---
title: "Event-driven Video Deblurring via Spatio-Temporal Relation-Aware Network"
authors:
  - "Chengzhi Cao"
  - "Xueyang Fu"
  - "Yurui Zhu"
  - "Gege Shi"
  - "Zheng-Jun Zha"
doi: "10.24963/ijcai.2022/112"
url: "https://ijcai.org/proceedings/2022/112"
pdf: "https://ijcai.org/proceedings/2022/0112.pdf"
venue: "Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence"
year: 2022
pages: "799-805"
track: "Main Track"
keywords:
  - "Computer Vision: Applications"
  - "Computer Vision: Computational photography"
---

# Event-driven Video Deblurring via Spatio-Temporal Relation-Aware Network

Chengzhi Cao, Xueyang Fu, Yurui Zhu, Gege Shi, Zheng-Jun Zha

*Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence*, pages 799-805. DOI: [10.24963/ijcai.2022/112](https://doi.org/10.24963/ijcai.2022/112)

## Abstract

Video deblurring with event information has attracted considerable attention. To help deblur each frame, existing methods usually compress a specific event sequence into a feature tensor with the same size as the corresponding video. However, this strategy neither considers the pixel-level spatial brightness changes nor the temporal correlation between events at each time step, resulting in insufficient use of spatio-temporal information. To address this issue, we propose a new Spatio-Temporal Relation-Attention network (STRA), for the specific event-based video deblurring. Concretely, to utilize spatial consistency between the frame and event, we model the brightness changes as an extra prior to aware blurring contexts in each frame; to record temporal relationship among different events, we develop a temporal memory block to restore long-range dependencies of event sequences continuously. In this way, the complementary information contained in the events and frames, as well as the correlation of neighboring events, can be fully utilized to recover spatial texture from events constantly. Experiments show that our STRA significantly outperforms several competing methods, e.g., on the HQF dataset, our network achieves up to 1.3 dB in terms of PSNR over the most advanced method. The code is available at https://github.com/Chengzhi-Cao/STRA.

## Full text

## 1 Introduction

As an important data source in the computer vision community, video usually contain inevitable blur due to movement of objects [Gallego et al., 2021; Zou et al., 2021]. To eliminate the adverse effects, video deblurring have attracted considerable attentions [Touvron et al., 2021; Li and Xu, 2021]. Recently, a new sensor, called event camera for recording and capturing scene intensity changes at the microsecond level, has been recommended to promote video blurring [Zhu et al., 2019].

∗Corresponding author

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000000_f00eccc1a47fae6f4e7a8394d8bd624fa8974c6982d9f7bf28bbd9ea81f07421.png)

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000001_b5027867916af7986431c435235f10d3f0b228b074a6d2bcd636fa073e4b4c7b.png)

GT PSNR | SSIM

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000002_ee9e78e0c7ef1c060ad2eddc46dc60e4c3e74c6ef822203071c1ef81264302c0.png)

Blurry Frame 16.17 | 0.492

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000003_ed146a7f4454bc5d51d3e58fa8e6f743bd6d597f6a54d9330c7eb8d13a3e604d.png)

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000004_81d68e669aebfebe1e8e973d2c526f7abdd303d25733b87f13f411064306ba20.png)

STFAN 20.32 | 0.626

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000005_dbf84c18cb416a6936363af3ca21685eed02284d1ab8c974c7135136ae06ed2b.png)

Event

eSL-Net 23.25 | 0.735

STRA, 25.05 | 0.838

Figure 1: Quantitative and qualitative comparisons on deblurring results by state-of-the-art video deblurring STFAN [Zhou et al., 2019], eSL-Net [Wang et al., 2020] and our STRA.

