Channel Distortion-Aware Deep Image Super-Resolution Reconstruction for Wireless Internet of Things Applications

2.1 Overall framework of the method

The deep image super-resolution reconstruction method incorporating channel distortion modeling proposed in this paper adopts an end-to-end collaborative optimization architecture as a whole. The core logic lies in realizing the deep coupling between channel distortion modeling and image super-resolution reconstruction, breaking the limitations of traditional decoupled processing. The overall process can be described as follows: taking the clean low-resolution image $I_{L R}$ as the initial input, it is first fed into the DCDM. This module completes the joint modeling of multipath fading, additive noise, and random block loss based on the learnable parameter set $\theta_c$, and generates a distorted low-resolution image that matches the characteristics of real wireless channels:

$I_{L R}^{d i s t}=D_{\theta_c}\left(I_{L R}\right)$                      (1)

Then, $I_{L R}^{ {dist }}$ is input into the CASR-Net. Through channel state feature extraction, dynamic feature modulation, and collaborative attention mechanism, the network completes accurate restoration of distorted features and super-resolution reconstruction, and outputs the high-resolution reconstructed image:

$I_{S R}=G\left(I_{L R}^{d i s t}, \theta_g\right)$                     (2)

where, $\theta_g$ denotes the parameters of the super-resolution network. Finally, the reconstructed result is supervised by a joint loss function:

$L_{ {total }}=L_{S R}+\lambda_1 L_{ {dist\_consistency }}+\lambda_2 L_{ {perceptual }}$                     (3)

The gradients are backpropagated along the super-resolution network to the channel distortion module, realizing the adaptive collaborative update of $\theta_c$ and $\theta_g$, ensuring that the channel distortion modeling and super-resolution reconstruction processes are mutually adapted and collaboratively optimized, thereby fundamentally improving the super-resolution reconstruction performance of distorted images in WIoT scenarios. The overall framework is shown in Figure 1.

Figure 1. Overall framework of the proposed end-to-end deep image super-resolution reconstruction method

2.2 Differentiable channel distortion module

Multipath fading is one of the core impairments in WIoT channels that leads to image quality degradation. Its frequency-selective attenuation characteristic destroys the distribution of image frequency-domain features. Traditional fixed channel simulation methods are difficult to adapt to dynamically changing channel environments, and cannot achieve collaborative optimization with the super-resolution network. The multipath fading simulation mechanism designed in this paper has the core innovation of realizing differentiable modeling and parameter-adaptive learning of fading characteristics, without manually presetting fixed channel parameters, and can directly optimize fading features from distorted images in a backward manner. The internal structure and processing flow of DCDM are shown in Figure 2. Specifically, first the input clean low-resolution image $I_{L R}$ is subjected to a two-dimensional Fourier transform, converting the image from spatial domain to frequency domain, and obtaining frequency-domain features:

$F\left(I_{L R}\right)=F F T 2\left(I_{L R}\right)$                (4)

where, FFT2 denotes the two-dimensional fast Fourier transform operation. Then, a complex frequency response $H(u, v)$ is introduced to modulate the frequency-domain features to realize frequency-selective attenuation simulation. The magnitude of $H(u, v)$ follows a Rayleigh or Rician distribution, and the phase follows a uniform distribution in [0, 2π). Its magnitude and phase parameters are all learnable variables, forming differentiable channel fading coefficients. The mathematical expression of the frequency-domain modulation process is:

$F_{ {fade }}=F\left(I_{L R}\right) \odot H(u, v)$          (5)

where, ⊙ represents element-wise Hadamard product. Finally, the frequency-domain features are transformed back to the spatial domain through the two-dimensional inverse Fourier transform to obtain the image with multipath fading distortion:

$I_{ {fade }}={IFFT2}\left(F_{ {fade }}\right)$               (6)

The core advantage of this design is that all parameters of $H(u, v)$ can be adaptively updated through backpropagation, which can accurately match the multipath fading intensity of different wireless channels, and realize end-to-end collaborative optimization between fading characteristics and super-resolution reconstruction.

