Real-world Image Dehazing with Coherence-based Pseudo Labeling and Cooperative Unfolding Network

Authors: chengyu  fang
chunming  he
fengyang  xiao
yulun  zhang
longxiang  tang
yuelin  zhang
kai  li
xiu  li
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-04 18:14:42

Abstract: Real-world Image Dehazing (RID) aims to alleviate haze-induced degradation in real-world settings. This task remains challenging due to the complexities in accurately modeling real haze distributions and the scarcity of paired real-world data. To address these challenges, we first introduce a cooperative unfolding network that jointly models atmospheric scattering and image scenes, effectively integrating physical knowledge into deep networks to restore haze-contaminated details. Additionally, we propose the first RID-oriented iterative mean-teacher framework, termed the Coherence-based Label Generator, to generate high-quality pseudo labels for network training. Specifically, we provide an optimal label pool to store the best pseudo-labels during network training, leveraging both global and local coherence to select high-quality candidates and assign weights to prioritize haze-free regions. We verify the effectiveness of our method, with experiments demonstrating that it achieves state-of-the-art performance on RID tasks. Code will be available at https://github.com/cnyvfang/CORUN-Colabator.

Main paper: 
 claims: 
 Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes]Justification: Relevant information is included in section 1.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
real-world image dehazing: 
 The dissonance between synthetic and real haze distributions often hinders existing Learning-based dehazing methods [14] [15] [16] [17] [18] from effectively dehazing real-world images. Consequently, there's a growing emphasis on tackling challenges specific to real-world dehazing [19] [20] [21] [22] [23] .Given the characteristics of real haze, RIDCP [7] and Wang et al. [24] proposed novel haze synthesis pipelines. However, relying solely on synthetic data limits models' robustness in real-world dehazing scenarios. Recognizing the distributional disparities between synthetic and real haze, methods like CDD-GAN [25] , D4 [26] , Shao et al. [27] , and Li et al. [28] have utilized CycleGAN [29] for∑ ∑ P & !! ' (!"# ! (#) "# ! ! 1 & !! # S-CPMM P (!"# (#) "# ' (! (! #(&) ! (i)The architecture of the proposed CUN.(ii) Details of CUN at the ! !" stage. ) dehazing. Despite this, the challenges inherent in GAN [30] training often result in artifacts. Some approaches combine synthetic and real-world data, applying unsupervised loss to supervise real-world dehazing learning [19] . However, these losses lack sufficient precision, leading to suboptimal results. Other methods leverage pseudo-labels [31, 32] , but the erroneous pseudo-labels cause degrade quality.∑ ∑ T-CPMM %& ' !# !#!" ( )#!" ! (#) !" ! ! 1 (i) The architectu (ii) Details of C 1 !(#) ! & !! !(#) !(#) T-CPMM !!"# & !!"# (!"#To address these challenges, we introduce a coherence-based pseudo labeling method termed Colabator. Our approach selectively identifies and prioritizes high-quality regions within pseudo labels, leading to enhanced robustness and superior generation quality for real-world image dehazing.Deep Unfolding Networks (DUNs) integrate model-based and learning-based approaches [33, 34] and thus offer enhanced interpretability and flexibility compared to traditional learning-based methods. Increasingly, DUNs are being utilized for various image tasks, including image super-resolution [35] , compressive sensing [36] , and hyperspectral image reconstruction [37] . DGUN [10] proposes a general form of proximal gradient descent to learn degradation. However, it fails to decouple prior knowledge, relying solely on single-path DUN to model degradation and construct mappings, posing challenges in comprehending complex degradation. Yang and Sun first introduced DUNs to the image dehazing field and proposed PDN [11] . However, PDN does not exploit the complementary information between the dehazed image and the transmission map, resulting in detail blurring. Our CORUN optimizes the atmospheric scattering model and the image scene feature through dual proximal gradient descent, thus preventing overfitting and facilitating detail restoration. According to eq. ( 1), given a hazy image P ∈ R H×W ×3 , we initialize a transmission map T ∈ R H×W ×1 . In gradient descent, we simplify the atmospheric light A ∈ R 3 and implicitly estimate it in the CORUN pipeline to focus on the detailed characterization of the scene and the relationship between volumetric haze and scene. Hence, eq. ( 1) can be rewrite asEQUATIONWhere J means the clear image without hazy, I is the all-one matrix. Based on eq. ( 2), we can define our cooperative dehazing energy function likeEQUATIONwhere ψ(J) and ϕ(T) are regularization terms on T and J. We introduce two auxiliary variables T and Ĵ to approximate T and J, respectively. This leads to the following minimization problem:EQUATIONTransmission optimization. Give the estimated coarse transmission map T and dehazed image Ĵk-1 at iteration k -1, the variable T can be updated as:EQUATIONWe construct the proximal mapping between T and T by a encoder-decoder like neural network which we named T-CPMM and denoted as prox ϕ :EQUATIONthe auxiliary variables T, which we calculate by our proposed TGDM can be formulated as:EQUATIONThe variable λ k is a learnable parameter, we enable CORUN to learn this parameter at each stage during the end-to-end learning process, allowing the network to adaptively control the updates in iteration.Scene optimization. Give Tk and J, the variable J can be updated as:EQUATIONSame as the proximal mapping process in the transmission optimization, S-CPMM has the similar structure as T-CPMM but different inputs, we denote S-CPMM as prox ψ :EQUATIONwhere the Ĵk we process by our SGDM can be presented as:EQUATIONas the λ k in transmission optimization, µ k is also a learnable parameter to bring more generalization capabilities to the network.T-CPMM and S-CPMM share the same structure for improved mapping quality. Each CPMM block uses a 4-channel convolution to embed T and J into a 30-dimensional feature map. The distinction between T-CPMM and S-CPMM lies in their outputs: T-CPMM produces a 1-channel result to aid TGDM in predicting a scene-compliant transmission map, whereas S-CPMM generates a 3-channel RGB image. This enables S-CPMM to learn additional scene feature information, such as atmospheric light and blur, assisting SGDM in generating higher-quality dehazed results with more details. For more efficient computation, each CPMM comprises only 3 layers with [1, 1, 1] blocks, doubling the dimensions with increasing depth.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes]Justification: Relevant information is included in section 5Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