Due to the success of convolutional neural networks (CNNs) [Wang et al., 2021; Nikzad et al., 2021], event-driven deblurring has been extensively developed and achieved promising performance [Xu et al., 2021]. However, these methods still have some limitations. On the one hand, existing video deblurring networks directly utilize events as an extra prior without considering the correlation among different events [Wang et al., 2019] [Zhou and Teng, 2021]. These networks fulfill an independent feature map by compressing the intensity changes into one time step, so the temporal information will be lost and the high temporal resolution of events cannot be fully utilized. On the other hand, eventdriven video recovery networks rely heavily on the deployment of events [Zhu et al., 2019]. However, these networks simply concatenate features maps of both the blurring frames and events as the input of CNNs, ignoring the rich brightness change information as well as spatial consistency between events and frames [Zou, 2020]. These problems limit the further development of principled work on event-based video deblurring.

In this paper, we develop a unique framework for the eventdriven video deblurring, where the spatial consistency between the event and frame is fully utilized to recover spatial textures, while the temporal correlation in event sequences is represented to record long-range dependencies of them continuously. To achieve these two goals, we design a frameevent Spatial Fusion Block (SFB) to combine the two types of features from frames and events. With the help of the brightness prior, this block calculates the non-local features to capture spatial consistency between each frame and event. Then, to utilize high temporal information provided by events, we introduce a Temporal Memory Block (TMB) to restore temporal information between different sequences of events continuously. This block computes the long-range dependency of different events to restore temporal event correlation. The final deblurring network is constructed based on the two blocks and trained in an end-to-end fashion. Furthermore, our proposed spatial fusion block and temporal memory block can cope with synthetic and real-world video deblurring datasets to achieve favorable performance, substantiating the effectiveness of our spatio-temporal relation-aware structure.

The main contributions of our work are three-fold:

- We propose a spatio-temporal relation-aware network for accurate event-driven video deblurring. Our network achieves better performance through fusing features of frames and events properly.
- A novel spatial fusion block is proposed for modeling the spatial relationship between frames and events, which greatly makes use of the spatial consistency.
- A temporal memory block is developed to record longrange dependencies of event sequences in each time step to utilize temporal information from events effectively.
- Extensive experiments show that our method can yield high-quality deblurred results, e.g., our network achieves superior performance by 1.3 dB compared with [Xu et al., 2021] on the HQF dataset.

## 2 RelatedWork

## 2.1 Video Deblurring

Due to the ill-posed nature of video deblurring, traditional methods always constrain this problem by using some assumptions or priors, which cannot adapt to complex dynamic scenes including moving things. The blurring effects come from several different scenes, such as depth variation, moving objects, camera shaking, etc [Li et al., 2020]. Recently, learning-based methods have been introduced to solve this problem and made considerable achievements. In particular, [Deng et al., 2021] proposes a separable-patch structure with channel spatial attention blocks to utilize multi-scale integration to obtain larger receptive field. To make better use of the consecutive sharp frames, [Li and Xu, 2021] designs a correlative module relying on spatial relations among blurring frames to enhance the correlations. [Durand, 2018] regards all frames as equal and construct them order-independently in the burst by putting them in arbitrary size. [Zhang and Luo, 2019] applies 3D convolution blocks in temporal domains to restore sharp frame details and use a GAN-based generator for effective adversarial training. Although the abovementioned methods achieve considerable performance, they always attach great importance to network structures but ignore other helpful information to improve the deblurring performance.

## 2.2 Event-based Video Deblurring

The event camera measures the pixel-level brightness change and outputs events when the change exceeds a pre-defined threshold. By introducing events into the deblurring issue, it is easier to handle the blurry texture erasure. Most eventbased video deblurring methods utilize neural networks and directly learn the relation from a blurry image to a sequence of sharp images with the aid of events. So the most important question is, how to make full use of its high temporal resolution. [Pan et al., 2019] finds that blur frames are always around in sharp frames. Based on this observation, the authors proposed a flexible fusion module to detect nearest sharp frames and obtain similarity in event and blur videos. To solve the degradation problem caused by the inconsistent data, [Xu et al., 2021] utilizes the self-supervised learning strategy to exploit latent information in events. D2Net [Shang et al., 2021] detects blurry frames as a binary classification task, adopt bidirectional LSTM (BiLSTM) to classify sharp frames and blurry frames, by which temporal correlations of adjacent frames in both forward and backward directions are leveraged. [Zou, 2020] finds that the integrals of events among sharp and blurry frames, and adopted events to predict the residual for video deblurring and interpolation. [Wang et al., 2020] applies sparse learning on the sparsity data of events, and perform super-resolution, deblurring and denoising simultaneously in an general network.

