Wave-Mamba: Wavelet State Space Model for Ultra-High-Definition Low-Light Image Enhancement

Authors: wenbin  zou
hongxia  gao
weipeng  yang
tongtong  liu
Venue: acmmm_org_ACMMM_2024_Conference
Published: 2024-04-08 16:50:26

Abstract: Ultra-high-definition (UHD) technology has attracted widespread attention due to its exceptional visual quality, but it also poses new challenges for low-light image enhancement (LLIE) techniques. UHD images inherently possess high computational complexity, leading existing UHD LLIE methods to employ high-magnification downsampling to reduce computational costs, which in turn results in information loss. The wavelet transform not only allows downsampling without loss of information, but also separates the image content from the noise. It enables state space models (SSMs) to avoid being affected by noise when modeling long sequences, thus making full use of the long-sequence modeling capability of SSMs. On this basis, we propose Wave-Mamba, a novel approach based on two pivotal insights derived from the wavelet domain: 1) most of the content information of an image exists in the low-frequency component, less in the high-frequency component. 2) The high-frequency component exerts a minimal influence on the outcomes of low-light enhancement. Specifically, to efficiently model global content information on UHD images, we proposed a low-frequency state space block (LFSSBlock) by improving SSMs to focus on restoring the information of low-frequency sub-bands. Moreover, we propose a high-frequency enhance block (HFEBlock) for high-frequency sub-band information, which uses the enhanced low-frequency information to correct the high-frequency information and effectively restore the correct high-frequency details. Through comprehensive evaluation, our method has demonstrated superior performance, significantly outshining current leading techniques while maintaining a more streamlined architecture. The code is available at https://github.com/AlexZou14/Wave-Mamba.

Main paper: 
 introduction: 
 The rapid advancements in imaging technology have enabled the widespread adoption of Ultra-High Definition (UHD) across diverse applications. However, the increased pixel count and highresolution nature of UHD images introduce significant challenges. UHD images are more susceptible to noise and lighting effects during capture, degrading quality and impacting high-level vision tasks. In this work, we focus on the crucial task of low-light image enhancement (LLIE) for UHD images.With the significant success of Convolutional Neural Networks (CNNs) and Transformers [46, 48, 49] in the field of image restoration, a lot of learning-based methods [2, 28, 32, 38, 47] have been proposed to tackle the task of LLIE. Although these methods have achieved remarkable performance on existing low-light datasets, they are trained on the LOL [28] and SID [3] datasets, where all images have resolutions below 1K (1920×1080). Furthermore, existing methods have sought higher performance through the design of more complex networks and an increase in network parameters. However, due to the discrepancy between the data distribution of UHD images and that of existing datasets, these advanced methods are not effectively applicable to 4K (3840×2160) scenarios. Therefore, as UHD images become increasingly prevalent, the domain of image restoration for UHD images is garnering more attention from researchers.With the release of some UHD LLIE datasets, such as UHD-LOL [13] and UHD-LL [15] , many methods [13, 15, 23, 31] tailored for UHD LLIE have also been proposed. Among these, Wang et al. [13] introduced an end-to-end UHD LLIE framework by incorporating Transformers and UNet. Leveraging the exceptional ability of the Transformer to capture long-distance information, the proposed method achieved superior restoration performance. However, due to the high computational cost of Transformers, this method could not be efficiently implemented for full-resolution UHD image inference on edge devices. To enable full-resolution inference of UHD images on consumer-grade GPUs, Li et al. [15] reduced the resolution of UHD images by 8× and embedded Fourier transform into a cascaded network, thus obtaining satisfactory results on real datasets. On this basis, Wang et al. [23] proposed a correction-matching Transformer module that utilizes high-resolution information to correct low-resolution features, achieving impressive performance through parallel enhancement of high and low-resolution. While these methods have demonstrated remarkable performance, they rely on significant downsampling to reduce computational costs, inevitably leading to the loss of critical image information. This process undoubtedly compromises the quality of image restoration. Therefore, enhancing the ability of the network to augment global information without sacrificing image detail is crucial.Inspired by the property of state space models (SSMs) [6, 8, 22 ] that long sequences can be modeled using linear complexity, it makes it possible to model global information in UHD images. In particular, the improved Mamba [6] has been successfully applied to several computer vision tasks [18, 20, 41] and achieved significant performance. However, the unidirectional modeling property of SSMs makes it susceptible to noise, which hinders the application of mamba to low-light scenes containing complex noise. Therefore, how to effectively apply the long sequence modeling capability of SSMs to UHD LLIE is a question worth exploring.To address the challenges of UHD low-light imaging, we propose an efficient method, called Wave-Mamba, that combines wavelet transform with Mamba. Unlike existing UHD LLIE methods, our approach avoids traditional downsampling, instead employing wavelet transform to prevent information loss. Additionally, the wavelet transform separates image content from noise, overcoming the limitations of standard SSMs, which are insensitive to noise. Particularly, our method is designed based on two observations in the wavelet domain of low-light noisy images: 1. In the wavelet domain, most image information resides in the low-frequency component, with only a minor portion of texture information in the highfrequency component. 