## 1 Introduction  
With the development of various high-resolution satellite sensors, it is possible to precisely monitor the surface of the earth [1]. In particular, multi-temporal satellite images are an effective data source that can detect changes in land use and land cover [2; 3]; however, it is difficult to maintain radiometric consistency in multi-temporal images due to changes in atmospheric conditions, sensor-target-illumination geometry, sensor calibration, and differences in phenological conditions [4; 5]. Therefore, radiometric normalization, which is a preprocessing procedure, is performed to reduce--or eliminate--radiometric differences due to the aforementioned influences and increase sensitivity to landscape changes [6; 7]. Radiometric normalization can be divided into two main categories: (1) absolute radiometric normalization and (2) relative radiometric normalization [7; 8]. Absolute radiometric normalization aims to convert digital numbers (DNs) that are recorded by satellite sensors to ground surface reflectance and corrects factors, such as sensor differences, solar angles, and atmospheric effects [9]. In other words, accurate sensor calibration parameters and atmospheric properties at the time of data acquisition are required. However, it is often difficult to collect such data in terms of cost or accessibility, and the process cannot be implemented when data are not available [10; 11; 12]. Relative radiometric normalization, on the other hand, is an image-based normalization method that selects one image as a reference and matches the radiometric characteristics of a subject image [13; 14]. That is, relative radiometric normalization is generally utilized since the multi-temporal images are normalized into common scales without extra parameters [12; 15]. Relative radiometric normalization can be classified into two categories: a global statistics-based method and a radiometric control set sample (RCSS)-based method. The former is performed by using statistical values of all pixels in the image, which includes histogram matching, minimum-maximum (MM), mean-standard deviation (MS), and simple regression (SR) [15; 16]. In contrast, the latter is based on invariant pixels, known as RCSSs, which include dark set-bright set (DB), pseudo invariant features (PIF), and no-change sets (NC) [17; 18; 19; 20]. At this time, except for histogram matching, normalization is performed through regression equations, while assuming a linear relationship between the pixels at the same position in each band [21]. However, most remote sensing data are nonlinearly distributed, and the surface of the earth is composed of a complex mixture of natural and man-made features that exhibit nonlinear characteristics [22; 23; 24]. Changes that are caused by vegetation in particular have the most typical characteristics, including nonlinearity, which induces serious disturbances when change detection is performed [25; 26]. In addition, since optical satellite imagery, which is the main source in change detection, is affected by clouds and atmospheric conditions, it is difficult to acquire images that meet the temporal requirements [27; 28]. In such cases, images with phenological differences as well as radiometric differences should be utilized [25; 26]. In other words, compositive normalizations, including phenological and radiometric properties, should be conducted. This study proposes a nonlinear relative radiometric normalization method while considering the phenological as well as radiometric properties for high-resolution satellite images in order to overcome these limitations. Among all of the nonlinear regression models, the proposed method is based on multilayer perceptron (MLP), which has advantages over statistical methods, such as a lack of assumptions regarding the probabilistic models of data, robustness to noise, and the ability to learn complex and nonlinear patterns [29; 30].