fuzzy background region availably. [PERSON] et al. combined visual effects with SML to guide the selection of low frequency [15], which enhanced the judgment depth of multi focus image fusion. However, the overlapping area image of adjacent strips is relatively noisy, and the coefficient selection of a low frequency sub-band based on the above criteria can easily cause false judgment, as well as the pseudo-contour of block flow at the target edge. For the sub-band coefficients of the high frequency image, the previous fusion criteria include maximum energy [16], regional variance [17], and direction contrast maximum [18], but they are easily susceptible to noise interference, making the edge contour of the target blurred. Pulse coupled neural network (PCNN) has been widely applied to guide the coefficient selection of high frequency [19]. Although the PCNN model has a good fusion effect, it contains a lot of non-linear parameters, and the region discrimination of image darkening is not very sensitive.