coherence-based pseudo labeling by colabator: 
 We generate and select pseudo labels using our proposed plug-and-play coherence-based label generator, Colabator. Colabator consists of a teacher network with weights θ tea shared with the student network θ stu via exponential moving average (EMA). It employs a tailored mean-teacher strategy with a trust weighting process and an optimal label pool to generate high-quality pseudo labels, addressing the scarcity of real-world data. Figure 3 illustrates the pipeline of our Colabator. Iterative mean-teacher dehazing. Given a real hazy image P R LQ ∈ R H×W ×3 , we initially apply augmentations to generate corresponding strongly degraded data using a strong augmentor A s (•), which randomly applies adjustments such as contrast, brightness, posterize, sharpness, JPEG compression, and Gaussian blur. Unlike the common mean-teacher strategy, we omit functions like solarize, equalize, shear, and translate to prevent unnecessary degradation that might mislead model learning. We use the non-augmented image as the input for the teacher network and the strongly augmented image for the student network, generating the following results:EQUATIONwhere P R HQ ∈ R H×W ×3 is the result from the teacher network using the non-augmented input, and P R HQ ∈ R H×W ×3 represents the result from the student network by strong augment input and T R HQ , T R HQ are the corresponding transmission map. The different degrees of data augmentation lead to varying dehazing results, typically resulting in P R HQ having better quality than P R HQ .This approach ensures the model descends in the correct direction and helps mitigate the overfitting issues often associated with direct pseudo-label learning methods. By iterating, our teacher network generates increasingly high-quality pseudo-labels, providing more reliable supervision.Label trust weighting. To better leverage the pseudo-dehazed images P R HQ generated by the teacher network for model supervision, we designed a composite image quality assessment strategy for further processing these pseudo-dehazed images and get the trusted weight w which means the reliability of each location of an image. Our composite strategy primarily consists of a haze density evaluator D(•) based on pre-trained CLIP [38] model and fixed text feature, and a non-reference image quality evaluator Q(•). We partition P R HQ into an sequence S R HQ ∈ R N ×N ×3×(H/N )×(W/N ) and use D(•) and Q(•) to predict the density score and quality score. The final trusted weight w we can get from:EQUATIONwhere Ψ is compose sequence to map and resize as P R HQ , norm(•) means normalize scores from 0 to 1, that higher score means lower haze density and better image quality.Optimal label pool. To ensure the use of optimal pseudo-labels and avoid domain adaptation collapse due to instability during training, we proposed an optimal label pool P to maintain the pseudo-labels in their optimal state. The overall procedure of our optimal label pool process is summarized in algorithm 1, compare pseudo-dehazed image P R HQ i with previous pseudo-label P R P sei and update pseudo-dehazed image as pseudo-label if it better than previous. To summarize the algorithm 1 and eq. ( 11), the overall process of Colabator can be formalize as:EQUATION)where C is our Colabator framework, P R P se is the paired pseudo label of A s (P R LQ ), T R P se is the corresponding pesudo transmission map, w pse means the trusted weight of the pseudo label.Weights update. The teacher network's weights θ tea are updated by exponential moving average (EMA) of the student network's weights θ stu , which is denoted as follows:EQUATION)where η is momentum and η ∈ (0, 1). Using this update strategy, the teacher model can aggregate previously learned weights immediately after each training step, ensuring updating stability.Require: Haze density evaluator D(•) and image quality evaluator Q(•); Optimal label pool P; Sample a batch of real hazy images {P R LQ i } b i=1 ; for each P R LQ i do Get teacher network prediction:P R HQ i , T R HQ i = f θtea (P R LQ i ); Partition P R HQ i into N × N and get S R HQ i ; Compute score map of S R HQ i : d i = norm(D(S R HQ i)), and q i = norm(Q(S R HQ i)); Load P R P sei , T R P sei , w P sei , d P sei , q P sei = P(i) if d i > d P sei and q i > q P sei then Compute trusted weight:w i = Ψ (d i + q i ) Update P(i) = (P R HQ i , T R HQ i , w i , d i , q i ) Return P R HQ i , T R HQ i, w i as pesudo label. else Return P R P sei , T R P sei , w pse i as pesudo label. end if end forTo achieve success in real-world dehazing, we designed several loss functions for our CORUN and Colabator to constrain their learning process. We introduce a reconstruction loss using the L 1 norm ∥ • ∥ 1 . To enhance visual perception, we employ contrastive and common perceptual regularization to ensure the consistency of the reconstruction results with the ground truth in terms of features at different levels. The perceptual loss is defined as follows:EQUATIONL contra Rec (P LQ , P HQ , P GT ) = ∥P GT ,EQUATIONwhere P HQ is the dehazed result, φ i (•) means the i th hidden layer of pre-trained VGG-19 [39] , τ i is the weight coefficient. Besides, to constrain the entire pipeline to obey physical laws while alleviating constraints on the intermediate layers, and prevent overfitting, we introduce a global coherence loss:EQUATION)where ⊙ is the Hadamard product, I means the all-ones matrix as the same size of P S LQ . The global coherence loss ensures that CORUN can more efficiently integrate physical information into the deep network to facilitate the recovery of more physically consistent details. In addition, we introduce a density loss L dens based on D(•) to score and constraint the model to dehaze in the semantic domain:EQUATIONPre-training phase. To ensure the capacity in dehazing and transmission map estimation, we pretrained CORUN on synthetic paired datasets which contained clear image P S GT ∈ R H×W ×3 and synthetic hazy image P S LQ ∈ R H×W ×3 . Setting P S LQ as input, we can get the result byEQUATIONwhere A w means weakly geometric data augment, P S HQ means the dehazed result of synthetic hazy image, and T S HQ is the corresponding transmission map. In the pre-training phase, our CORUN is Fine-tuning phase. In fine-tuning phase, we adapt our CORUN pre-trained on synthetic data to the real-world domain by our Colabator framework. For more steady learning, in this phase, we train with both synthetic and real-world data. As eq. ( 13), we generate P R HQ , T R HQ , P R P se , T R P se , w pse from P R LQ , and we get P S HQ , T S HQ use the eq. ( 19). The overall loss of the fine-tuning phase:EQUATION4 ExperimentsQuestion: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Answer Justification: There is no societal impact of the work performed as we explained in appendix A.4 Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.• The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
