Deep learning technology in SR task encompasses two distinct aspects. The first involves a fusion method based on paired images, while the second entails a direct reconstruction approach that leverages a single image such as those from CASSI or RGB systems. In the first category, a simultaneous capture of lrHS and hrMs images is employed, both possessing the same spectral and spatial resolution as HSIs separately. For example, Yao et al. [11] views hrMS as a degenerate representation of HSI in the spectral dimension and lrHS as a degenerate representation of HSI in the spatial dimension. It is suggested to use cross-attention in coupled unmixing nets based on the complementarities of the two features. Hu et al. [13], on the other hand, employed the Fusformer to obtain the implicit connection between global features and to solve the local neighborhood issue of the finite receptive field of the convolution kernel in the fusion problem using the transformer mechanism. The training process’s data load is decreased by learning the spectral and spatial properties, respectively. However, the majority of the models’ prior knowledge was created manually, which frequently results in a performance decrease when the domain is changed. Using the HSI denoising iterative spectral reconstruction approach based on deep learning, the MoG-DCN described by Dong et al. [38] has produced outstanding results in numerous datasets.

For the second category, where only single images are input, the model will learn the inverse function of the camera response function of a sensor using a single RGB image as an example. It will separate the RGB image’s hidden hyperspectral feature data from it and then combine it with the intact spatial data to reconstruct a fine HSI. Shi et al. [15], for instance, replaced leftover blocks with dense blocks to significantly deepen the network structure and achieved exceptional results in NTIRE 2018 [20]. The pixel-shuffling layer was employed by Zhao et al. [19] to achieve inter-layer interaction, and the self-attention mechanism was used to widen the perceptual field. Cai et al. [14] presented a cascade-based visual transformer model, MST++, to address the numerous issues with convolution networks in SR challenges. Its designed S-MSA and other modules further improved the ability of model to extract spatial and spectral features and achieved outstanding results in a large number of experiments.

The aforementioned analysis reveals that most previous models predominantly focused on enhancing feature extraction capabilities while neglecting the interpretability of physical modeling. This oversight often resulted in diminished performance in practical applications. In response, an SR model with robust interpretability was developed, capitalizing on the autoencoder’s prowess in feature extraction and the simplicity of LMM. By harnessing the ability of LMM to extract sub-pixel-level features, ample spatial information is concurrently gathered from RGB images. Subsequently, high-quality HSIs are restored during the reconstruction process.

Several deep learning models based on mathematical or physical modeling have been suggested recently and used in real-world tests with positive outcomes due to the growing demand for the interpretability of deep learning models. Among these, HU has made significant progress in tasks such as change detection (CD), SR, and other HSI processing tasks. Guo et al. [39] utilized HU to extract sub-pixel-level characteristics from HSIs to integrate the HU framework into a conventional CD task. In order to obtain the reconstructed HSI, Zou et al. [40] used the designed constraints and numerous residual blocks to obtain the endmember matrix and abundance matrix, respectively. Su et al. [41] used the paired lrHs and hrMs to learn the abundance matrix and endmember from the planned autoencoder network and then rearranged them into HSI using the fundamental LMM presumptions.

Moreover, deep learning-based techniques are frequently used to directly extract the abundance matrix or end endmembers from the HU mechanism. According to Hong et al. [42], EGU-Net can extract a pure-pixel directed abundance matrix extraction model and estimate the abundance of synchronous hyperspectral pictures by using the parameter-sharing mechanism and the two-stream autocoder framework. By utilizing the asymmetric autoencoder network and LSTM to capture spectral information, Zhao et al. [43] were able to address the issue of inadequate spectral and spatial information in the mixed model.

Based on the aforementioned research, utilizing the HU mechanism to drive the SR task evidently improves interpretability. In light of this, our method introduces a parallel feature fusion module that combines the rich geometric invariance present in the residual blocks with the global receptive field of the transformer. This approach ensures the generation of well-defined features and aligns the channel-wise information with the endmembers of the spectral library.

The transformer-based approach has achieved great success in the field of computer vision, but using it exclusively will frequently negate the benefits of the original CNN structure and add a significant amount of computing burden. Due to this, numerous studies have started fusing the two. Among these, Wu et al. [25] inserted CNN into the conventional vision transformer block, replacing linear projection and other components, and improved the accuracy of various computer vision tasks. Guo et al. [26] linked the two in succession, created the CMT model with both benefits, and created the lightweight visual model. He et al. [27] created the parallel CNN and transformer feature fusion through the developed RAM module and the dual-stream feature extraction component.

The integration of CNN and transformer is inevitable because they are the two most important technologies in the field of image processing. Many performance comparisons between the two have produced their own upsides and downsides [44,45]. Important information will inevitably be lost when using a single module alone. It is crucial to understand how to incorporate the elements that can be derived from both. In order to perform feature fusion for the parallel structure of PMSA, the channel size of the CNN that lacks modeling [37] can be well constrained utilizing the channel information in the transformer.