An adaptive fusion approach for infrared and visible images based on NSCT and compressed sensing

A novel nonsubsampled contourlet transform (NSCT) based image fusion approach, implementing an adaptive-Gaussian (AG) fuzzy membership method, compressed sensing (CS) technique, total variation (TV) based gradient descent reconstruction algorithm, is proposed for the fusion computation of infrared and visible images.Compared with wavelet, contourlet, or any other multi-resolution analysis method, NSCT has many evident advantages, such as multi-scale, multi-direction, and translation invariance. As is known, a fuzzy set is characterized by its membership function (MF), while the commonly known Gaussian fuzzy membership degree can be introduced to establish an adaptive control of the fusion processing. The compressed sensing technique can sparsely sample the image information in a certain sampling rate, and the sparse signal can be recovered by solving a convex problem employing gradient descent based iterative algorithm(s).In the proposed fusion process, the pre-enhanced infrared image and the visible image are decomposed into low-frequency subbands and high-frequency subbands, respectively, via the NSCT method as a first step. The low-frequency coefficients are fused using the adaptive regional average energy rule; the highest-frequency coefficients are fused using the maximum absolute selection rule; the other high-frequency coefficients are sparsely sampled, fused using the adaptive-Gaussian regional standard deviation rule, and then recovered by employing the total variation based gradient descent recovery algorithm.Experimental results and human visual perception illustrate the effectiveness and advantages of the proposed fusion approach. The efficiency and robustness are also analyzed and discussed through different evaluation methods, such as the standard deviation, Shannon entropy, root-mean-square error, mutual information and edge-based similarity index.