experimental setup: 
 Data Preparation. We use RIDCP500 [7] dataset, comprising 500 clear images with depth maps estimated by [41] , and follow the same way of RIDCP [7] for generating paired data. During the fine-tuning phase, we incorporate the URHI subset of RESIDE dataset [40] , which only consists of 4,807 real hazy images, for generating pseudo-labels and fine-tuning the network. We evaluate our framework qualitatively and quantitatively on the RTTS subset, which comprises over 4,000 real hazy images featuring diverse scenes, resolutions, and degradation. Fattal's dataset [42] , comprising 31 classic real hazy cases, serves as a supplementary source for cross-dataset visual comparison.Implementation Details. Our framework is implemented using PyTorch [43] optimizing it with AdamW [44] using momentum parameters (β 1 = 0.9, β 2 = 0.999) and an initial learning rate of 2 × 10 -4 , gradually reduced to 1 × 10 -6 with cosine annealing. In Colabator, the initial learning rate is set to 5 × 10 -5 with only 5K iterations. Following [7] , we employ random crop and flip for synthetic data augmentation. We use DA-CLIP [45] as our haze density evaluator and MUSIQ [46] as the image quality evaluator. Our CORUN consists of 4 stages and the trade-off parameters in the loss are set to β c , ρ r , ρ c are set to 0.2, 5, 10 -2 , respectively.Metrics. We utilize the Fog Aware Density Evaluator (FADE) [47] to assess the haze density in various methods. However, FADE focuses on haze density exclusively, overlooking other crucial image characteristics such as color, brightness, and detail. To address this limitation, we also employ Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE) [48] , and Neural Image Assessment(NIMA) [49] for a more comprehensive evaluation of image quality and aesthetic. Higher NIMA scores, along with lower FADE and BRISQUE scores, indicate better performance. We use PyIQA [50] for BRISQUE and NIMA calculations, and the official MATLAB code for FADE calculations. All of these metrics are non-reference because there is no ground-truth in RTTS [40] .We compare our method with 8 state-of-the-art methods: PDN [11] , MBDN [14] , DH [15] , DAD [27] , PSD [19] , D4 [26] , RIDCP [7] , DGUN [10] . The quantitative results, presented in table 1, show that our method achieved the highest performance, outperforming the second-best method (RIDCP) by 17.0%. Specifically, our method improved FADE, BRISQUE, and NIMA scores by 12.7%, 30.8%, and 7.6%, respectively. This demonstrates that our method surpasses current state-of-the-art techniques in both dehazing capability and the quality, and aesthetics of the generated images.The visual comparisons of our proposed method and state-of-the-art algorithms are shown in figs. 4 and 5. We can observe that these methods have demonstrated some effectiveness in real-world dehazing tasks, but when images containing white objects, sky, or extreme haze, the results from PDN, DAD, PSD, and RIDCP exhibited varying degrees of dark patches and contrast inconsistencies. Conversely, D4 caused an overall reduction in brightness, leading to detail loss in darker areas. Under these conditions, DGUN produced relatively aesthetically pleasing results but lost significant local detail, impairing overall visual quality. Notably, PSD achieved higher brightness but suffered from Effect of Colabator. We validate the effect of our Colabator. In table 3 , we systematically removed critical components, such as mean-teacher, trusted weighting, and the optimal label pool, from the model architecture. The outcomes indicate the performance deteriorates when these components are removed, highlighting their essential role in the system.Ablations on stage number. The number of stages in a deep unfolding network significantly impacts its efficiency and performance. To investigate this, we experimented with different stage numbers for CORUN+, specifically choosing k values from the set {1, 2, 4, 6}. The results detailed in table 4 , indicate that CORUN+ achieves high-quality dehazing with 4 stages. Notably, increasing the number of stages does not necessarily improve outcomes. Excessive stages can increase the network's complexity, hinder convergence, and potentially introduce errors in the results.User Study. We conducted a user study to evaluate the human subjective visual perception of our proposed method against other methods. We invited five experts with an image processing background and 16 naive observers as testers. These testers were instructed to focus on three primary aspects: (i) Haze density compared to the original hazy image, (ii) Clarity of details in the dehazed image, and (iii) Color and aesthetic quality of the dehazed image. The results for each method, along with the corresponding hazy images, were presented to the testers anonymously. They scored each method on a scale from 1 (worst) to 10 (best). The hazy images were selected randomly, with a total of 225 images from RTTS [51] and 54 images from Fattal's [42] dataset. The user study scores are reported in table 5 , showing that our method achieved the highest average score. Downstream Task Evaluation. The performance of high-level vision tasks, e.g. object detection and semantic segmentation, is greatly affected by image quality, with severely degraded images often leading to erroneous results [52, 53] . To address this performance degradation, some methods have incorporated image restoration as a preprocessing step for high-level vision tasks. To validate the effectiveness of our approach for high-level vision, we utilized pretrained YOLOv3 [54] , and tested it on the RTTS [40] dataset, and evaluated the results using the mean Average Precision (mAP) metric. As shown in table 6 and fig. 6 , our method demonstrates a substantial advantage over existing methods, verifying our efficacy in facilitating high-level vision understanding. 
limitations and future work: 