2. High-frequency information has a minimal impact on the results of LLIE. Inspired by these insights, our network design focuses on processing low-frequency information, using enhanced low-frequency information to adjust the high-frequency information, effectively saving computational resources. Specifically, we developed a Low-Frequency State Space Block (LFSSBlock) that leverages the robust global modeling capability of SSMs to effectively enhance the illumination and texture information within the low-frequency component. For the highfrequency component, we designed a High-Frequency Enhance Block (HFEBlock), which utilizes the enhanced low-frequency information to match and correct the high-frequency data, achieving accurate and clear textures. With the aforementioned design, our Wave-Mamba significantly reduces computational costs while delivering outstanding performance, as illustrated in Figure 1 .Our key contributions are summarized as follows:• We are the pioneers in introducing Mamba to the UHD LLIE task, proposing a novel method named Wave-Mamba, inspired by unique characteristics observed in the wavelet domain. Unlike existing UHD LLIE methods, our method exploits the wavelet transform to avoid information loss, and to overcome the shortcomings of SSMs which are insensitive to noise. that employs enhanced low-frequency information for match correction, thereby effectively avoiding texture errors and loss. • The proposed Wave-Mamba exhibits extraordinary effectiveness and efficiency in addressing the combined tasks of illumination enhancement and noise removal in ultra-highdefinition images. 
related work 2.1 low-light image enhancement: 
 It has seen substantial developments with the advent of various innovative models and frameworks aimed at improving underexposed photos and videos. Wang et al. [25] introduced networks for image-to-illumination mapping, while Zero-DCE [10] , and its extension Zero-DCE++ [14] have made significant strides in enhancing image brightness and visual appeal through image-specific curve estimation trained with non-reference losses. Moreover, Wang et al. [5] presented a dual-stage low-light image enhancement network, FourLLIE, which enhances brightness by estimating amplitude transformation mappings in the frequency domain. Feng et al. [24] proposed a learnability enhancement strategy based on noise modeling, which improves the denoising performance of raw images in low-light conditions. Additionally, diffusion models, as seen in DiffLL [12] , utilize a sequence of denoising refinements for realistic detail generation in LLIE tasks, showing potential for low-light image enhancement. Despite these methods achieving excellent results, the direct application to Ultra-High-Definition (UHD) images is constrained by the high computational demand, marking a challenge for future research directions in efficiently processing UHD content.In recent years, UHD image restoration has emerged as a field of growing interest, with significant contributions from researchers [9, 16, 34, 45] . Zheng et al. [39, 40] pioneered the use of bilateral learning for UHD image dehazing and High Dynamic Range (HDR), leveraging the concept of learning local affine coefficients from downscaled images to enhance images at their original resolution.Innovations such as UHD-SFNet [29] and FourUHD [15] have advanced the field by focusing on enhancing underwater and low-light UHD images within the Fourier domain, capitalizing on the insight that illumination primarily resides in amplitude components.To address the limitations imposed by the need for downsampling in traditional UHD restoration techniques, NSEN [33] introduced an innovative, spatially-variant, and reversible downsampling method. This approach dynamically adapts the downsampling rate to the image's detail density, enhancing the detail preservation in the restoration process. Furthermore, LLFormer [13] represents the first attempt to employ a transformer-based model for the UHD Low-Light Image Enhancement (UHD-LLIE) task. Despite its pioneering status, LLFormer encounters challenges in executing full-resolution inference on standard consumer GPUs.Derived from control theory fundamentals, SSMs [7, 8, 22] have advanced remarkably in deep learning, exhibiting extraordinary efficiency in handling long-range dependencies due to their linear scalability with sequence length. Recently, the emergence of Mamba [6] , a selective, data-focused SSM optimized for hardware, has outperformed Transformer models in NLP tasks, displaying linear scalability concerning input size. Furthermore, the application of Mamba has extended to vision-related tasks, including image classification [18, 41] , image restoration [11, 21] , and biomedical image segmentation [20] . On this basis, some researchers [42] [43] [44] combine linear representation with incremental learning to propose efficient incremental learning methods. Currently, while Mambabased image restoration approaches show promise, they fall short of direct application to UHD image restoration due to inference challenges. Given the exceptional computational efficiency and scalability of Mamba, this study aims to pioneer the application of Mamba in UHD low-light image enhancement. 