Figure 2. Internal structure and processing flow of the differentiable channel distortion module (DCDM)

Additive noise is another typical channel impairment in wireless transmission, and its intensity is directly related to the signal-to-noise ratio (SNR) of the channel. Traditional simulation methods with fixed noise variance cannot adapt to dynamically changing channel noise levels, which easily leads to insufficient noise suppression ability of the super-resolution network. The additive noise superposition mechanism proposed in this paper realizes differentiable adaptive adjustment of noise intensity. The core idea is to treat the noise variance $\sigma_n^2$ as a learnable parameter and include it into the module parameter set $\theta_c$, and jointly train it with the super-resolution network. Specifically, taking the image $I_{ {noise }}$ after multipath fading distortion as input, zero-mean Gaussian white noise n is added, where the noise satisfies $n \sim N\left(0, \sigma_n^2\right)$. The mathematical expression of the superposition process is:

$I_{{noise }}=I_{ {fade }}+n$                      (7)

where, the noise variance $\sigma_n^2$ is obtained through a lightweight fully connected network mapping and is dynamically associated with the channel SNR. When the channel SNR decreases, the network automatically increases $\sigma_n^2$ to simulate a strong noise environment; when the channel SNR increases, it automatically decreases $\sigma_n^2$ to match a weak noise transmission scenario. Different from traditional fixed noise simulation, this differentiable noise superposition mechanism allows the network to autonomously learn the distribution characteristics of different channel noises. By optimizing $\sigma_n^2$ through backpropagation, the noise simulation is more consistent with real wireless channel environments, while ensuring the differentiability of the noise addition operation, providing a foundation for subsequent end-to-end joint training with the super-resolution network.

The collaborative effect of multipath fading simulation and additive noise superposition constitutes the core distortion modeling capability of the DCDM module. Both follow a differentiable design principle, and all parameters can be updated through backpropagation. This design breaks the limitation of traditional separation between channel distortion simulation and super-resolution reconstruction, enabling channel distortion modeling to directly respond to super-resolution reconstruction requirements. Through parameter collaborative optimization, the simulated distortion features are more consistent with real wireless channel impairments, providing accurate channel state information support for the subsequent CASR-Net dynamic modulation, while avoiding the subjectivity and limitations caused by manually setting channel parameters.

For the burst packet loss phenomenon in WIoT links, this paper designs a structured random block erasure mechanism to simulate real channel packet loss distortion. Different from traditional unstructured global pixel random erasure methods, the image after noise processing is uniformly divided into non-overlapping image blocks of two sizes, 8 × 8 and 16 × 16. The block structure is consistent with wireless communication data packet transmission formats, which can more accurately reproduce real transmission packet loss characteristics. The module independently samples each image block using a learnable packet loss probability $p_{ {drop }}$, and performs pixel zeroing on blocks where packet loss is triggered. The overall distortion mapping relationship can be expressed as:

$I_{L R}^{ {dist }}=M \bigodot I_{ {noise }}$                      (8)

where, $I_{L R}^{{dist }}$ is the intermediate image after multipath fading and additive noise processing, and $M$ is a mask matrix corresponding to the block structure. The mask values are dynamically controlled by the learnable parameter $p_{ {drop }}$. The final output is the complete distorted low-resolution image $I_{L R}^{{dist }}$. The packet loss probability $p_{ {drop }}$ is included in the overall learnable parameter set $\theta_c$ of the module and can be adaptively adjusted during training, effectively improving the matching degree between distortion simulation and real WIoT channel environments.

This paper performs gradient-friendly reconstruction of all operations in the DCDM, fundamentally solving the inherent limitation that traditional discrete channel simulation cannot be integrated into end-to-end training. The two-dimensional Fourier transform and inverse transform are linear, invertible, and differentiable operations, and additive Gaussian noise superposition is a continuous and smooth mapping; both can directly support gradient backpropagation. For the inherently non-differentiable discrete hard-threshold block erasure problem, this paper introduces a continuous relaxation mask mechanism to replace the original binary discrete mask, transforming step-wise block erasure into a continuous weighted differentiable operation, so that block packet loss simulation also satisfies differentiability conditions.

All distortion parameters of the module are uniformly denoted as the parameter set $\theta_c$, and the entire distortion modeling process forms a continuous differentiable mapping:

$I_{L R}^{ {dist }}=D_{\theta_c}\left(I_{L R}\right)$                    (9)

Gradients can be fully propagated bidirectionally between the distortion module and the super-resolution network, realizing adaptive collaborative optimization between channel distortion modeling and image super-resolution reconstruction. This fundamentally changes the traditional decoupled processing mode where preprocessing and reconstruction models are independent and parameters are uncoupled, enabling channel distortion characteristics to actively adapt to super-resolution reconstruction requirements, and further improving reconstruction stability under complex channel environments.