The existing methods, however have not considered the use of rich brightness change information by mining the spatial consistency between image features and event features. In addition, the long-time dependency in different event sequences is also not fully exploited. Therefore, we propose a novel framework to solve the event-based video deblurring by constantly being aware of the spatial consistency and temporal correlation between frames and events.

## 3 Methodology

## 3.1 Network Structure

Figure 2 presents the workflow of our proposed network. Given a sequence of video frames B and their corresponding events E, the network processes frames in temporal order with brightness prior of events to generate the final output O. To complete a target sharp frame, our network firstly takes three consecutive frames into an U-Net structure to extract features. Then, the spatial fusion block is adopted to fuse two types (frames and events) of features properly by calculating non-local operation with the help of brightness prior. To take advantages of high temporal information provided by events, the temporal memory block will restore temporal information between different sequences of events continuously. Since the core components of our network are the spatial fusion block and temporal memory block, below we detail these two parts.

## 3.2 Spatial Fusion Block

Inspired by the asymmetric fusion between intra-scale features from different scales [Cho et al., 2021], we take three different feature maps as input and combine multi-scale features by resizing three different maps to the same scale and concatenating them for fusion with event features. Specifically, this process is formulated as:

Figure 2: Our proposed network architecture, which is based on the U-Net structure, contains two specifically designed blocks: spatial fusion block (SFB) and temporal memory block (TMB). Given the triplet blurring consecutive frames and their corresponding event sequences, SFB is utilized to calculate the spatial consistency between frames and events, and then fuse them properly; TMB restores the long-range dependencies of different event sequences continuously and records them in temporal order, providing event features for SFB.

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000006_d8f1fdc36d5e7660797a72ea5c0acdfa97a01c177ffd1b5e7af15bd88982bd32.png)

<!-- formula-not-decoded -->

where CB1, CB2 and CB3 represent the three different maps from U-Net encoder, CB represents the output of feature fusion. Downsampling (↓) is applied in order to concatenate features from different scale. For events, we use a downsampling layer to keep the same scale with the frame feature. Then, with consideration of spatial correlation between all positions in each frame and the corresponding brightness changes in events, we apply the non-local attention operation to fuse spatial feature [Wang et al., 2018; Li et al., 2019] from frames and events as:

<!-- formula-not-decoded -->

where i is the index of the output position and j is the index that enumerates all possible positions. F and E represent the input frame feature maps and event feature maps, respectively. Feat is the output of the same size as F. The function g(·) calculates the representation of the input frame feature maps at the position j. The result will be normalized by factor C(x) = N, where N is the number of positions in E. The function f(·, ·) is defined as follows:

<!-- formula-not-decoded -->

We use softmax operation as activation function. Finally, to make the connection with U-net decoder feature maps, we also upsample the output to three maps (EB1,EB2,EB3) with different scales. The whole structure of SFB is shown in Figure 2(b). Different from the traditional non-local network that only calculates the weighted sum of features at all positions in a single feature map, our SFB fuses three frame feature maps with different scales and captures correlation with corresponding event sequences.

## 3.3 Temporal Memory Block

Motivated by the spatial and temporal non-local correlation to generate segmentation to current frame [Xie et al., 2021], our temporal memory block consists of a memory encoder and a reader. For T - 1 and T + 1 event sequence, we use one common-used and two special-used convolutional layers to obtain the key and the value. Each key and value will be obtained by deploying their own convolutional layer on the common feature map Fm so that all keys and values of each frame will be stored by temporal order [Yao et al., 2021]. The equations are shown as follows:

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

In the memory reader, the keys and values of previous events and next events are concatenated, and the similarities between query and keys are used to measure temporal nonlocal correspondence with current events, which will generate the corresponding value to aware temporal changes [Zhang and Zhu, 2021]. Then, the value is processed based on the non-local attention operation [Hu et al., 2018] as shown in Figure 2(c). In this way, the temporal correlation between the current event sequence and its neighbor sequences will be fully utilized to record long-range dependencies.

