# A Learning-Based Image Fusion for High-Resolution SAR and Panchromatic Imagery
## 1 Introduction
For image fusion based on these methods, the SAR and panchromatic images are represented by the fixed orthogonal basis function, and the image fusion is performed by the fusion of the coefficients of different sub-bands in the transform domain [24]. Because some features cannot be represented sparsely, this fusion cannot represent all useful features accurately due to limited fixed transforms [20]. In particular, the discrete wavelet transforms (DWT) fusion method only uses features of single pixels to make decisions, and it is not shift-invariant [25]. Similarly, the contourlet transform (CT)-based fusion method lacks shift-invariance, which results in pseudo-Gibbs phenomena around singularities, and it has difficulty in preserving edge information. The non-subsampled contourlet transform (NSCT)-based method, which is a fully shift-invariant form of the CT, leads to better frequency selectivity and regularity [26]. However, this method still fails to fuse the features of physically heterogenous images [5]. Another approach is the sparse representation method, in which the generation of dictionary and sparse coding is crucial [24]. This method can extract potential information from input images in addition to representing them sparsely; however, this method does have limitations. Firstly, the advanced sparse coefficients fusion rule may cause spatial inconsistency, and secondly, the trained dictionary cannot accurately reflect the complex structure and detail of the input images [27]. To overcome these limitations, this study proposes a new image-fusion method that utilizes useful features as much as possible and considers the differences in imaging mechanisms. Instead of directly fusing pixels or decomposing them to perform fusion in a limited transform, this algorithm aims to extract sufficient features and establish relationships to fuse the SAR and panchromatic images. This makes it possible to contain the structural and detailed information of panchromatic images and increase the overall interpretability of SAR images [28]. Furthermore, a learning-based approach is used to account for the differences in imaging mechanisms of the SAR and panchromatic images. Random forest (RF) regression, which can model non-linear relationships, is utilized, and learning is performed for each class to reduce the complexity of the algorithm and for better predictions [29; 30]. Then, experiments are performed on multiple scenes to demonstrate the capability and performance of the proposed method. The results are comprehensively compared with those of conventional image-fusion methods. The main contributions of this study can be summarized as follows: (1) this is the first learning-based approach for fusing single high-resolution SAR and panchromatic images; (2) to consider the differences in imaging mechanisms, this method uses RF regression, which can model non-linear patterns, avoids overfitting, and is relatively robust to the presence of noise; (3) this method performs classification of the image, where the complexity is reduced by establishing relationships for each class. ; and (4) this method extracts various features to consider sufficient information. The rest of this paper is organized as follows: Section 2 describes materials used in detail and the proposed algorithm in detail. In Section 3, the results of the proposed method are presented, and they are compared with those of the conventional image-fusion methods and discussed. Finally, Section 4 concludes the paper.