preliminaries: state space models: 
 Structured State Space Models (S4), fundamentally based on continuous systems, explain the dynamic relationship between inputs 𝑥 (𝑡) and outputs 𝑦 (𝑡) within linear time-invariant frameworks. Essentially, this system maps a one-dimensional function or sequence 𝑥 (𝑡) ∈ R 𝐿 to 𝑦 (𝑡) ∈ R 𝐿 via an implicit latent state ℎ(𝑡) ∈ R 𝑁 . From a mathematical perspective, this system is succinctly represented by a linear ordinary differential equation (ODE), detailed as follows:EQUATIONEQUATIONwhere A ∈ R 𝑁 ×𝑁 , B ∈ R 𝑁 ×1 , C ∈ R 1×𝑁 are the parameters for a state size 𝑁 , and D ∈ R 1 denotes the skip connection.To integrate SSMs within deep learning algorithms, researchers have discretized the aforementioned ODE process and aligned the model with the sample rate of the underlying signal present in the input data. Typically, this discretization employs the zerothorder hold (ZOH) method, incorporating the time scale parameter Δ to transition continuous parameters A and B into their discrete counterparts Ā and B. This process is defined as follows:EQUATIONEQUATIONwhereΔ ∈ R 𝐷 and B, C ∈ R 𝐷 ×𝑁 .The recently developed state space model, Mamba [19] , has been further improved to make the parameters B, C, and Δ dependent on the input, thereby enabling dynamic feature representation. In essence, Mamba adopts a similar recursive structure as seen in Eq. ( 3), allowing it to process and retain information from exceptionally long sequences. This capability ensures that a greater number of pixels contribute to the restoration process. Additionally, Mamba utilizes a parallel scan algorithm [19] , mirroring the parallel processing benefits outlined in Eq. ( 3), thereby optimizing the training and inference process for efficiency. 
methodology: 
 In this section, we first discuss the observation and method design motivation when analyzing low-light images in the wavelet domain. Next, the structure of our proposed method and the proposed modules were described in detail.Here, we provide additional discussion details on low-light images in the wavelet domain to clarify our observations emphasized in the Sec. 1, and provide a concise explanation in Figure 3 . Wavelet Transformation: Given an image 𝐼 ∈ R 𝐻 ×𝑊 ×𝐶 , it is decomposed into four frequency subbands by wavelet transform.EQUATIONwhere𝑐𝐴, 𝑐𝐻, 𝑐𝐻, 𝑐𝐷 ∈ R 𝐻 2 × 𝑊2 ×𝐶 denote the low-frequency information of the input image and the high-frequency information in three different directions (vertical, horizontal, and diagonal directions), respectively. The 𝐷𝑊𝑇 (•) denotes the 2D discrete wavelet transform operation. Subsequently, we can reconstruct the decomposed frequency subbands to the original map without any loss of information by inverse wavelet transform 𝐼𝑊𝑇 (•), i.e.EQUATIONTherefore, leveraging this characteristic enables the execution of multiple DWT on an image, effectively downsampling the image while preserving information. This is one of the main reasons that prompted us to use DWT for the UHD LLIE task. Observations I: As illustrated Figure 3 , we decompose both lowlight and normal-light images using a 2D wavelet transform. Subsequently, the decomposed four frequency sub-bands are broadly The above observations and analyses of low-light images in the wavelet domain have inspired us to design an efficient framework using wavelet transform for the UHD LLIE task, named Wave-Mamba, as shown in Figure 2 . Specifically, we have introduced an effective Mamba architecture to create a Low-Frequency State Space Block (LFSSBlock), targeting the information-rich low-frequency component. This enables the network to enhance and repair global information with linear complexity. Additionally, we propose a High-Frequency Enhance Block (HFEBlock) that utilizes the enhanced low-frequency component to correct high-frequency information, ensuring the network accurately captures high-frequency texture information. We provide the overall pipeline of our method and further details on the critical components of our approach below.Figure 2 shows our overall framework of Wave-Mamba. Our Wave-Mamba is constructed using a multi-scale UNet structure. In the downsampling phase, we employ DWT to prevent the information loss encountered with traditional