 In fig. 7 , our CORUN+ model struggles to maintain result quality and preserve texture details when dealing with severely degraded inputs, such as strong compression and extreme high-density haze. This challenge persists across existing methods and remains unresolved. We attribute this difficulty to the model's struggle in reconstructing scenes from dense haze, where information is often severely lacking or entirely lost, affecting the reconstruction of both haze-free and low haze density areas. Moreover, the model solely focuses on dehazing and lacks the capability to address other image degradations, such as image deblurring [55] and low-light image enhancement [56, 57] , limiting its ability to achieve high-quality reconstruction results from complex degraded images. To address this limitation in future research, we propose not only focusing on environmental degradation but also considering additional information about image degradation when solving real-world dehazing problems. In addition to this, we can integrate robust generative methods to improve the network's ability to restore dense haze regions [58] [59] [60] [61] [62] , synthesize haze that matches real-world distributions [63] [64] [65] [66] , and introduce more modalities as supplements to RGB images, enhancing the model's ability to effectively recover details [67] . 
conclusions: 
 In this paper, we introduce CORUN to cooperatively model atmospheric scattering and image scenes and thus incorporate physical information into deep networks. Furthermore, we propose Colabator, an iterative mean-teacher framework, to generate high-quality pseudo-labels by storing the best-ever results with global and local coherence in a dynamic label pool. Experiments demonstrate that our method achieves state-of-the-art performance in real-world image dehazing tasks, with Colabator also improving the generalization of other dehazing methods. The code will be released. Red region reflects all past methods have had haze residues, but our method have the least in the same case. Purple region shows our method restores richer detail and truer colors. Please zoom in for a better view. 
safeguards: 
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: 
 Real-world image dehazing (RID) is a challenging task that aims to restore images affected by complex haze in real-world scenarios. The goal is to generate visual-appealing results while enhancing the performance of downstream tasks [1, 2] . The atmospheric scattering model (ASM), providing a physical framework for real-world dehazing, is formulated as follows: P (x) = J(x)t(x) + A(1 -t(x)), (1) where P (x) and J(x) are the hazy image and the haze-free counterpart. A signifies the global atmospheric light. t(x) characterizes the transmission map reflecting varying degrees of haze visibility across different regions.Conventional methods [3, 4] are limited by fixed feature extractors, which struggle to handle the complexities of real haze. Although existing deep learning-based methods [5] [6] [7] [8] [9] demonstrate improved performance, they face two significant challenges: (1) These methods do not accurately model the complex distribution of haze, leading to color distortion, as illustrated in fig. 1 DGUN [10] . (2) Real-world settings lack sufficient paired data for network training while optimizing the network with synthesized data brings a domain gap, limiting the generalizability of the models.To overcome the first challenge, PDN [11] first introduces unfolding network [12, 13] to the RID field. In specific, PDN unfolds the iterative optimization steps of an ASM-based solution into a deep network for end-to-end training, incorporating physical information into the deep network. However, PDN does not effectively leverage the complementary information between the dehazed image and the transmission map, bringing overfitting problems and resulting in detail blurring (see fig. 1 ).In this paper, we introduce the COopeRative Unfolding Network (CORUN), also derived from the ASM-based function, to address PDN's limitations and better model real hazy distribution. CORUN cooperatively models the atmospheric scattering and image scene by incorporating Transmission and Scene Gradient Descent Modules at each stage, corresponding to each iteration of the traditional optimization algorithm. To prevent overfitting, we introduce a global coherence loss, which constrains the entire pipeline to adhere to physical laws while alleviating constraints on the intermediate layers. These design choices collectively ensure that CORUN effectively integrates physical information into deep networks, thereby excelling in restoring haze-contaminated details, as depicted in fig. 1 .To enhance generalizability in real-world scenarios, we introduce the first RID-oriented iterative mean-teacher framework, named Coherence-based label generator (Colabator), designed to generate high-quality dehazed images as pseudo labels for training dehazing methods. Specifically, Colabator employs a teacher network, a dehazing network pretrained on synthesized datasets, to generate dehazed images on label-free real-world datasets. These restored images are stored in a dynamically updated label pool as pseudo labels for training the student network, which shares the same structure as the teacher network but with distinct weights. During network training, the teacher network generates multiple pseudo labels for a single real-world hazy image. We propose selecting the best labels to store in the label pool based on visual fidelity and dehazing performance.To achieve this, we design a compound image quality assessment strategy tailored to the dehazing task, evaluating the global coherence of the dehazed images and selecting the most visually appealing ones without distortions for inclusion in the label pool. Additionally, we propose a patch-level certainty map to encourage the network to focus on well-restored regions of the dehazed pseudo labels, effectively constraining the local coherence between the outputs of the student model and the teacher model. As shown in fig. 1 , Colabator, generating high-quality pseudo labels for network training, enhances the student dehazing network's capacity for haze removal and color correction.Our contributions are summarized as follows:(1) We propose a novel dehazing method, CORUN, to cooperatively model the atmospheric scattering and image scene, effectively integrating physical information into deep networks.(2) We propose the first iterative mean-teacher framework, Colabator, to generate high-quality pseudo labels for network training, enhancing the network's generalization in haze removal.(3) We evaluate our CORUN with the Colabator framework on real-world dehazing tasks. Abundant experiments demonstrate that our method achieves state-of-the-art performance. 
 
