Pan-sharpening aims to preserve the spectral information of the multi-spectral (MS) image while leveraging the high-frequency details from the guided high-resolution panchromatic (PAN) image to enhance its spatial resolution. The key challenge is how to preserve the spectral information from the MS image and the spatial details from the PAN image as much as possible. Diffusion models have achieved favorable results in image restoration and synthesis tasks but suffer from excessive computational resource and time consumption. In this paper, we design a novel and computationally efficient diffusion-based pan-sharpening network that achieves accelerated diffusion while reducing task complexity by decoupling the high and low-frequency components of the fused image. Specifically, leveraging the information-preserving characteristic of the wavelet transformation, we introduce a Wavelet-based Low-frequency Diffusion Model (WLDM). WLDM generates the low-frequency coefficient of high-resolution MS (HRMS) image from the low-resolution MS (LRMS) image. This approach significantly reduces computational resources and complexity compared to the direct restoration of the HRMS image. Furthermore, we have devised a High-frequency Information Restoration Module (HIRM) to restore the high-frequency information in the HRMS image through the interaction of high-frequency coefficients from the PAN image in three directions. Extensive experiments on three different datasets demonstrate that our method outperforms existing approaches in both quantitative metrics, qualitative metrics, and inference efficiency.

Hyperspectral image (HSI) reconstruction aims to restore the original 3D HSIs from the 2D hyperspectral snapshot compressive images (SCIs). The key to high-fidelity HSI reconstruction lies in designing refined spatial and spectral attention mechanisms, which are crucial for generating fine-grained representations of HSI based on the limited spatial and spectral information available in SCI. Recently, Mamba has demonstrated remarkable performance and efficiency in modeling spatial correlations. Its implicit attention mechanism generates three orders of magnitude more attention matrices than transformers, significantly raising the performance ceiling for HSI reconstruction. In this paper, we propose a novel joint SSM network named Sp3ctralMamba for HSI reconstruction. Sp3ctralMamba integrates frequency domain knowledge and physical priors to enhance reconstruction quality. Specifically, we first perform hierarchical decomposition of the 3D HSI embedding to mitigate the negative impact of distant bands on reconstruction. Next, we design a joint SSM block S3Mamba (S3MAB) to perform parallel scans of the embeddings from different bands. In addition to the conventional vanilla scan, S3MAB introduces a local scanning scheme to address the reconstruction challenges posed by the spatial sparsity of spectral information. Furthermore, a spiral scanning scheme in the frequency domain is incorporated to enhance the order correlation between different frequency signals. Finally, we introduce energy priors and structural priors to constrain the generation of spectral and spatial representations during the training process. Extensive experiments on both simulated and real datasets demonstrate that Sp3ctralMamba significantly elevates HSI reconstruction performance to a new level, surpassing SOTA methods in both quantitative and qualitative metrics.

Generating hyperspectral images (HSIs) from RGB images through spectral reconstruction can significantly reduce the cost of HSI acquisition. In this paper, we propose a Fractal-Based Recursive Spectral Reconstruction Network (FRN), which differs from existing paradigms that attempt to directly integrate the full-spectrum information from the R, G, and B channels in a one-shot manner. Instead, it treats spectral reconstruction as a progressive process, predicting from broad to narrow bands or employing a coarse-to-fine approach for predicting the next wavelength. Inspired by fractals in mathematics, FRN establishes a novel spectral reconstruction paradigm by recursively invoking an atomic reconstruction module. In each invocation, only the spectral information from neighboring bands is used to provide clues for the generation of the image at the next wavelength, which follows the low-rank property of spectral data. Moreover, we design a band-aware state space model that employs a pixel-differentiated scanning strategy at different stages of the generation process, further suppressing interference from low-correlation regions caused by reflectance differences. Through extensive experimentation across different datasets, FRN achieves superior reconstruction performance compared to state-of-the-art methods. Code is available at https://github.com/mongko007/frn.

Multi-focus image fusion (MFIF) aims to combine multiple images with different focused regions into a single all-in-focus image. Existing unsupervised deep learning-based methods only fuse structural information of images in the spatial domain, neglecting potential solutions from the frequency domain exploration. In this paper, we make the first attempt to integrate spatial-frequency information to achieve high-quality MFIF. We propose a novel unsupervised spatial-frequency interaction MFIF network named SFIMFN, which consists of three key components: Adaptive Frequency Domain Information Interaction Module (AFIM), Ret-Attention-Based Spatial Information Extraction Module (RASEM), and Invertible Dual-domain Feature Fusion Module (IDFM). Specifically, in AFIM, we interactively explore global contextual information by combining the amplitude and phase information of multiple images separately. In RASEM, we design a customized transformer to encourage the network to capture important local high-frequency information by redesigning the self-attention mechanism with a bidirectional, two-dimensional form of explicit decay. Finally, we employ IDFM to fuse spatial-frequency information without information loss to generate the desired all-in-focus image. Extensive experiments on different datasets demonstrate that our method significantly outperforms state-of-the-art unsupervised methods in terms of qualitative and quantitative metrics as well as the generalization ability.