downsampling operations. In line with the observations made in Sec. 4.1, we specifically apply DWT downsampling to the low-frequency component, which contains a greater amount of information, thus effectively reducing computational costs. Regarding the high-frequency component, we employ the enhanced low-frequency component for the correction and restoration of high-frequency information. Specifically, given UHD low-light image 𝐼 𝑖𝑛 ∈ R 𝐻 ×𝑊 ×3 , we first apply a 3×3 convolution to obtain low-level embeddings 𝐹 0 ∈ R 𝐻 ×𝑊 ×𝐶 , where 𝐻,𝑊 , and 𝐶 denotes height, width, and channel, respectively. Then the hierarchical encoding is achieved through three layers of DWT downsampling and LFSS blocks. The lowfrequency feature 𝐹 𝐿1 , 𝐹 𝐿2 and 𝐹 𝐿3 , processed by DWT downsampling at different layers, are downsampled to size 𝐻 2 × 𝑊 2 , 𝐻 4 × 𝑊 4 , and 𝐻 8 × 𝑊 8 respectively. To fully utilize the input image information, we also fused obtained 𝑖-th layer of low-frequency feature 𝐹 𝐿𝑖 with the corresponding downsampled input image 𝐼 ↓×2 𝑖 and the enhanced low-frequency features 𝐹 𝑒 𝐿𝑖 are obtained by adjusting the global information through the stack LFSS blocks. The highfrequency features 𝐹 𝐻 1 , 𝐹 𝐻 2 , and 𝐹 𝐻 3 of each layer are first reduced from channel 3 * 𝐶 to channel 𝐶 by Selective Kernel Feature Fusion (SKFF) [36] , thus facilitating correction by the HFEBlock using the low-frequency components. Subsequently, the enhanced highfrequency features undergo further refinement in conjunction with the enhanced low-frequency features, employing the LFSSBlock and the HFEBlock, respectively. The restored features are progressively upsampled using the wavelet inverse transform through each layer. Finally, we use the element-wise sum to obtain the high-quality (HQ) output image 𝐼 ℎ𝑖𝑔ℎ .The LFSSBlock is employed to extract and model low-frequency information flows from the spatial domain of feature embedding, as illustrated in Figure 2 right. Given the input low-frequency feature 𝐹 𝑖 𝐿 ∈ R 𝐻 ×𝑊 ×𝐶 , we initially apply Layer Normalization (LN), followed by the Vision State Space Module (VSSM), to capture the spatial long-term dependencies. Additionally, it incorporates a Gate Feed-Forward Network (GFFN) to improve the efficiency of channel information flow. This process can be formulated as follows:EQUATIONEQUATIONwhere 2 right. Building upon prior work [18] , the input feature 𝑋 ∈ R 𝐻 ×𝑊 ×𝐶 is processed through two parallel branches. In the first branch, a linear layer expands the feature channel to 𝜆𝐶, with 𝜆 being a predetermined channel expansion factor. This expansion is succeeded by In the second branch, channel expansion to 𝜆𝐶 is achieved using a linear layer, then activated by SiLU. Following this, a Hadamard product combines the outputs of both branches. To finalize, channels are reduced back to 𝐶, producing an output 𝑋 𝑜𝑢𝑡 same as the input dimensions. It can be written as follows:EQUATIONEQUATIONEQUATIONwhere 𝐷𝑊 𝐶𝑜𝑛𝑣 (•) and 𝐿𝑖𝑛𝑒𝑎𝑟 (•) denote depth-wise convolution and linear projection. ⊙ denotes the Hadamard product. Gate Feed-Forward Network: In our framework, the Gated Feature Fusion Network (GFFN) employs a nonlinear gating mechanism to regulate information flow, enabling individual channels to concentrate on fine details that complement those from other layers. The operation of the GFFN is defined as follows:EQUATIONwhere 𝛿 𝑁𝐺 (•) is the function of non-linear gate mechanism. Similar to SimpleGate [4] , the non-linear gate mechanism divides the input along the channel dimension into two featuresF 1 , F 2 ∈ R 𝐻 ×𝑊 × 𝐶 2 .The output is then calculated by non-linear gating as 𝛿 𝑁𝐺 (F') = 𝐺𝐸𝐿𝑈 (F 1 ) ⊙ F 2 , where 𝐺𝐸𝐿𝑈 (•) denotes the activation function. The 𝐹 𝑖𝑛 and 𝐹 𝑜𝑢𝑡 denote the input and output of GFFN.The original Mamba processes input data causally, efficiently handling the sequential data typical of NLP tasks but encountering difficulties with non-sequential data like images. To adeptly manage 2D spatial information, we adopt the approach from [38] and deploy the 2D-SSM. As depicted in Figure 4 , this technique transforms a 2D image feature into a linear sequence by scanning across four distinct orientations: top-left to bottom-right, bottom-right to top-left, top-right to bottom-left, and