The presence of haze leads to a severe attenuation of image information, resulting in a degraded image quality. Not only does it impair human visual perception by reducing image clarity, causing color distortion and detail blurring, but it also adversely affects the accuracy of advanced computer vision tasks such as face recognition, image seg- mentation, and autonomous driving. Therefore, research on image dehazing techniques is of significant importance for improving image quality and improving the robustness and practicality of vision systems.

Traditional image dehazing methods are primarily categorized into two groups: those based on image enhancement and those relying on the atmospheric scattering model. The former approach leverages image enhancement techniques [1–5] to improve image contrast and clarity, thereby enhancing visual quality, but it does not address the physical formation mechanism of haze. The latter approach is built upon the atmospheric scattering model [6], utilizing priors such as the dark channel prior [6] and the color attenuation prior [7] to estimate the transmission map and atmospheric light. Although these physics-based methods produce more physically plausible results, they often exhibit limited generalization in complex scenarios and tend to introduce artifacts or loss of fine details.

With the emergence of synthetic datasets and rapid advancements in deep learn- ing, image dehazing methods have progressively shifted toward end-to-end deep neural network models [8–14], primarily encompassing convolutional neural network (CNN)- based and Transformer-based architectures. These approaches learn direct mapping relationships from hazy to clear images, achieving notable progress in visual quality. However, several challenges persist: on one hand, CNN-based methods are constrained by their limited receptive fields, struggling to effectively model multi-scale structural information in images; on the other hand, while Transformers [15] can capture global features through multi-head attention mechanisms, their high computational costs and resource demands hinder practical deployment. Consequently, more efficient and advanced techniques are currently imperative for image dehazing. Recently, visual state space models like Mamba [16] have garnered significant attention due to their capability of modeling long-range dependencies with linear complexity, demonstrat- ing exceptional performance across various vision tasks, including image segmentation [17]. Nevertheless, research on Mamba for image dehazing remains in its nascent stage, with substantial room for improvement in both dehazing performance and model adaptability, positioning it as a promising research direction in the field. f

Deep learning-based image dehazing methods have achieved notable success in recent years. However, the inherent ill-posed nature of image dehazing remains a challenging problem. Modeling and analyzing the physical characteristics of the haze degradation process can enhance the network’s perception of useful image informa- tion, thereby facilitating more efficient and robust dehazing. Nevertheless, few existing approaches explicitly exploit these physical properties, which increases the risk of overfitting. From this perspective, we introduce the wavelet transform to decompose an image into low-frequency subbands representing structural information and high- frequency subbands encoding textural details through multi-scale and time-frequency localized decomposition, as illustrated in Fig. 3. Inspired by this observation and

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prior works [18–23], we decompose the task into two subtasks: position-guided chan- nel attention enhancement and spatial-aware multi-receptive field feature extraction. This decomposition enables the network to aggregate effective information, thereby achieving high-fidelity image restoration.

This paper proposes USF-Net, a novel wavelet degradation prior-guided visual Mamba framework for image dehazing. The framework sequentially integrates UVM- Net and PosSE modules during the encoding stage: the former leverages state space modeling (SSM) to capture spatial sequential dependencies for efficient global fea- ture extraction, while the latter incorporates position awareness through a channel attention mechanism to generate position-sensitive channel weights, thereby enhanc- ing dehazing accuracy and flexibility in non-uniform haze scenarios. The decoding stage employs a symmetric upsampling path to progressively restore spatial resolu- tion, supplemented by skip connections to incorporate shallow-level details. To further improve performance in complex haze conditions and detail recovery, we introduce the PosASPP module for multi-scale spatial position awareness, which enhances mod- eling of global context, depth variations, and spatial hierarchical information. This enables more accurate estimation of transmission maps and atmospheric light, ulti- mately reconstructing haze-free images with sharper edges and a more visually natural appearance. Figure 1 presents a comparative analysis between our USF-Net and state- of-the-art approaches in terms of both performance and computational complexity. The main contributions of this work are summarized as follows:

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hancing the U- haped network with wavelet features and spatial position fusio (USF-Net)

H,W,3

H/8,W/8,4C

Skip Connect

H/16,W/16,8C

Figure 2 USF-Net Architecture Overview. USF-Net employs an encoder-decoder framework, where the hazy image is initially decomposed via a wavelet transform. The decomposed features are then fed into the encoder, which progressively processes them through a series of interconnected UVM-Net and PosSE modules to efficiently aggregate spatial and channel information with linear complexity. Skip connections are incorporated to directly transmit shallow features to the decoding stage. In the decoder, a CoordAspp block is integrated following the initial convolutional layers, enabling gradual restoration of spatial resolution while effectively fusing multi-scale spatial information.