(a) GT PSNR | SSIM

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000007_553a99c6928598ac2b2888652c1f8f66d496be9a597b81b75716bb7cdde25b7b.png)

(e) Event

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000008_88276c1ae761451bed54d778cd8af249bc8450c15c0614bb3ecac376b0a98267.png)

(b) Blurry Frame 16.64 | 0.556

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000009_5405850ef28c51870dda98215b29372ad020f73f9009cb7e926ea6d6bef25e80.png)

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000010_b376f1f7d8136868e7c0115e630b8b5d26eb7c268151c371480a641d156871a6.png)

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000011_337cd7bba6060175bbf93b61084bffc2e199c9e321ad0c185ca6ead15e267459.png)

(f) STFAN 23.35 | 0.790

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000012_1f088039ddb8aa9fd19cbde81b464090b004a2c680b7b56900a3b30c719d3c9c.png)

(c) LEDVDI 19.52 | 0.626

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000013_cfaafbf5f95b5ce8bd4de7c28b96c360d201b4481437a201bcae948ee5ee9e95.png)

(g) eSL-Net 22.60 | 0.744

(d) CSD 24.53 | 0.801

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000014_f63b0b9495fb4af81ead61d21619a25507d1f83fd0f1ce635ecfb974eba3a58d.png)

(h) STRA, 26.53 | 0.862

Figure 3: Visual results of event-driven video deblurring in HQF dataset. Quantitative results are presented by PSNR | SSIM values.

| Metrics   |   Methods LEDVI |   D2Net |   eSL-Net |   CSD |   STFAN |   RED-Net |   STRA | Ideal value   |
|-----------|-----------------|---------|-----------|-------|---------|-----------|--------|---------------|
| PSNR      |           22.22 |   26.16 |     25.42 | 24.71 |   24.17 |     25.72 |  27.54 | +∞            |
| SSIM      |           0.687 |   0.864 |     0.754 | 0.724 |   0.711 |     0.763 |  0.834 | 1.00          |

Table 1: Average PSNR and SSIM results on the HQF dataset.

## 3.4 Loss Function

In this paper, we use Mean squared error (MSE) to train our network in an end-to-end fashion:

<!-- formula-not-decoded -->

where B and GT is the blurry frame and its ground truth counterpart, respectively. f(·) represents the network.

## 4 Experiments

## 4.1 Experimental Settings

Dataset. Our Spatio-Temporal Relation-Aware network (STRA) is trained based on the benchmark GoPro dataset [Nah et al., 2017], composed of synthetic events, 2,103 pairs of blurring frames and sharp clear ground-truth frames. The blurry image is offered by averaging nearby (the number varies from 7 to 13) frames. To increase the noise diversity, V2E [Hu et al., 2021] is utilized to generate the corresponding event sequences with consideration of different contract thresholds for pixel-level from Gaussian distribution N(0.18, 0.03) [Zou, 2020]. For evaluation in real-world events, we utilize HQF dataset [Stoffregen et al., 2020], including both real-world events and ground-truth frames captured from a DAVIS240C [Brandli et al., 2014], which is a dynamic event-based vision sensor to report brightness changes. The blurring frames are generated by using the same strategy as the GoPro dataset. We also test our network on the GoPro testing datasets, where the number of frame pairs is 1,111.

Implementation Details. Our network is implemented using Pytorch on a single NVIDIA RTX 2080Ti GPU. In the training process, we randomly cropped the sampled frames with the size of 256×256. For data augmentation, each patch was horizontally flipped with the probability of 0.5. We use a batch size of 8 training pairs and ADAM optimizer [Kingma and Ba, 2017] with parameter β1 = 0.9, β2 = 0.999. The maximum training epoch is set to 200, with the initial learning rate 10-4 , then decays by 25% every 50 epochs.