2.3 Channel-Aware Super-Resolution Network (CASR-Net)

The CASR-Net proposed in this paper is based on an improved residual channel attention network as the backbone. The network does not perform redundant reconstruction of the basic residual attention structure, but instead introduces two core modules: a channel state feature extractor and a dynamic feature modulation layer. These two modules fundamentally solve the inherent defects of traditional super-resolution networks, which have static feature representations and cannot autonomously perceive dynamic channel impairments in WIoT, and realize implicit channel perception and adaptive super-resolution reconstruction of distorted images.

The architecture of CASR-Net is shown in Figure 3. The channel state feature extractor is the core component for realizing channel perception capability in the network. This module performs progressive spatial downsampling on the input distorted image features through a three-layer convolution structure with stride 2, compressing the feature dimension to 8 × 8, and fully aggregating local distortion spatial distribution information. Then, global average pooling is applied to complete global distortion feature aggregation, followed by two consecutive fully connected networks to perform feature dimension normalization and nonlinear mapping, and finally output a 64-dimensional dense channel embedding vector $z_{c h}$. This vector can fully represent channel impairment information such as multipath fading strength, noise level, and block packet loss degree corresponding to the current image. Different from traditional conditional super-resolution methods relying on manually annotated channel parameters, the channel state feature extractor directly performs implicit channel state encoding from the distorted image, without additional channel supervision labels, and all parameters can be jointly optimized end-to-end with the network backbone.

Figure 3. Architecture of the Channel-Aware Super-Resolution Network (CASR-Net)

The dynamic feature modulation layer is uniformly deployed after each residual block in the network and is responsible for adaptive transformation of channel-aware information into feature space. This module takes the embedding vector $z_{c h}$ output by the channel state feature extractor as the only input, and generates channel scaling parameter $\gamma$ and channel bias parameter $\beta$ through two independent lightweight fully connected mapping networks $\phi_\gamma\left(z_{c h}\right)$ and $\phi_\beta\left(z_{c h}\right)$, respectively. Then, channel-wise affine transformation is performed on the output features of the residual block. The mathematical expression is:

$F_{{out }}=\gamma \odot F_{ {in }}+\beta$                     (10)

where, $F_{i n}$ is the input feature map before modulation, $\odot$ represents channel-wise Hadamard product, and $F_{ {out }}$ is the output feature map after channel-adaptive modulation.

This dynamic modulation mechanism can autonomously adjust the response strength of each feature channel according to real-time channel impairment levels, and has fine-grained adaptive optimization characteristics. In strong noise channel environments, the network automatically reduces the gain of high-frequency noise-related channels to suppress noise interference expansion in the reconstruction process; in channel environments with severe block packet loss, the network autonomously enhances the weights of texture-related channels in missing regions to strengthen detail restoration capability. Compared with traditional fixed conditional fusion methods such as feature concatenation and element-wise addition, channel-wise dynamic affine modulation achieves fine-grained channel-adaptive feature regulation, and significantly improves the adaptability and robustness of the network to complex dynamic wireless channel environments with only a small increase in computational cost.

The distortion–super-resolution collaborative attention module, as a core enhancement component of CASR-Net for accurate distortion restoration, adopts a multi-head self-attention variant structure. The core innovation is to break the limitation that query, key, and value in traditional attention mechanisms are from the same source, and achieve collaborative optimization of distortion localization and detail restoration through heterogeneous feature interaction. The query vector is taken from deep semantic features of the network. Deep features, after multiple rounds of residual learning and dynamic modulation, have stronger global semantic representation capability and can accurately identify the spatial distribution of severely distorted regions in the image. The key vector and value vector are taken from shallow features. Shallow features retain more detailed texture information of the original distorted image and can provide accurate feature support for distortion region restoration. The module maps deep query features and shallow key-value features into the same feature space through lightweight linear mapping. The attention weight calculation expression is:

$\operatorname{Attn}(Q, K, V)=\operatorname{Softmax}\left(\frac{Q K^T}{\sqrt{d_k}}\right) V$                    (11)

where, Q, K, V are deep query features, shallow key features, and shallow value features respectively, and $d_k$ is the feature dimension, used to alleviate attention weight deviation caused by dimensionality disaster. To control computational complexity, the module adopts a channel compression strategy, reducing the input feature channels to 1/2 of the original before attention computation, and limits the number of attention heads to 4, ensuring that the computational cost of the module increases only by 15% compared with the baseline network, achieving a balance between performance and efficiency.