 Appendix: A.1 Declaration of eq. ( 7) and eq. ( 10)Having gotten eq. ( 5) and eq. ( 6), the solution of T can be formulated according to the proximal gradient algorithm:EQUATION)Then we obtain the partial derivative:EQUATION)Let the partial derivative be equal to zero, we archieve the closed-form solution for T in eq. ( 7).Similarly, the solution of Ĵ can be formulated asEQUATION)The corresponding partial derivative isEQUATION)The closed-form solution for Ĵ is presented in eq. ( 10) when let the partial derivative be equal to zero.The haze density evaluator D(•) can be formulated as:EQUATIONThe text we used is "hazy" from the DA-CLIP provided in the text list. Impact of Trusted Weight Representations. We investigate the effect of using trusted weights as either a map or a value. As seen in table 8 , the combination of partitioned and full trusted weights (CORUN+) achieves better results compared to using only full trusted weights. This emphasizes the value of our trusted weight representation in improving the accuracy of dehazing.To analyze the contribution of individual components within the Colabator framework, we performed ablation studies, with the results presented in table 9 .Removing essential elements, such as strong augmentation or DA-CLIP, results in performance deterioration, confirming the importance of each Colabator component in ensuring optimal dehazing outcomes.Ablation on Dataset Configurations. We evaluate our methods with different dataset settings. As shown in table 10, the results verify our method still achieves a leading place under the three settings compared with existing methods.Effectiveness of the Simplified ASM Formula.We assess the impact of simplifying the Atmospheric Scattering Model (ASM) formula. The results in table 11 indicate that using the simplified ASM formula will lead to a slight decrease in the dehazing ability, but it can evidently improve the image quality of the results.Influence of Loss Functions. We compare the effect of using different loss functions (eq. ( 15) and eq. ( 16)). Table 12 shows that combining both loss functions yields better performance than using either one alone, demonstrating the advantage of this combined loss strategy in refining the dehazing process. Integration with Other Dehazing Methods. To test the generalizability of Colabator, we integrated it with various state-of-the-art dehazing models, such as C2PNet [22] , FFA-Net [17] , and GDN [16] . As shown in table 13 , incorporating Colabator leads to performance gains across all metrics, demonstrating its effectiveness as a plug-and-play module for improving dehazing in various architectures.Real-world image dehazing is a crucial task in image restoration, aimed at removing haze degradation from images captured in real-world scenarios. In computer vision, dehazing can benefit downstream tasks such as object detection [68] [69] [70] [71] [72] , image segmentation [73] [74] [75] [76] [77] [78] [79] [80] [81] , tracking [82, 83] , depth estimation [84, 85] , and more vision related tasks [86] [87] [88] [89] [90] [91] [92] [93] [94] , with applications ranging from autonomous driving to security monitoring. Our paper introduces a cooperative unfolding network and a plug-and-play pseudo-labeling framework, achieving state-of-the-art performance in real-world dehazing tasks. Notably, image dehazing techniques have yet to exhibit negative social impacts.Our proposed CORUN and Colabator methods also do not present any foreseeable negative societal consequences.NeurIPS Paper Checklist 