## 4.2 Comparison with State-of-the-art Methods

We compare our proposed STRA with several state-of-theart event-driven video deblurring methods, including LEDVI [Zou, 2020], eSL-Net [Wang et al., 2020], CSD [Wang et al., 2021], STFAN [Zhou et al., 2019], and RED-Net [Xu et al., 2021] D2Net [Shang et al., 2021]. The quantitative results in GoPro testing dataset and HQF dataset are presented in Tables 1 and 2. It is clear that our network achieves outstanding improvements compared with the state-of-the-arts, on average 0.91 dB in GoPro dataset and 1.3 dB in HQF dataset with real-world events. This is because our STRA can benefit from the temporal correlation between different event sequences, whose brightness changes can be used to reconstruct sharp frames. Moreover, our model can fully utilize spatial consistency between each frame and the corresponding event sequence.

Figure 4: Visual results of event-driven video deblurring in GoPro dataset. Quantitative results are presented by PSNR | SSIM values.

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000015_f70073c0830163d909dcbedc6bb8394a48f9257b4969da531ddb925edd65ae90.png)

Table 2: Average PSNR and SSIM results on the GoPro dataset.

| Metrics Methods   |   LEDVI |   D2Net |   eSL-Net |   CSD |   STFAN |   RED-Net |   STRA | Ideal value   |
|-------------------|---------|---------|-----------|-------|---------|-----------|--------|---------------|
| PSNR              |   22.86 |   28.10 |     22.59 | 27.54 |   28.07 |     28.98 |  29.73 | +∞            |
| SSIM              |   0.733 |   0.897 |     0.750 | 0.834 |   0.836 |     0.849 |  0.927 | 1.00          |

Table 3: Comparison of different backbones on parameter numbers, FLOPS and Thoughput. The Throughput is measured as the number of images processed per second on a RTX 2080Ti GPU.

| Methods   | # Params   | FLOPS   |   Throughput (images/s) |
|-----------|------------|---------|-------------------------|
| LEDVI     | 4.73M      | 1.54G   |                   11.57 |
| eSL-Net   | 1.32M      | 4.97G   |                   17.21 |
| CSD       | 2.07M      | 3.32G   |                   20.03 |
| STFAN     | 3.64M      | 1.18G   |                   14.78 |
| STRA      | 2.36M      | 1.10G   |                   22.54 |

Table 4: Comparisons of different baselines between D2Net and STRA in GoPro dataset.

| Methods   |   frame-based - D2Net |   frame-based - STRA |   frame-event-based - D2Net |   frame-event-based - STRA |
|-----------|-----------------------|----------------------|-----------------------------|----------------------------|
| PSNR      |                 25.93 |                26.82 |                       28.10 |                      29.73 |
| SSIM      |                 0.770 |                0.792 |                       0.897 |                      0.927 |

Figures 3 and 4 present deblurring results of STRA and other comparing methods. Visual quality comparisons demonstrate that the proper fusion of frames and events data in spatial and temporal dimensions can accomplish highquality video deblurring with more structural details. For example, in Figures 3 (e), the event data can capture much more brightness changes of one scene and contribute to the final deblurring results. In Figure 4, the letter 'P' in the GoPro testing dataset can be restored better by our STRA. Other comparison methods, such as eSL-Net [Wang et al., 2020] and LEDVI [Zou, 2020], however, did not make full use of high temporal information and spatial consistency in events and frames, so the reconstructed frames are unstable on both synthetic and real-world event datasets.

## 4.3 Runtime and Parameter Numbers

We use 200 images with the size of 180 × 320 for testing on a RTX 2080Ti GPU. Results in average running time and parameters are presented in Table 3. It is obvious that our STRA has comparable FLOPS and running time with consideration of acceptable storage consumption to achieve promising video deblurring performance.

## 4.4 Ablation Study

To find out what contributes to the superior performance of our approach, we conducted ablation study to demonstrate the effectiveness of each component.

