**1. Introduction**

Hyperspectral pansharpening aims to combine the preponderance and complementary information of the hyperspectral (HS) and panchromatic (*P*) images for image analysis and various applications [1]. Spatial information and spectral information plays an important role in remote sensing image analysis. Unfortunately, due to the limitation of sensor and theoretical aspects, most satellites cannot provide a remote sensing image with both high spatial and spectral resolution [2,3]. However, hyperspectral images with high spectral and spatial resolution have been in demand. Therefore, it is important to introduce hyperspectral pansharpening techniques to improve the spatial resolution of hyperspectral images.

Many methods dedicated to hyperspectral pansharpening have been proposed in the last two decades [4,5]. These hyperspectral pansharpening methods can be grossly divided into four groups: component substitution (CS), multiresolution analysis (MRA), matrix factorization, and Bayesian. In recent years, there has been increasing interest in Bayesian methods and matrix factorization methods. Bayesian methods usually model the HS and the *P* images as the degraded high-resolution HS images and then restore the HS images through solving optimization problems, such as Sparse

Representation [6,7], Bayesian HySure [8], and Bayesian Naive Gaussian prior (Bayesian Naive) [9]. Matrix factorization methods utilize the linear mixture model, and use it for the fusion optimization model. The coupled non-negative matrix factorization (CNMF) [10] method is a representative among the matrix factorization methods. Bayesian and matrix factorization methods have shown considerable potential in improving the quality of the fused images. However, for purpose of estimating a good solution, researchers have also made efforts to solve the ill-posed inverse problem, which is time consuming and computational expensive [11,12]. From a perspective of practical applications, it is a difficult problem.

The CS and MRA methods are easy and fast to implement [13,14]. The component substitution (CS) methods include algorithms, such as intensity hue saturation (IHS) [15,16], Gram–Schmidt (GS) [17], and principal component analysis (PCA) [18–20]. The primary concept of CS methods is that the HS image can be separated into spectral and spatial components, and the *P* image is a good substitution for the separated spatial component. The final fused image is obtained by the inverse spectral transformation [21]. The fusion step of the CS methods is summarized as

$$H\_F^k = H^k + \mathfrak{a}^k (P - S) \tag{1}$$

where, *k* = 1, 2, ... , *λ*, *λ* is the number of the HS image bands, *αk* is the *k*th injection gain, matrix *P* is the panchromatic image, matrix *S* is the spatial component of the HS image, *P* − *S* is generally called the detail map, matrix *H* is the interpolated HS image, *H<sup>k</sup> F* and *H<sup>k</sup>* are the *k*th band of the fused image and the interpolated HS image, respectively. The injection gain is a gain used for merging the detail map and the interpolated HS image into a fused HS image. The CS methods have simple and fast implementation [22]. However, the spectral distortion is serious due to the spectral mismatch between the *P* image and the replaced component [23].

The multiresolution analysis (MRA) has algorithms such as modulation transfer function (MTF) generalized Laplacian Pyramid (MTF-GLP) [24], smoothing filter-based intensity modulation (SFIM) [25] and MTF-GLP with high pass modulation (MGH) [26]. The spatial filtering is performed on the *P* image to extract the high-frequency spatial details. The fused HS image is obtained by injecting the extracted spatial details into each band of the interpolated HS image. Following, a formulation of MRA methods is defined as [4]

$$H\_F^k = H^k + \beta\_k (P - P\_\text{L}) \tag{2}$$

where, *k* = 1, 2, ... , *λ*, *λ* denotes the number of the HS image bands, *βk* denotes the *k*th injection gain, and *PL* denotes low-frequency component of the *P* image. The advantages of the MRA methods are good performance, temporal coherence, spectral consistency and acceptable computational complexity. In addition, the MRA methods can be easily adopted when the source of the high spatial frequencies is another multispectral/hyperspectral image [27]. However, blurry images may occur when the shapes of low-pass filters adopted have problems [24].

To overcome the problems of the CS and MRA methods, the CS-MRA hybrid frameworks were proposed [20,28,29]. These methods focus on fusing the *P* image and the spatial component of the HS image by multiscale transforms. The final fused image is obtained by the inverse spectral transformation. The performance of the CS-MRA hybrid methods has shown improvement compared with that of the CS or MRA methods. However, the fused images obtained by these hybrid methods suffer from spectral distortion of different degrees, since the structure of the HS image is not fully considered. To overcome the drawbacks of the CS-MRA hybrid methods, we propose a new CS-MRA hybrid framework based on intrinsic image decomposition and weighted least squares filter. Specifically, we filter the sharpened *P* image by the weighted least squares (WLS) filter to obtain the high-frequency component of the *P* image at first. Subsequently, the MTF-based deblurring method is performed on the interpolated HS image. The intrinsic image decomposition (IID) is applied to the deblurred interpolated HS image to extract the illumination component of the HS image. The detail map is generated by merging the high frequency information of *P* image with the illumination component of the HS image. Finally, the detail map is injected into the deblurred interpolated HS image to obtain the fused HS image.

The following are the major contributions of the proposed method using IID and WLS:


This paper is organized as follows. We describe the related work in Section 2. The proposed method is discussed in Section 3. Section 4 displays the experimental results and discussion. Section 5 concludes the paper.