Decision: This paper was reviewed by four experts. The reviewers generally appreciated the central concept and were persuaded by the effectiveness of the proposed technique. Initially, the review scores were varied and included several concerns. However, during the rebuttal phase, the authors effectively addressed most of these issues. As a result, reviewers who had previously given lower scores revised their assessments to favor acceptance. Given the unanimous recommendation for acceptance, AC believes the paper is a clear  acceptance case.

Reviews: review: paper_summary: paper_summary: This paper focuses on Real Image dehazing. They propose a cooperative unfolding network (CORUN) to integrate physical knowledge for image dehazing. The proposed CORUN exploits the complementary information between components in Atmospheric Scattering Model. Besides, due to the lack of real paired data, this paper proposes a Coherence-based Label Generator to generate pseudo labels for real hazy inputs. The experimental results demonstrate that the proposed method achieves good dehazing performance.
strength_weakness: strength_weakness: 1.	There is still room for improvement in the writing of this paper.
a)	Typo in line 167
b)	How to simplify A in line 111 is unclear. According to my understanding, after simplification, P in Eq. 2 has different physical meaning as defined in line 110.
c)	In lin3 172, the same symbols are used to indicate different images.
d)	Line 187 presents two kinds of reconstruction loss, which is inconsistent with the perceptual loss in line 186.
2.	The experiment is a bit unfair. This paper utilizes the data generation pipeline proposed in RIDCP, which has been proved that can improve the real image dehazing performance of dehazing networks. However, the quantitative results of PDN and MBDN reported in Table 1 seem to be calculated by using their original models, rather than re-training on the same training data used in this paper.
3.	The experiment is a bit insufficient. 
a)	The author only validates the effectiveness of Colabator on DGUN, neglecting other widely-used dehazing networks.
b)	The full-reference evaluation on real dehazing benchmarks (e.g., O-HAZE, I-HAZE, etc.) can also be an important evidence to support the effectiveness of the proposed method.
questions: questions: Please see the weakness for more details.
Besides, I was wondering:
1.	What are the essential advantages of CORUN compared to state-of-the-art end-to-end dehazing models? Are there any experiments?
2.	Whether the proposed method can remove medium or dense haze correctly. Since the dehazing results shown in Fig. 4 still have haze residues even if the hazy input is not very dense. 
3.	Why use both perceptual loss and contrastive loss simultaneously? There are overlapping parts between them.
4.	How robust is the estimation of haze density by DA-CLIP?
limitations: limitations: The authors have discussed the limitations.
paper_summary: paper_summary: The paper aims for real-world image dehazing, where the paper tries to handle the difficulties of modeling real haze distributions and the scarcity of real data. For modeling haze, the paper proposes to jointly model atmospheric scattering and image scenes by a cooperative unfolding network. To handle the scarcity of data, the paper proposes to generate pseudo labels using an iterative mean-teacher network, which the paper terms Coherence-based label Generator (Colabator).
strength_weakness: strength_weakness: - The major concern I have for this paper is that the proposed method seems to be mostly combination of existing works. 
   - The joint estimation of atmospheric scattering/transmission (or atmospheric light) and clean image is not new:
      - Mondal et al., Image Dehazing by Joint Estimation of Transmittance and Airlight using Bi-Directional Consistency Loss Minimized FCN  
      - Im et al., Deep Variational Bayesian Modeling of Haze Degradation Process
      - Zhang et al., Joint Transmission Map Estimation and Dehazing using Deep Networks
      - Ren et al.,  Single image dehazing via multi-scale convolutional neural network
    - Deep Unfolding Networks (DUNs) has been utilized for dehazing by Yang and Sun [50], mentioned in the paper
    - The use of PGD for DUNs in the context of image restoration has been done by DGUN [33], as mentioned in the paper.
    - Also, using mean teacher for creating pseudo labels is commonly performed in deep learning.
   - Considering all of the above, the proposed method seems to be the combination of the existing methods.
   - What is a major difference and technical novelty in comparison to the combination of existing methods above?
- Since the proposed method is a combination of many components, a detailed ablation study would be needed to justify the effectiveness of each component.
questions: questions: My major concern and questions have been written in the weakness section.
limitations: limitations: The authors have mentioned the limitation of their work in the supplementary document.
paper_summary: paper_summary: This paper focuses on challenging real-world image dehazing problem. The authors develop their network based on unfolding network, while leveraging cooperative proximal mapping modules to facilitate the estimation of transmission map and image content. In addition, the authors propose an interesting teacher network, named as Colabator, with newly developed quality assessment metrics to better provide the high-quality pseudo-labels for dehazing. The subjective metrics on different benchmark, and the user study with downstream tasks evaluation demonstrate the effectiveness of this work.
strength_weakness: strength_weakness: 1.	The derivation of equation (7) and (10) are unclear. The authors may need to provide some basic theories before stating these equations.
2.	The details of using DA-CLIP as haze density evaluator is unclear, the statement in line 164 indicates that the authors use a fixed text feature, which is also missing in the article. Moreover, the reason behind the patch partition in line 165 is not clearly stated, the information about patch size N cannot be found in the article.
3.	The article lacks ablation studies about CPMM modules. I wonder how network will performance if removing all CPMM modules.
questions: questions: First of all, please address my concerns listed in the weakness part. I have some additional questions:

1.	About density loss: similar as the problems in the second point of weakness, how does this loss function formulate?
2.	In the fine-tuning phase, as the student network is optimized using strong augmented data, is the performance gain coming from this augmentation strategy?
3.	Why partition images before quality assessment? How about using full-resolution images as input?

I hope to see the answers and will adjust my rating accordingly.
limitations: limitations: The authors have stated the limitations of their article in the supplementary materials.
paper_summary: paper_summary: This paper posits that real-world image dehazing is particularly challenging due to the intricacies of accurately modeling haze distributions and the limited availability of paired real-world data. Traditional and deep learning-based methods struggle to address the complexities of real haze, often resulting in color distortion and suboptimal outcomes. To tackle these issues, this paper introduces the CORUN model, which integrates atmospheric scattering and image scenes to incorporate physical information into deep networks. Furthermore, it proposes the Coherence-based Label Generator to produce high-quality pseudo labels for network training, thereby improving the network's generalization in haze removal.
strength_weakness: strength_weakness: 1. The paper contains some inconsistencies in the use of symbols. While images are generally denoted by P, in the loss functions (15, 16, 17), the authors use I to represent images. Although the text explains the use of these symbols, it can still impact readability. Additionally, in line 172, the pseudo-label symbol is misspelled and should be corrected to P^{R}\_{Pse\_{i}}. 
2. In line 175, the symbols contain unnecessary tildes, which should be removed. The symbols in Figure 2 should also be consistent with those used in the formulas.

3. Equations (5) and (7) do not address the consistency of the number of channels between the Transmission Map and the image. Although this is illustrated in Figure 2, it still needs to be clearly stated in the equations to facilitate readability.

4. This paper adequately demonstrates its method's performance in real-world dehazing tasks through thorough experiments in both visualization and quantitative results. However, the provided ablation studies are insufficient. The authors should conduct more comprehensive ablation studies and experiments on different datasets to further validate the effectiveness of their method and its components.
questions: questions: 1. This paper introduce Colabator, a plug-and-play coherence label generation method designed to fine-tune models pre-trained on synthetic datasets using real degraded images, thereby achieving better real-world image processing results. Can the authors provide additional results of this framework's fine-tuning on various tasks to support this claim?
2. I noticed that the authors assign weights to the local quality of pseudo-labels using a weighted combination of CLIP scores and NR-IQA scores, instead of the more common approach of using their dot product. Can the authors provide experimental results to demonstrate the effectiveness of this choice?
3. Regarding the choice of NR-IQA, why did this paper select MUSIQ over other methods? What are the reasons behind this decision?
4. There is a small portion of similar or identical image content between the RTTS and URHI subsets of the RESIDE dataset. Did the authors notice this issue during their experiments? Have they addressed this issue, or did they directly use the full URHI subset for fine-tuning? If the authors used the entire URHI subset for fine-tuning, have they considered the model's performance on the RTTS subset after removing these similar images?
limitations: limitations: Regarding limitations, the proposed method partially addresses previous issues such as the lack of paired real-world data and the difficulty in modeling complex real-world haze distributions. Section A.1 "Limitations and Future Work" in the appendix discusses the current work's limitations and potential future research directions to address these unresolved issues. As for broader impacts, Section A.2 in the appendix provides a thorough discussion. As stated in the paper, this work has no foreseeable negative impacts on the field or society and offers substantial positive contributions.

Comments: title: Thanks for recognizing our work!
Thanks for recognizing the value of our work!
Thanks for recognizing the value of our work!
final score
Thanks for your encouraging reply!
Thank you for your detailed reponse
Thanks for recognizing the value of our work!
Thanks for recognizing the value of our work!
Read the rebuttal and discuss with the authors
comment: I would like to note that I have updated the rating, as noted in the previous comment, considering that authors would make the changes to the final version
Your acknowledgment holds great importance to us and serves as a meaningful validation of our dedicated efforts to advance this critical area of research. 

In this work, we are the first to propose a plug-and-play iterative mean-teacher framework (Colabator) for real-world image dehazing, along with a robust dehazing algorithm (CORUN) with theoretical guarantees. 

It’s important to emphasize that the Colabator framework is not limited to dehazing; it can also be applied to other significant low-level vision tasks, such as image desmoking and underwater image enhancement. In this case, **we believe this work has the potential to inspire advancements across the entire field of low-level vision for real-world image processing.**

We would greatly appreciate any further discussion, as well as a reconsideration of the rating.
Thanks for the update. I have no further concerns at the moment.
We wish to express our sincere appreciation to the reviewer for recognizing the substantial significance of our contribution, specifically the Colabator framework and the CORUN method, within the realm of real-world image dehazing!

