# A Learning-Based Image Fusion for High-Resolution SAR and Panchromatic Imagery
## 1 Introduction  
Recently, various high-resolution satellite sensors have increasingly been developed, especially the synthetic aperture radar (SAR) imaging sensor, which has an important advantage in Earth observations [1, 2]. It is an active sensor that provides its own source of illumination, which is independent of solar illumination and is not affected by daylight or night darkness [3]. It can also penetrate through atmospheric effects, allowing for Earth observation regardless of weather conditions such as rain, fog, smoke, or clouds [4, 5]. Information contained in a SAR image depends on the backscattering characteristics of the surface targets and is sensitive to the geometry of the targets [6]. The image provides information on surface roughness, object shape, orientation, or moisture content [7, 8]. Furthermore, the SAR image can highlight objects that have a low contrast in optical images. However, interpreting the details in SAR images is a challenging task for several reasons: (1) SAR images inherently contain geometric distortions due to distance-dependence along the range axis and signatures related to radar signal wavelengths [9]; (2) the human eye is familiar with the visible part of the electromagnetic spectrum and is not adapted to the microwave-scattering phenomenon [10]; (3) the reflectance properties of objects in the microwave range depend on the frequency band used and may significantly differ from the usual assumption of diffuse reflection at the Earth's surface [11]; (4) since SAR images are inherently coherent during the process of their generation, speckle noise is inevitable in the resulting images, rendering the images unintuitive [12]; and (5) such images also contain the after-effects caused by foreshortening, slant-range scale distortion, layover, andshadows [13; 14]. Thus, the SAR image can be visually difficult to interpret and, ultimately, this data improvement approach is designed at the end to be implemented in the monitoring and analyzing earth surface issues that offering an advanced solution for many applications including environmental studies [15]. To improve the quality and interpretability of SAR images, image fusion with optical images, which contain information regarding reflective and emissive characteristics, can be a good alternative [16; 17; 18]. In particular, the panchromatic image can be utilized because it is physically sensitive to ground objects and reflects the objects' contour information with high spatial resolution and abundant textural features [19]. The overall concept of image fusion between the SAR and panchromatic images is to incorporate spatial details extracted from the panchromatic image into the SAR image by using an appropriate algorithm [20]. Therefore, the fusion of the SAR and panchromatic images makes it possible to use complementary information and contributes to a better understanding of the objects in target areas [21]. Furthermore, the fusion of SAR and panchromatic images has additional benefits, such as the sharpening of image quality, enhancement of certain features that are invisible with either data set in the non-combined state, complementation of data sets for improved classification, detection of changes using multi-temporal data, and substitution of missing information in one image with signals from another sensor image [1]. However, because of the significant differences between the imaging mechanisms of the SAR and optical sensors, the generation of surface features of the same object are different in SAR and panchromatic images [5]. Conventional image-fusion methods such as principal component analysis (PCA) and high-pass filtering are not appropriate because they do not consider the differences in imaging mechanisms and the spectrum characteristics between the two image types [22]. An alternative approach is multiscale decomposition, based on which various methods have been proposed for the fusion of SAR and panchromatic images; however, these methods have some limitations [19; 20; 22; 23].