Effect of Events. We test the importance of events by training D2Net [Shang et al., 2021] and our STRA without events over the synthetic GoPro dataset, and the quantitative results are shown in Table 4, which shows that the frame-event-based Fusion Block GoPro HQF

� 27.81 25.03

� 29.04 25.94

28.50 25.38

29.73 27.54

Table 5: Quantitative ablation study on the two relation-aware blocks. We evaluate the effect of two blocks on PSNR values.

| Temporal Memory Block   | Spatial Fusion Block   |
|-------------------------|------------------------|
| �                       | �                      |
| ✓                       | �                      |
| �                       | ✓                      |
| ✓                       | ✓                      |

Res-unit # R = 4 R = 8 R = 12

28.02 28.51 28.73

29.29 29.73 29.11

28.71 29.08 29.45

Table 6: PSNR values on different parameter settings.

| Channel # Res-unit #   |   R = 4 |
|------------------------|---------|
| C = 16                 |   28.02 |
| C = 32                 |   29.29 |
| C = 48                 |   28.71 |

method has better performance than other baselines. Moreover, our STRA also achieves superior performance than STFAN in all baselines.

Effect of TMB and SFB. We validate the importance of temporal memory block by training STRA without neighboring correlation of events over the synthetic GoPro dataset, and there is a great performance gap of quantitative results

over two datasets in the first two rows of Table 5. It shows that temporal dependency between different events can efficiently improve the deblurring performance by 1.23 dB in GoPro dataset and 0.91 dB in HQF dataset.

We also test the effect of spatial fusion block in the same way, and results are shown in the first and third row in Table 5. Apparently, spatial fusion with events and frames achieves PSNR gains up to 0.69 dB and 0.35 dB on GoPro and HQF dataset, respectively. Most importantly, when both spatial fusion block and temporal memory block are embedded in STRA, we achieve even higher deblurring performance than inserting only one block.

Effect of the ResNet Depth. Note that in Figure 2, each res-block has several basic res-units, and the number of channels attaches importance to the performance of STRA. So we also evaluate the influence of the number of channels and res-units in STRA. Specifically, we set channel number C ∈ (16, 32, 48) and res-unit number R ∈ (4, 8, 12) . Table 6 shows the PSNR and SSIM performance in different settings. To achieve a good trade-off between efficiency and performance, we set C = 32 and R = 8 as the default setting.

## 4.5 Visualization

We first visualize some attention maps to see the representation of the spatial non-local operation between frames and events [Mou et al., 2021]. In Figures 5 (b), it is clear that similar brightness can contribute more to query patches, which demonstrates that our spatial fusion block can also present long-range spatial correlations to particular patches. 1

1 More results and visualizations can be found in the supplement.

Figure 5: Visualizations of similarity matrixes in the spatial and temporal blocks. Regions of query points are labeled with red and yellow cross. The similarity matrixes of query points are presented in the form of heat maps in (b) and (e). For illustration purpose, we present some greatly correlated neighbors (labeled with green boxes) in (c) and (f).

![Image](https://ijcai.org/proceedings/2022/fulltext/112/image_000016_824dff9a2f3c02a8ebfd38e4799e87ee0f750b8eb804b2bf94afd70e833394dd.png)

For temporal dependency between different events, we show some similarity matrixes with neighbor events in Figure 5 (e). One can see that regions of frequent brightness changes are more important for event patches, which illustrates that temporal connection between neighbor event sequences has been built in this way.

## 5 Conclusion

We proposed a new relation-aware network for event-driven video deblurring by rethinking the problem at both the spatial and temporal level. One advantage of this method over most deep-learning-based deblurring models is that we attach importance to the temporal correlation between different event sequences, and restore it continuously to achieve better deblurring performance in consecutive frames. While other event-driven deblurring models take a single frame and corresponding events as input with no consideration of high temporal information in events. On the other hand, our network calculates spatial consistency between events and frames by improving non-local operations to capture blurring contexts. Our network learns to reconstruct sharp edges by relying on sufficient temporal and spatial information in events to create high-quality frames. Both subjective and objective results on synthetic and real-world datasets have demonstrated the effectiveness of our proposed network.

## Acknowledgements

This work was supported by the National Key R&amp;D Program of China under Grant 2020AAA0105702, the National Natural Science Foundation of China (NSFC) under Grants U19B2038 and 61901433, the University Synergy Innovation Program of Anhui Province under Grants GXXT-2019-025, the Fundamental Research Funds for the Central Universities under Grant WK2100000024.

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