# Hyperspectral Super-Resolution Technique Using Histogram Matching and Endmember Optimization
## 1 Introduction  
Hyperspectral images (HSIs) are widely used in many scientific and engineering fields, because they are capable of collecting the light spectrum from a broad wavelength and saving the spectral data with high spectral resolution. Most HSI applications in scientific and engineering fields aim to identify materials in an image on the basis of the spectral characteristic of each chemical reflecting the light. HSIs have been used as a powerful tool for detecting certain materials in an object, or measuring quantitative chemical content in the fields of agriculture [1; 2], environment [3; 4], surveillance [5; 6], biomedical imaging [7; 8], and geosciences [9; 10]. Low-resolution is, however, one of the shortcomings of HSIs in practice. The low-resolution results from the way in which hyperspectral cameras acquire the spectrum from light. Currently, two types of hyperspectral cameras are available--push-broom and snapshot. Push-broom cameras scan a line in an image and put the reflected light through optical spectroscopic sensors [11], while snapshot cameras use a focal-plane array to generate a two-dimensional image with a single shot [12]. Regardless of the hyperspectral camera type, all hyperspectral cameras slice the light input into small units of spectral bands to obtain fine spectral resolution, and this process inevitably leads to a low amount of energy collected by a pixel on the sensor. Therefore, pixel size of hyperspectral cameras should be larger than that of general cameras, to avoid high signal-to-noise ratios in the collected spectrum. To overcome this innate limitation of hyperspectral cameras, much research has been conducted to increase the resolution of HSIs, by integrating other types of images. The techniques are variously referred to as hyperspectral image fusion [13; 14; 15], hyperspectral super-resolution (HSR) [16; 17], or hyperspectral image upsampling [18]; HSR is the term used to refer to the technique in thispaper. Most common HSR techniques are based on pan-sharpening, which can also be applied to RGB images. Pan-sharpening merges a low-resolution multispectral image with a high-resolution panchromatic image to create a single multispectral image with higher resolution features [19]. One of the most common types of pan-sharpening algorithms, component substitution [20], is comprised of six steps: up-sampling, alignment, forward transformation, intensity matching, component substitution, and reverse transformation. However, because HSR is an ill-posed problem, assumptions of the previous pan-sharpening techniques to resolve the ill-posedness are imperfect, which leads to the need for new assumptions, based on new perspectives [21]. HSR techniques based on deep learning have been developed in recent years, as deep learning techniques are rapidly emerging for image processing. [PERSON] et al. [22] proposed an HSR model combining a deep convolutional neural network with an extreme learning machine for HSI classification. [PERSON] et al. [23] trained the nonlinear relationship between low- and high-resolution images using a convolutional neural network, and proposed a collaborative non-negative matrix factorization, to enforce collaborations between the observed low-resolution HSI and the transferred high-resolution HSI. Among various HSR techniques, those based on the linear mixing model (LMM) are widely studied by many researchers. The LMM represents an HSI as a matrix factorization of linear spectral bases, so-called endmembers, and it can solve difficult HSI fusion problems with multispectral images, including RGB images. [PERSON] et al. [24] formulated an HSR problem in the form of a sparse non-negative matrix factorization, and applied alternating optimization and convex optimization solvers. [PERSON] et al. [25] obtained a spectral dictionary using K-singular value decomposition, and computed sparse fractional abundances with a sparse coding technique of orthogonal matching pursuit. [PERSON] et al.