The core role of the Distortion–Super-resolution Collaborative Attention (DSCA) module is to establish a collaborative relationship between deep semantic distortion localization and shallow detail restoration, guiding network resources to focus on severely distorted regions. Deep semantic query features can accurately capture the spatial location and intensity of distortions such as noise and packet loss, and through attention weight allocation, focus the restoration on regions with obvious artifacts and missing textures. Shallow key-value features provide original texture details for these regions, and through attention-weighted fusion, shallow effective features are transferred to deep features to guide precise restoration. This design effectively solves the problems of inaccurate restoration of distorted regions and excessive smoothing of non-distorted regions in traditional super-resolution networks. Together with Channel State Feature Extractor (CSFE) for channel state extraction and Dynamic Feature Modulation (DFM) for dynamic feature modulation, it forms a synergistic effect, enabling the network to adaptively allocate restoration resources according to channel impairment distribution, suppress artifacts while maximally preserving original image details, and further improve both subjective and objective quality of reconstructed images.

${Attn}(Q, K, V)={Softmax}\left(\frac{Q K^T}{\sqrt{d_k}}\right) V$

2.4 Joint loss function and training strategy

The core of the joint loss function design is to realize deep synergy between super-resolution reconstruction and channel distortion modeling, breaking the limitation that traditional loss functions only focus on reconstruction quality while ignoring channel characteristics. Through multi-loss collaborative constraints, reconstruction accuracy, detail preservation, and channel adaptability are jointly considered. The total loss expression is:

$L_{ {total }}=L_{S R}+\lambda_1 L_{ {dist\_consistency }}+\lambda_2 L_{ {perceptual }}$                       (12)

where, $\lambda_1$ and $\lambda_2$ are the weight coefficients of channel consistency loss and perceptual loss respectively. Experimental results show that when set to 0.5 and 0.3, optimal balance among losses can be achieved. The innovation of this loss function lies in introducing reversibility constraints of channel distortion into super-resolution training, so that the super-resolution network can not only perform image restoration but also adapt to dynamically changing channel environments, fundamentally solving the insufficient robustness of traditional super-resolution models in complex channel scenarios.

The super-resolution reconstruction loss $L_{S R}$ adopts a combination of Charbonnier loss and edge loss to jointly consider reconstruction accuracy and contour integrity. The Charbonnier loss is a smooth approximation of L1 loss, and its expression is:

$L_{ {Charbonnier }}=\sqrt{\left\|I_{S R}-I_{H R}\right\|^2+\epsilon^2}(\epsilon=1 e-3)$                          (13)

It can effectively alleviate the edge blurring problem caused by traditional L1 loss and reduce the influence of outliers on training. The edge loss is based on the Sobel gradient operator, which strengthens contour restoration by computing the gradient difference between reconstructed image and ground truth high-resolution image. The expression is:

$L_{ {edge }}=\left\|{Sobel}\left(I_{S R}\right)-{Sobel}\left(I_{H R}\right)\right\|_1$                       (14)

It makes the edge details of reconstructed images clearer and more three-dimensional. The channel consistency loss $L_{{dist\_consistency }}$ is the core innovative loss, and its expression is:

$L_{ {dist\_consistency }}=\left\|C_{\theta_c}\left(I_{S R}\right)-I_{L R}^{ {dist }}\right\|_1$                     (15)

where, $C_{\theta_c}(\cdot)$ denotes the differentiable channel module with the same parameters as the initial distortion modeling.