bottom-left to top-right. It then captures the extensive range dependencies for each sequence via the discrete state space equation. Subsequently, a summative merging of all sequences, followed by a reshaping process, reinstates the original 2D framework.To enhance the feature representation within the high-frequency components more effectively, we propose the construction of a feature transformation from the low-frequency component to the high-frequency component. This transformation aims to enhance the high-frequency components by leveraging similar information in the low-frequency component. To accomplish this goal, we introduce the High-Frequency Enhance Block (HFEBlock), as illustrated in Figure 5 (a) . The HFEBlock enriches the missing information in high-frequency components by selecting more representative high-frequency similarity features in low-frequency components. This process is achieved through Frequency Matching Transformation (FMT), depicted in Figure 5 (b) . Each HFEBlock contains a Frequency Matching Transformation Attention (FMTA) and a Frequency Correction Forward Network (FCFN), which are used to explore frequency matching and correction within the attention mechanism and forward network, respectively:EQUATION)EQUATION)where 𝐹 𝑖𝑛 𝐻 and 𝐹 𝑜𝑢𝑡 𝐻 denote the input and output high-frequency features of HFEBlock. 𝐹 𝑀𝑇 𝐴(•, •) and 𝐹𝐶𝐹 𝑁 (•, •) represent the operation of FMTA and FCFN, respectively. Frequency Matching Transformation Attention: Drawing on previous work [23] , the impact of a more potent query can be substantial on the outcomes. We enhance the query by substituting it with the refined and improved low-frequency features 𝐹 𝑒 𝐿 , thereby imbuing the query with more significant content. We introduce the Feature-Modified Transformer Attention (FMTA) to achieve this enhancement of the query representation, thereby optimizing the attention mechanism. The FMTA initially produces the query (Q), key (K), and value (V) projections from the normalized highfrequency features 𝐹 𝑖𝑛 𝐻 through 1x1 convolution 𝑊 𝑝 and 3x3 depthwise convolution 𝑊 𝑑 , followed by executing the FMT between Q and 𝐹 𝑒 𝐿 . Subsequently, FMTA applies attention as follows:EQUATIONwhereQ, K, V = 𝑆𝑝𝑙𝑖𝑡 (𝑊 𝑑 𝑊 𝑝 (𝐹 𝑖𝑛 𝐻 )); A (Q,K,V) = V•𝑆𝑜 𝑓 𝑡𝑚𝑎𝑥 ( K•Q 𝛼 ).Here, 𝐹 𝑀𝑇 (•, •), 𝑆𝑝𝑙𝑖𝑡 (•), and 𝑆𝑜 𝑓 𝑡𝑚𝑎𝑥 (•) mean the operation of FMT, split, and softmax. 𝛼 is a learnable scaling parameter to control the magnitude of the dot product of K and Q. Frequency Correction Forward Network: Initially, the Feed-Forward Network (FFN) is composed of a layer normalization, a 1x1 convolution, and a 3x3 depth-wise convolution. Similar to the FMTA, we incorporate the corresponding FMT within the FFN to facilitate enhanced augmentation of high-frequency component information. This process is represented as follows:EQUATIONFrequency Matching Transformation: The FMT, depicted in Fig. 3 (a), is designed to convert low-frequency features into highfrequency ones, thereby supplying the high-frequency component with more descriptive features through a correlation matching scheme to achieve superior enhancement. Initially, we compute a similarity matrix M between the high-frequency and low-frequency components. Subsequently, we select the 𝑇𝑜𝑝 -1 vector 𝐷. The similar channels in the low-frequency component are then selected as the output based on the indices of vector 𝐷, which can be expressed as follows:EQUATIONEQUATIONEQUATIONwhere 𝑆𝑖𝑚(•, •) denotes the operation of the computer similarity, which is measured in terms of Euclidean distances. 𝑆𝑒𝑙𝑒𝑐𝑡 (•|•) and 𝐼𝑛𝑑𝑖𝑐𝑒𝑠 (•) represent the select feature and obtain indices value operation. Finally, the selected features 𝑌 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 are concatenated with the original high-frequency features, and a parallel branch is utilized to fuse the high-frequency features. Specifically, one branch calculates an attention map using a 1 × 1 convolution 𝑊 𝑝 and a Sigmoid function. The other branch undergoes a 3 × 3 convolution 𝑊 𝑑 . The outputs of both branches are then multiplied and merged through another 1 × 1 convolution 𝑊 𝑝 to produce the output features 𝐹 𝑜𝑢𝑡 𝐻 .EQUATIONEQUATION 
experiments 5.1 implementation details: 
