Hyperspectral image super-resolution (HSI-SR) is fundamentally more difficult than RGB image SR, since its ultrahigh spectral dimensionality. Existing supervised methods rely on labeled training data to obtain data prior, which incurs prohibitive collection costs and limits generalization. Unsupervised methods individually preset the band and kernel with handcrafted priors, whereas this decoupling modeling artificially creates a complexity-performance trade-off in the selected band number. To address these issues, we propose BKX-HMM, a unified statistical framework for blind HSI-SR, which uniformly models the band selection, kernel estimation, and HSI restoration through the state transition of a hidden Markov model (HMM). BKX-HMM redefines the trade-off as a distributional fitting problem: each Markov transition progressively learns optimal parameters of full-band distribution via limited spectral observations. Based on BKX-HMM, we propose BKSR, the first unsupervised blind HSI-SR method, which consists of three synergistic modules: Gibbs sampling-based band selection (GBS), test-time-training kernel estimation (TKE), and robust HSI restoration (RHR). These modules form a closed-loop optimization cycle: i) In GBS, the dynamic ergodicity of Gibbs sampling provides a global spectral view for kernel estimation and HSI restoration while maintaining local spectral computations; ii) In TKE, the GBS-sampled bands guide the kernel estimator update, achieving a learnable sampling-based mechanism, which refines kernel estimation to regularize RHR's diffusion trajectory; iii) In RHR, a spectral hyper-Laplacian prior is integrated into the reverse process of an off-the-shelf diffusion model, which achieves non-i.i.d. noise robust HSI restoration, feedback reweights band and kernel importance for subsequent GBS and TKE iterations. Extensive experiments on both synthetic and real HSI datasets demonstrate our BKSR's superiority over baseline methods across diverse scenarios (e.g., unknown Gaussian/motion kernel, non-i.i.d. noise) while maintaining comparable computational costs to the classic band selection methods.

Methods for hyperspectral image (HSI) super-resolution employing deep learning have been pivotal in a range of fields. Despite this, many current approaches face challenges like the scarcity of paired datasets, simplified degradation models, and a lack of image prior information, leading to weak generalization over different datasets and degradation conditions. To overcome these challenges, this paper introduces a single hyperspectral image blind super-resolution algorithm supplemented by an unsupervised blur kernel estimation module. Random kernels from Gaussian distributions form pseudo-label kernels to handle arbitrary degradation kernels. These are processed by a DIP-based network, channel-by-channel, using a batch gradient acceleration algorithm for network parameter updates. This unsupervised, pre-training-free method achieves single HSI super-resolution through alternating iterative optimization. This method necessitates solely the input of the degraded image and requires no extra data, demonstrating a minimal reliance on data. Simulated experiments across datasets and scenarios demonstrate the proposed method’s superior ability to estimate degradation blur kernels, outperforming existing state-of-the-art methods.

Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our survey, we systematically and comprehensively review on diffusion-based graph generative methods. We first make a review on three mainstream paradigms of diffusion methods, which are denoising diffusion probabilistic models, score-based genrative models, and stochastic differential equations. Then we further categorize and introduce the latest applications of diffusion models on graphs. In the end, we point out some limitations of current studies and future directions of future explorations.