The re-distorted image is:

$I_{L R}^{ {re-dist }}=C_{\theta_c}\left(I_{S R}\right)$                         (16)

The above expression is the re-distorted image after the reconstructed image passes through the channel module. This loss constrains pixel consistency between $I_{L R}^{ {re-dist }}$ and the original distorted image $I_{L R}^{ {dist }}$, forcing the super-resolution network to preserve the reversibility of channel distortion, avoiding loss of key channel state information during the restoration process, and ensuring that reconstruction results match real channel environments. The perceptual loss $L_{ {perceptual }}$ is based on a pretrained VGG-19 network, selecting feature outputs from layer relu4_4, and computing Euclidean distance between reconstructed image and ground truth image in high-level feature space. The expression is:

$L_{ {perceptual }}=\left\|V G G\left(I_{S R}\right)-V G G\left(I_{H R}\right)\right\|_2^2$              (17)

It can effectively improve visual realism of reconstructed images and reduce the “pseudo-sharpness” phenomenon.

A two-stage training strategy is adopted to achieve efficient convergence and performance optimization. The core innovation lies in progressively achieving collaborative adaptation between super-resolution network and channel module through staged constraints, avoiding gradient vanishing or training instability. In the first stage (basic training stage), the parameters of the differentiable channel module DCDM are fixed, and a preset channel distribution is used to simulate typical wireless transmission environments. The training focus is on the backbone of CASR-Net and the CSFE. The training loss at this stage is: $L_{S R}+L_{ {perceptual }}$. The purpose is to allow the super-resolution network to first learn basic anti-distortion reconstruction capability and initially handle distortion restoration under fixed channel conditions. In the second stage (collaborative training stage), the parameters of DCDM are released to make them learnable, and $L_{ {dist\_consistency }}$ is included in the total loss, enabling joint training of DCDM and CASR-Net. At this stage, the model can adaptively adjust channel simulation parameters according to reconstruction performance, forming a closed-loop collaboration between channel modeling and super-resolution reconstruction. The training uses the Adam optimizer, with an initial learning rate of 1 × 10⁻⁴, cosine annealing strategy for learning rate decay, batch size set to 16, and training datasets DIV2K and Flickr2K. Total training epochs are 200, where the first 50 epochs are stage one and the remaining 150 epochs are stage two. Early stopping strategy is used to avoid overfitting, ensuring full convergence of the model and achieving deep synergy between channel modeling and super-resolution reconstruction.

2.5 Lightweight deployment scheme

To achieve efficient deployment on WIoT edge devices and solve the problems of large parameter size and slow inference speed of traditional super-resolution models, this paper proposes a distillation–pruning collaborative lightweight scheme. Under the premise of ensuring reconstruction performance, the model complexity and inference latency are greatly reduced to adapt to edge device resource constraints. The scheme takes knowledge distillation as the core and constructs a teacher–student network architecture, where the teacher network is the complete CASR-Net, and the student network adopts a lightweight structure design. Lightweighting is achieved by reducing the number of residual blocks and compressing feature channel dimensions. The core innovation lies in the dual-constraint design of the distillation loss, which not only includes reconstruction error loss at the output layer, but also introduces intermediate feature loss guided by CSFE channel embedding. The distillation loss function is constructed as:

$L_{ {distill }}=\alpha\left\|G_t(x)-G_s(x)\right\|_2^2+\beta\left\|E_t(x)-E_s(x)\right\|_2^2$                      (18)

where, $G_t$ and $G_s$ are the output features of the teacher and student networks respectively, $E_t$ and $E_s$ are the CSFE embedding features of the two networks respectively, and $\alpha= 0.6, \beta=0.4$ are weight coefficients. This ensures that the student network can not only fit the output results of the teacher network, but also inherit its channel-aware capability, avoiding degradation of channel adaptation performance during lightweighting. After distillation, a channel pruning strategy is used to further compress the model size. Based on the L1 norm of filter weights, filters with larger absolute weights are retained. The pruning rate is strictly controlled within 30%. Through layer-wise pruning and fine-tuning verification, it is ensured that the performance drop after pruning does not exceed 5%, achieving a balance between performance and lightweighting. Finally, the lightweight model parameter size is reduced to 2.1M, and the inference time on NVIDIA Jetson Nano edge device is only 45ms, which is far below the 50ms threshold for real-time deployment, fully meeting the real-time processing requirements of WIoT scenarios. At the same time, its lightweight structure also reduces computational and power consumption pressure on edge devices, providing a feasible path for practical deployment of the method. Figure 4 shows the flowchart of the lightweight deployment scheme based on distillation and pruning collaboration.