 The number of LFSSBlocks is [1, 2, 4] and the number of HFEBlocks is [1, 1, 1] at each layer in the network encoder and decoder. The number of attention heads is 8, and the number of channels 𝐶 is 32. We train models using AdamW [19] optimizer with the initial learning rate 5 × 10 -4 gradually reduced to 1 × 10 -7 with the cosine annealing for a total 500k iterations. We use random rotations of 90, 180, 270, random flips, and random cropping to 512 × 512 size for the augmented training data. To constrain the training of Wave-Mamba, we use the 𝐿 1 loss function. All experiments are conducted on two NVIDIA 3090 GPUs.Our experiments leverage three prominent benchmarks for evaluating low-light image enhancement algorithms:The UHD-LL dataset [23] is a real-world, paired image collection that contains 2,150 pairs of 4K ultra-high-definition (UHD) data saved in 8-bit sRGB format. This dataset is split into 2,000 training pairs and 115 test pairs.The UHD-LOL benchmark [13] consists of two subsets -UHD-LOL4K and UHD-LOL8K -featuring 4K and 8K resolution images captured under low-light conditions, respectively. For our study, we utilize the UHD-LOL4K subset, which encompasses a total of 8,099 image pairs. Of these, 5,999 pairs are allocated for training, and the remaining 2,100 pairs are reserved for testing.In addition, we also evaluate our method on the widely adopted LOL dataset [28] , which is a standard benchmark for low-light image enhancement algorithms. The LOL dataset contains 500 image pairs in total, with 485 pairs used for training and 15 pairs set aside for testing. We also used LOLv2-Real to test model performance. In this section, we compare our proposed Wave-Mamba quantitatively and qualitatively with the current State-of-the-Art methods. We use the PSNR, SSIM [26] , and LPIPS [37] to evaluate our method. PSNR measures the quality of reconstructed images by comparing pixel intensity differences, SSIM evaluates image quality based on luminance, contrast, and structure, and LPIPS assesses perceptual similarity using deep learning models. Quantitative Results: To validate the effectiveness of our method on the UHD dataset, we compared it with state-of-the-art (SOTA) low-light enhancement methods, including Zero-DCE [10] , Zero-DCE++ [14] , RUAS [17] , Uformer [27] , Restormer [35] , LLFormer [13] , UHDFour [15] , and UHDFormer [23] . Given that the vast majority of existing methods are not designed to handle the full resolution of UHD images, we employ a sliding window approach to generate the final enhanced image. This way involves chunking the input UHD image into patches, inference each patch independently, and then stitching the predictions back together to obtain the output. Table 1 shows the performance of our Wave-Mamba and other methods. As shown in Table 1 , our approach achieves the best PSNR performance results with few parameters on all UHD datasets. In addition to this, our method is also far better in terms of perceptual metrics than the current most superior UHDFormer.For further validation of the effectiveness of our methods, we additionally compare these methods on the LOLv1 and LOLv2-Real datasets, as shown in Table 2 . Due to the low-resolution images in the LOLv1 and LOLv2-Real datasets, the downsampling operation in the existing UHD LLIE methods can cause information loss, which leads to poor results. In contrast, benefiting from the information preservation feature of the wavelet transform, our method can also achieve state-of-the-art results on low-resolution datasets. All these results clearly suggest the outstanding effectiveness and efficiency advantage of our Wave-Mamba. Qualitative Results: To complement the quantitative assessments, we also conduct qualitative comparisons of our proposed method. As shown in Figures 6 and 7 , existing UHD LLIE methods that rely on high-magnification downsampling suffer from the issue of introducing artifacts in the restored images. Furthermore, in comparison to the state-of-the-art UHDFormer approach, our Wave-Mamba method can achieve results that are closer to the true colors and textural details. Our Wave-Mamba demonstrates its capabilities in enhancing low-visibility and low-contrast regions, reliably removing noise without introducing unwanted artifacts, and robustly preserving