First, we will incorporate the experiments and major changes conducted during the rebuttal phase into our revised manuscript. Our initial plan is to include critical experiments, such as detailed comparisons with existing methods and essential ablation studies, directly in the main text, while other experiments will be placed in the supplementary material due to space constraints. To make room for these important experiments, we will move some less critical visual results to the appendix.

Additionally, following the approach in **W1**, we have added comparisons with existing methods on the RTTS dataset. As shown in the table, we observed significant performance improvements when integrating either our joint estimation component or our unfolding framework proposed in CORUN. This experiment will also be included in our revised version.

Please feel free to let us know if you have any further concerns. We would be happy to address them.

| Metrics | Ren[66] | Ren+CORUN | Mondal[64] | Mondal+CORUN | Im[65] | Im+CORUN | PDN[50] | PDN+CORUN | DGUN[33] | DGUN+CORUN’s model | DGUN+CORUN | CORUN (Ours) |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| NIMA↑ | 3.173 | 3.420 | 3.372 | 3.518 | 3.304 | 3.414 | 2.925 | 3.271 | 4.272 | 4.419 | 4.583 | 4.823 |
| BRISQUE↓ | 31.335 | 28.441 | 29.951 | 27.773 | 26.906 | 25.103 | 33.186 | 29.342 | 29.753 | 27.728 | 25.308 | 20.944 |
| FADE ↓ | 2.065 | 1.878 | 1.732 | 1.626 | 1.719 | 1.633 | 2.159 | 2.006 | 1.663 | 1.535 | 1.376 | 1.051 |
We wish to express our sincere appreciation to the reviewer for recognizing the substantial significance of our contribution, specifically the Colabator framework and the CORUN method, within the realm of real-world image dehazing!

Your acknowledgment holds great importance to us and serves as a meaningful validation of our dedicated efforts to advance this critical area of research.
I was convinced by the statement from the authors.
This work is somewhat acceptable.
I decide to raise my score to 5.
I appreciate the authors' rebuttal, which has addressed most of my concerns.
One additional concern I have after reading the rebuttal is the authors have made comparisons against other methods on I-HAZE, O-HAZE, but not on RTTS, a benchmark the authors have used in the main paper. I believe this has to do with the other reviewer's recommendation.
It would be great if the authors could make comparisons on RTTS as well in the final version.
Also, the authors have presented a lot of new experimental results during the rebuttal, requiring a major change to the paper.
I'm ok with the acceptance and hence raise the rating, given that the authors make these major changes to the final version of the paper, along with new comparisons on RTTS as well.
We would like to sincerely thank the reviewer for the encouraging feedback.

In our **seven** response to reviewer Udmv, we have added **nine** tables and **two** figures to thoroughly demonstrate the superiority of our CORUN dehazing model and the generalizability of our Colabator framework.

Additionally, we encourage reviewer Udmv to briefly review the content in the global rebuttal as well as our responses to the other reviewers. These sections further validate the generalization of our Colabator framework across other critical low-level tasks and provide a detailed comparison between our method and existing dehazing techniques, supported by extensive experimental evidence.

We believe this will help the reviewer fully understand the novelty, contributions, and insights of our paper. Specifically, **we are the first to propose a plug-and-play iterative mean-teacher framework (Colabator) for real-world image dehazing, along with a robust dehazing algorithm (CORUN) with theoretical guarantees.**
The detailed rebuttal from the authors addresses most of my concerns.
I want to thank the authors for their work.
At this stage, I am considering the overall rating of this work mainly based on its novelty, contributions, and insights.
We wish to express our sincere appreciation to the reviewer for recognizing the substantial significance of our contribution, specifically the Colabator framework and the CORUN method, within the realm of real-world image dehazing, along with image desmoking and underwater image enhancement. Your acknowledgment holds great importance to us and serves as a meaningful validation of our dedicated efforts to advance this critical area of research. We will update the missing information about DA-CLIP in our final version.
We thank the authors for providing a detailed rebuttal in such a short time duration. After reviewing the rebuttal, I believe the authors have solved all my concerns about their paper. I will raise my rating to accept, and I support accepting this paper.
However, PLEASE make sure to update missing information about DA-CLIP and equation parts in the final revision to make the paper more comprehensive.
We wish to express our sincere appreciation to the reviewer for recognizing the substantial significance of our contribution, specifically the Colabator framework and the CORUN method, within the realm of real-world image dehazing, along with image desmoking and underwater image enhancement. Your acknowledgement holds great importance to us and serves as a meaningful validation of our dedicated efforts to advance this critical area of research.
After reviewing all the materials and discussions on this page, I believe the authors have made significant efforts to address my main concerns. The proposed framework Colabator has strong generalization performance, including dehazing, desmoking and underwater image enhancement tasks. I believe that this quality-evaluation-based pseudo-label selection framework provides a new direction for real-world image restoration.
I am now happy to update my rating to strong acceptance.
Hi Reviewers, 

The authors have submitted their rebuttal responses addressing the concerns and feedback you provided. We kindly request that you review their responses and assess whether the issues you raised have been satisfactorily addressed.

If there are any areas where you believe additional clarification is needed, please do not hesitate to engage in further discussion with the authors. Your insights are invaluable to ensuring a thorough and constructive review process.

Best
AC