Single-image dehazing methods can generally be categorised as being based on image enhancement, prior knowledge or, deep learning. Among image enhancement-based approaches, Retinex theory and its derivative algorithms have a significant influence. Land et al. [5] first proposed the Retinex perceptual model, which simulates stable colour perception in the human visual system under varying illumination conditions. Building on this, Jobson et al. [3]introduced the multiscale Retinex algorithm to sim- ulate how the human visual system adapts to different levels of illumination. Rahman et al. [4] further refined the multiscale filter to overcome the limitations of single- scale Retinex. Furthermore, Seow et al. [1] proposed an image enhancement method that combines homomorphic filtering with colour ratio rules to achieve contrast

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enhancement and colour preservation through frequency-domain filtering and colour correction. Stark et al. [2] introduced a generalised histogram equalisation framework that adaptively adjusts image contrast through a parameterised mapping function and normalisation constraints. However, image enhancement methods generally suffer from poor generalisation, a lack of rigorous physical modelling, and inadequate noise handling, which limits their effectiveness in practical applications.

A physical model based on prior knowledge. He et al. [6] proposed the widely recognised Dark Channel Prior (DCP) method, which uses atmospheric scattering models for image restoration. However, this method has significant limitations and exhibits poor dehazing performance in sky regions, being prone to colour shifts and excessive darkness. Zhu et al. [7] introduced the Color Attenuation Prior (CAP), which posits a positive correlation between brightness and saturation values in hazy images relative to the scene. However, this assumption often fails under complex lighting or non-uniform haze conditions, leading to inaccurate depth estimation.

Image dehazing techniques based on deep learning methods have evolved to achieve end-to-end fog-free image restoration through complex convolutional neural networks (CNNs) or Transformer architectures. Cai et al. [8] pioneered modelling the dehazing problem as an end-to-end learning task in DehazeNet, enabling CNNs to learn image transmittance mapping relationships autonomously, without the need for manually designed prior knowledge. In AOD-Net, Li et al. [11] restructured atmospheric scat- tering model equations, enabling the network to directly reconstruct fog-free images rather than estimating intermediate transmission values. Qin et al.[24] proposed FFA- Net, which integrates feature fusion attention mechanisms. This significantly enhances structural recovery and detail preservation capabilities by applying adaptive weighting to features through channel-level and pixel-level attention. Dong et al. [9] addressed non-uniform haze distribution by proposing the Multi-Scale Boosting Dehazing Net- work (MSBDN), which is based on image pyramids and achieves fog-free images through progressive feature extraction and reconstruction. Wu et al. [25] developed AECR-Net based on the U-Net architecture. By modelling hazy images through an encoder-decoder structure, AECR-Net enhances the network’s ability to process low- contrast regions and blurred structures, thereby improving the clarity and naturalness of the final results.

Following the remarkable progress of CNN and Transformer-baseddeep learning methods for image dehazing, the recently emerging State Space Models (SSMs) [26, 27] offer a novel alternative for efficient long-range dependency modeling. Originating from classical control theory and signal processing, SSMs aim to mathematically rep- resent the evolution of system states over time. By leveraging their recursive structure and historical memory mechanism, SSMs have become an efficient and interpretable approach for addressing long-sequence dependency problems. Gu et al. [28] proposed a selective state space (Mamba) model capable of dynamically adjusting parameters to implement content-aware retention and forgetting mechanisms. Concurrently, Mamba incorporates a hardware-aware parallel scanning algorithm, enabling linear compu- tational complexity during inference while surpassing the Transformer in processing speed and enhancing its capability for handling long sequences. In this paper, we adapt the Mamba model for image dehazing tasks.