the original color information. More results are provided in the supplementary material. In this section, we utilize the UHD-LL dataset to perform an ablation study evaluating the key design choices in our Wave-Mamba model. More results are provided in the supplementary material. Effectiveness of Proposed Blocks: We present ablation studies to demonstrate the effectiveness of the main component in our design, including LFSSBlock, HFEBlock, and FMT. The experimental results are shown in Table 3 . As shown in the results of Setting 1 and 2 in Table 3 , the lack of restoration and enhancement of low-frequency information is unable to improve image quality. Furthermore, we conducted a comparative experiment using Residual Blocks and LFSSBlocks with similar parameters, which demonstrates that our proposed LFSSBlock, leveraging its powerful global modeling capability through SSMs, can achieve better performance. Additionally, the ablation study on the HFEBlock indicates that while high-frequency information cannot primarily determine the quality of the restored image, it does have some influence on the restoration results. Therefore, compared to simply stacking high-frequency information, the addition of the HFEBlock with FMT in our method allows us to achieve optimal performance. The visualization in Figure 8 4 . As can be seen in Table 4 , the HFEBlocks have a greater impact on the parameters of the model compared to the LFSSBlocks, but the performance improvement is relatively small. Furthermore, during the process of increasing the number of LFSS-Blocks, we found that increasing the number of the second-level LFSSBlocks leads to a greater performance boost than increasing the number of the last-level LFSSBlocks. To verify the impact of increasing the second-level LFSSBlocks on performance, we compared Experiments 2 and 3, and found that performance did not increase as the number of modules grew. Considering the balance between performance and computational cost, we adopted the configuration of Experiment 2 as our final setting. 
conclusion: 
 In this paper, inspired by the characteristics of real low-light images in the wavelet domain, we propose a novel paradigm called Wave-Mamba that leverages state space models (SSMs) for the UHD LLIE task. Specifically, we employ wavelet-based downsampling to avoid the information loss issues associated with high-magnification downsampling. Additionally, we introduce Mamba to propose a low-frequency state space block (LFSSBlock), which relies on the excellent global modeling capability of SSMs to obtain excellent recovery results. Furthermore, to exploit the similarities between different frequency components, we design a high-frequency enhance block (HFEBlock) that utilizes the low-frequency information to correct the high-frequency details. Owing to these unique designs targeting the different frequency components in the wavelet domain, our Wave-Mamba outperforms state-of-the-art methods in UHD LLIE with appealing efficiency. 
 
 Appendix:  


Decision: The authors propose a method that uses combines wavelet transform and state-space models (SSMs) for ultra-high-definition (UHD) low-light image enhancement (LLIE). The method is technically sound and sufficient novel for publication. It is clear and the authors have performed enough experimental validation. In their rebuttal, the authors have addressed issues concerning the comparison with other methods and complexity.

Reviews: review: paper_summary: paper_summary: This paper introduces wavelet transform and Mamba architecture into UHD low-light image enhancement. In detail, the authors design encoder-decoder architecture and consider low-/high-frequency information separately. Experimental results prove the effectiveness of their proposed method in UHD LLIE.
strength_weakness: strength_weakness: Overall, this paper is well-written and motivation is clear.
limitations: limitations: - Lack of comparison with existing Mamba-based restoration model.
- Previous ACMMM papers on Low-Light Image Enhancement (LLIE) [1-2] should be discussed and cited to establish the relevance of this paper to ACMMM.

[1] "Learnability Enhancement for Low-light Raw Denoising: Where Paired Real Data Meets Noise Modeling," ACMMM 2022.

