# Hyperspectral Super-Resolution Technique Using Histogram Matching and Endmember Optimization
## 1 Introduction
[26] defined an HSR model as the standard linear inverse problem model, using a form of regularization based on vector total variation, by considering spatial and spectral characteristics of the given data. [PERSON] and [PERSON] [18] proposed a two-step RGB-guided HSI upsampling scheme that consists of spatial upsampling and spectrum substitution stages. One aspect of note in this work is that the spectrum substitution stage learns a local spectral dictionary, from the superpixel neighborhood. [PERSON] et al. [27] developed a sparse representation model based on superpixels, that learns a spectral dictionary via online dictionary learning. This method adopts joint sparse regularization to simultaneously decompose the superpixel on the transformed dictionary, to obtain the corresponding coefficient matrix. However, in most HSR techniques, it is implicitly assumed that the mismatch between low-resolution and high-resolution images is negligible. When a hyperspectral camera is used together with an RGB camera, it is rarely possible, in practice, to match the fields of view (FOVs) of the two cameras exactly. In remote sensing, such as for satellite photography and aerial photography, the mismatch of FOVs resulting from different camera angles or lens distortion can be adjusted and made negligible because the imaged objects are far enough from the cameras. However, if imaged objects are close to the cameras, it is difficult to avoid these mismatches between images. Furthermore, the two cameras have different sensitivities, even in the same light bandwidths, owing to differences in imaging sensors and filming mechanisms. HSR techniques based on the LMM potentially diverge in the process of finding the coefficient if there is a significant mismatch between images. This divergence problem occurs when an HSI and other RGB or multispectral images do not perfectly fit each other at the pixel level, because most of the linear-mixing-model-based HSR techniques simultaneously optimize the coefficient towards the pixel location of both the HSI and RGB or multispectral image. [PERSON] et al. [28] formulated the super-resolution problem as a searching procedure for an image that has both high-spatial and high-spectral resolution. The high-resolution HSI is defined as a factorization of a matrix of endmembers and a matrix of per-pixel abundances. A low-resolution HSI is reconstructed by multiplying a spatial downsampling matrix, and a high-resolution RGB image is reconstructed by multiplying a spectral downsampling matrix. Then, the differences between reconstructed images and original images are minimized using a gradient descent optimization algorithm. However, if the input HSI and the RGBimage are mismatched, the high-resolution HSI diverges, because it is impossible for the per-pixel abundance matrix to satisfy pixel locations of both images. The divergence problem has to be overcome to develop an HSI-RGB image integrated system that can be used to take an image of a close object. We faced this problem while developing an HSI-RGB image integrated system detecting chemical leaching on the surface of a concrete structure. The features of chemical leaching on the concrete surface were too obscure to be detected, because of the low resolution of the HSI. One of the methods used to increase the resolution is to gain access closer to the concrete surface, but most concrete structures are too far away to be accessed. Therefore, it is necessary to develop an HSI-RGB image integrated system that can reconstruct a high-resolution HSI from an RGB image taken with different camera sensitivities and from different FOVs. In this paper, we propose an HSR method that uses an HSI and an RGB image taken from a different FOV. This method mainly uses histogram matching and the endmember abundance optimization process proposed in [28]. First, a low-resolution RGB image is obtained, by applying spectral sensitivity of an RGB camera to a low-resolution HSI. The acquired low-resolution RGB image contains the color distribution of the low-resolution HSI.