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In contrast to most existing dehazing methods, the proposed model in this study integrates the degradation priors of wavelet decomposition, channel information, and multi-scale spatial features, while combining the complementary advantages of Mamba and CCNN architectures. This integration enables the model to effectively capture global contextual relationships, crucial fine-grained details, and spatial structural awareness, thereby significantly enhancing both the accuracy and visual fidelity of image dehazing. In this section, we first introduce the essential preliminary knowl- edge, and subsequently elaborate on the overall pipeline and detailed architectural components of the proposed model.

weighted combination of L1 loss, perceptual loss, and SSIM loss, with the corresponding weights set to λ 1 = 1.0, λp = 0.04, and λs = 0.5, respectively. All experiments are implemented on a NVIDIA H100 GPU using the PyTorch 1.12 framework.

Beyond its exceptional accuracy, USF-Net also demonstrates remarkable com- putational efficiency. In comparison with DehazeFormer-L, the proposed approach yields a 2.26 dB enhancement while maintaining a commensurate model size (26.12M vs. 25.44M parameters) and exhibiting a 27% reduction in computational demands (203.68G vs. 279.7G MACs). This efficiency enhancement is attributable to the lin- ear complexity of the Mamba architecture and the enhancement modules, which have been meticulously designed. In comparison to attention-based methods such as FFANet [24] (287.8G MACs) and DehazeFormer-L [15](279.7G MACs), which have been shown to have complexities that grow quadratically with input resolution, USF-Net demonstrates superior scalability for high-resolution image processing. Fur- thermore, USF-Net outperforms lightweight CNN approaches such as MSCNN [9] andAOD-Net [11] (0.115G MACs) on ITS, achieving a substantial enhancement of + 22.47 dB and + 21.80 dB, respectively. This enhancement is achieved while main- taining reasonable computational costs, thereby demonstrating an optimal balance between accuracy and efficiency.

To conduct an in-depth qualitative analysis, we present some representative dehazing results. Given that we did not retrain the baseline methods on RESIDE-Full, we only provide test results on the RESIDE-6K and RS-Haze datasets. We selected several representative dehazing methods for qualitative comparison with USF-Net, as shown in Fig. 6. This figure displays four samples chosen from different scenarios to evaluate dehazing performance, including both indoor and outdoor hazy images. For outdoor images, DCP and AOD-Net exhibit poor parameter estimation, particularly in the sky region. For indoor images, these methods are prone to color distortion and may produce artifacts such as halos and checkerboard patterns. While FFA-Net and Dehaze-Former demonstrate promising dehazing results on both indoor and outdoor datasets, they still suffer from color distortion in low-illumination scenes and at edge details. In com- parison to our USF-Net, our network achieves a more precise restoration of these details. Specifically, in the overall restoration of the buildings shown in the first row of the figure, the details and main structure recovered by our USF-Net are closer to the ground truth image. The dehazing performance on remote sensing images is shown in Fig. 7. We selected four hazy images with varying topographical features (moun- tains and rivers) and haze concentrations to present the dehazing performance. DCP and AOD-Net are generally incapable of recovering clear results, showing extremely poor dehazing effects. FFA-Net and Dehaze-Former show significant improvements in dehazing, with performance on non-uniform haze regions comparable to our USF- Net. However, in terms of texture detail recovery and color fidelity for mountains and rivers, they are inferior to our proposed network. Notably, there is a small white geo- graphical marker in the upper right of the sample in the fourth row of the figure; our network’s restoration effect is slightly more pronounced than that of Dehaze-Former, demonstrating superior dehazing performance.

The proposed single-image dehazing architecture, designated USF-Net, integrates CNN-based local feature extraction, Mamba’s efficient global modeling, and frequency- domain prior knowledge. Specifically, the precise multi-scale frequency-domain feature modeling is achieved while maintaining linear complexity by introducing DWT multi-scale decomposition, channel attention modules, and position-aware multi-scale modules. In the context of the ITS, OTS, RESIDE-6K, and RS-Haze benchmarks, USF-Net attains 42.31/36.58/33.76/41.47 dB PSNR, thereby demonstrating supe- riority over DehazeFormer-L by + 2.26/+1.63/+2.31/+1.60 dB while concurrently reducing computational expense by 27%. Ablation studies demonstrate that the syn- ergistic interaction among modules yields a + 2.14 dB gain. USF-Net has been shown to establish a new benchmark for haze removal and to showcase the immense potential of hybrid architectures in image restoration, positioning it as a promising backbone architecture for next-generation image restoration networks.