# Hyperspectral Image Super-Resolution Based on Spatial Group Sparsity Regularization Unmixing
## 2 Related Work  
Hyperspectral imaging has been widely adopted in the field of remote sensing over the past two decades, and has become popular in the field of traditional computer vision. It is difficult to obtain a high spatial resolution HSI, due to hardware limitations [20], which has led to a notable amount of research into HSI super-resolution. HSI super-resolution is also referred to as HS-MS image fusion as it fuses the high-resolution spectral information of an HSI and high-resolution spatial information of an MSI. We roughly divide the related work into the following categories: (1) Pan-sharpening-based methods; (2) Matrix factorization-based methods; (3) Tensor factorization-based methods; and (4) Deep Learning-based methods. The recent development of HS-MS image fusion is illustrated as follows. Pan-sharpening fuses an HSI with a high spatial resolution panchromatic image. It is considered a special case of HS-MS image fusion. [PERSON] et al. [9] first introduced a pan-sharpening-based fusion method by using a wavelet transform. Then, [PERSON] et al. [10] proposed an improved method using a 3D wavelet transform. However, the performance of wavelet transform-based methods is highly restricted by spectral resampling. With the development of pan-sharpening techniques, more advanced attempts have been made to solve HS-MS image fusion problems. For example, a framework has been proposed in [11] that uses pan-sharpening to divide the spectrum of the hyperspectral data into several regions. A synthetic image resampled from an MSI is then used as a high-resolution image in the spectral range covered by the hyperspectral bands. [PERSON] et al. [21] proposed a new framework, termed _hypersharpening_. It adapts multi-resolution analysis (MRA)-based pan-sharpening methods to HS-MS fusion. In this work, a high-resolution image is synthesized for each hyperspectral band, as a linear combination of MSIs, by linear regression. Matrix factorization-based methods are mainly based on the assumption that an HSI can be approximated by a basis and corresponding coefficients. Based on different bases, Matrix factorization-based methods can be divided into two sub-categories: methods based on the spectral basis are also known as spectral unmixing-based methods, which transform the HS-MS fusion problem into a coupled matrix factorization problem. The spectral basis and coefficients are updated using HS-MS images with specific priors. The HSI is unmixed into endmembers and abundances with suitable spatial and spectral constraints. For example, [PERSON] et al. [12] fused HS and MS images to a super-resolution image by spectral unmixing. In this work, Non-negative Matrix Factorization (NMF) and least-squares regression were separately used to unmix the input HSI and MSI. An improved method, termed coupled NMF (CNMF), was proposed by [PERSON] et al. [13]. The improvement of this method was mainly in conducting spectral unmixing based on NMF with the constraints of an observation model, combining both spectral response functions (SRFs) and point spread functions (PSFs). [PERSON] et al. [22] proposed a method that uses non-parametric Bayesian sparse representations for HS-MS image fusion, which contributed to inferring distributions for the spectra of endmembers in the scene. [PERSON] et al. [23] addressed HSI super-resolution as a coupled matrix factorization problem, jointly solving HSI super-resolution and unmixing. The other sub-category of matrix factorization-based methods tries to make full use of the spatial structures of the HSI, in order to obtain better super-resolution performance. For example, [PERSON] et al. [24] proposed a method, in which G-SOMP+ dictionary learning and sparse coding were used with the extracted spectra to reconstruct the super-resolution HSI. [PERSON] et al. [25] presented an unsupervised spectral unmixing-based HS-MS image fusion algorithm. The problem was formulated as an inverse problem with non-negativity and sum-to-one constraints. [PERSON] et al.