**1. Introduction**

Remote sensing images are widely used in environmental monitoring, remote sensing analysis, and target detection and classification. However, in practical applications, it is difficult to obtain multi-spectral remote sensing data, especially high-resolution infrared remote sensing data, and spectrally poor data may be available for longer periods of time than spectrally rich data [1]. Many researchers have explored the acquisition of demanded spectral remote sensing images based on simulation methods [2–4]. The spectral characteristics are determined by the optical characteristics of the underlying surface type, atmosphere, sunlight, and terminal sensors [5]. The traditional methods based on radiation transfer models [6–8] require pre-building a large database of ground features and environmental characteristics. However, it is still difficult to model the complex and random atmosphere and clouds. When the input condition is insufficient for simulating the images of earth background, based on the correlation between the spectral domains, the known spectral images can be used to achieve target spectral image synthesis [9–11]. However, the correlation between the spectral domains is implicit and non-linear.

As deep learning technology can obtain feature correlations in complex spaces through a large amount of data to realize end-to-end image generation, generative adversarial networks (GAN) have achieved rapid development in recent years [12], from the initial supervised image translation [13–15] to the subsequent unsupervised image translation [16] and the later multi-modal image translation [17]. Domain adaptation is critical for the successful application of neural network models in new, unseen environments [18]. Many

**Citation:** Wang, B.; Zhu, L.; Guo, X.; Wang, X.; Wu, J. SDTGAN: Generation Adversarial Network for Spectral Domain Translation of Remote Sensing Images of the Earth Background Based on Shared Latent Domain. *Remote Sens.* **2022**, *14*, 1359. https://doi.org/10.3390/rs14061359

Academic Editors: Saeid Homayouni and Claudio Piciarelli

Received: 19 January 2022 Accepted: 8 March 2022 Published: 11 March 2022

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tasks that support translation from one domain to another have achieved excellent results. Spectral domain translation refers to generating an image of the target spectral do-main based on the image of the source spectral domain while ensuring that each pixel of the generated image conforms to the physical mapping relationship. In the field of spectral imaging, super-resolution [19], spectral reconstruction [20,21], and spectral fusion [22,23] have successively adopted the GAN technology. Rongxin Tang et al. [24] used generative adversarial networks to achieve RGB visualization through hyperspectral images. The method reduces the dimensionality of the spectral data from tens to hundreds to three dimensions (RGB). CHENG Wencong [25] combined satellite infrared images and numerical weather prediction (NWP) products to generate adversarial network based on conditions. Then, night satellite visible-light images were synthesized. However, this method is limited to the field of view specified by the data set, and it is difficult to express the underlying surface stably and accurately. In cross-domain research, GANs are used for image fusion of SAR images, infrared images, and visible-light images [22,23,26]. This type of method combines the source-domain data with different characteristics to synthesize a fusion image that is easy to understand.

Hyperspectral image reconstruction is an example of spectral-domain translation [20,21]. Arad et al. [27] collected hyperspectral data and built a sparse hyperspectral dictionary based on the sparse dictionary. Then, they used it as prior information to map the RGB image to the spectral image. These methods usually learn a nonlinear mapping from RGB to hyperspectral images based on a large amount of training data. Wu, J et al. [21] applied hyperspectral reconstruction based on super-resolution technology. Pengfei Liu et al. [28] proposed a generative adversarial model based on a convolution neural network for hyperspectral reconstruction from a single RGB image.

Although these methods have achieved satisfactory results in image-to-image translation, they still cannot be directly applied to the spectral domain translation of remote sensing images mainly due to the following limitations.


To overcome the limitations mentioned above, this paper explores the spectral translation by introducing the conditional GAN, which focuses on the migration and amplification of a small amount of spectral data to multi-dimensional data.

As shown in Figure 1, the translation task into two steps: the first step is to encode the source spectral domain image and add additional feature maps to the shared latent domain through the source domain encoder. The second step is to decode the shared latent domain code to the target spectral domain through the target domain decoder.

**Figure 1.** The framework of SDTGAN.

The main contributions of this paper are as follows:


The structure of this paper is as follows: In Section 2, the structure and loss functions of the GAN used in this study are introduced. In Section 3, the building of the datasets and the experiments to evaluate different methods are elaborated. Finally, future work and conclusions are given in Section 4.