[2] "FourLLIE: Boosting Low-Light Image Enhancement by Fourier Frequency Information," ACMMM 2023.
paper_summary: paper_summary: Based on the observation of the wavelet domain, this paper proposes a method that combines wavelet transform and state-space models to address the high computational complexity and information loss in UHD LLIE. Moreover, a high-frequency enhancement module is introduced to restore the high-frequency details. Experimental results demonstrate the effectiveness of the method on UHD LLIE.
strength_weakness: strength_weakness: 1. The motivation of this paper is reasonable, and there is sufficient discussion and validation to support the motivation.
2. There are numerous experiments, demonstrating the effectiveness of the method through quantitative metrics and visual results
limitations: limitations: 1. The efficiency of the method encompasses not only the number of parameters but also requires comparisons of computational load and runtime. I will consider raising the rating if the author can provide comparisons of computational load and runtime with other approaches.
2. Some typographical errors in the paper need to be modified, such as those on line 132 and line 298.
paper_summary: paper_summary: The authors propose a wavelet-based Mamba (Wave-Mamba) for ultra-high-definition low-light image enhancement. The Wave-Mamba is based on two pivotal insights derived from the wavelet domain: 1) most of the content information of an image exists in the low-frequency component, less in the high-frequency component. 2) The high-frequency component exerts a minimal influence on the outcomes of low-light enhancement. The Wave-Mamba is composed of low-frequency state space (LFSS) modules and high-frequency enhancement modules (HFEMs) to leverage the advantages of both wavelet transform and Mamba. The experimental results seem good.
strength_weakness: strength_weakness: 1) The authors are the pioneers in introducing Mamba to UHD LLIE task. 
2) By adopting Mamba to wavelet domain, Wave-Mamba exploits the wavelet transform to avoid information loss, and to overcome the shortcomings of SSMs which are insensitive to noise. 
3) The authors propose two novel module LFSS-block and HFE-block in Wave-Mamba.
4) The experimental results are promising compared with recent low-light image enhancement methods.
limitations: limitations: 1) In the observations, the wavelet transform is adopted in image domain. However, the wavelet transform is adopted in the feature domain after convolutional layers in Wave-Mamba. The inconsistency between these two domains should be discussed.
2) The scales of wavelet transform should be ablation studied. Why do the authors choose to adopt four times wavelet transform?
3) In eq.(19-21), it is confusing how to select the Top-1 vector D and how to select low-frequency components on the indices of D? F_L is of size HWxC, D is of size 1xC. What is the size of Y_selected?
4) Lots of typos in the manuscript, for example:
a) on page 2, left column, “Therefor, Therefore, how to…”;
b) on page 3, right column, “As illustrated in Figure 1” should be Figure 2 according to context;
c) on page 4, right column, “(SKFE)[]”.
paper_summary: paper_summary: This paper proposes a novel approach that combines wavelet transform and state-space models (SSMs) for ultra-high-definition (UHD) low-light image enhancement (LLIE). This method uses  a low-frequency state space (LFSS) module by improving SSMs to focus on restoring the information of low-frequency sub-bands, and proposes a high-frequency enhancement module (HFEM) for high-frequency sub-band information. Numerous qualitative and quantitative experiments have demonstrated the effectiveness and efficiency of the proposed method.
strength_weakness: strength_weakness: The proposed method has sufficient detailed background introduction, novel insights, and clear motivation. This paper provides a detailed introduction to the background of LLIE and the shortcomings of UHD LLIE. At the same time, the motivation of the paper is clear, cleverly combining the characteristics of wavelet transform and mamba for UHD LLIE tasks.
limitations: limitations: (1) Line 132, "Therefore, Therefore, ......", There is an incorrect spelling here.
(2) Section 3.1 is empty. 
(3) Line 440, "In line with the observations made in Sec. 3.2, ......", Section 3.2 does not exist.
(4) Lines 460-461, " by Selective Kernel Feature Fusion (SKFF) []", The reference is empty.
(5) Why was UHD-LOL8K not selected in Section 5.2.
(6) Need to add references to estimated metrics, SSIM and LPIPS, and provide a brief introduction to them.
(7) Not mandatory. Can we add a set of experiments in Table 4 with parameters set to LFSSBlocks: [1,1,4], HFEBlocks: [1,1,2].

Overall, I think the overall quality of this paper is good, but there were significant errors in the writing. Therefore, currently I tend to reject this paper. The author should reshape the content of Sections 3 and 4