# Compression Reconstruction Network with Coordinated Self-Attention and Adaptive Gaussian Filtering Module

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## Abstract

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## 1. Introduction

- We propose a coordinated self-attention module (CSAM), which not only introduces information into the channel and the spatial domain but also captures the global information of the image, improving the network’s ability to capture long-range relationships for better imaging results.
- We propose an adaptive Gaussian filter sub-network in the frequency domain to make up for the defect of global average pooling in the CSAM. It can capture information on different frequency components of the image selectively when the measurement rate is changed.
- We propose a loss function with attention based on the traditional MSE-Loss (AMLoss) to match the gradient descent algorithm with the attention mechanism and focus more on the important parts of the image during optimization. Extensive experiments prove that the AMLoss can significantly improve the reconstruction quality.

## 2. Background and Related Work

#### 2.1. Deep Learning Based on Compressed Sensing Reconstruction

^{2}-Net based on the ReconNet, which once again improved the accuracy of the reconstructed images [17]. In 2018, S. Lohit et al. proposed a variant of the ReconNet that used an adversarial loss to further improve the reconstruction quality [21]. In 2020, Yang et al. proposed the ADMM-SCNet, which used traditional model-based compressed sensing methods and data to drive deep learning methods for reconstructing images from sparsely sampled measurements. The method achieves good reconstruction accuracy at fast computation speed [22]. In the same year, inspired by generative networks and attention mechanisms, Yuan et al. proposed a down-sampled MRI reconstruction method based on SARA-GAN. The method applies the relative average discriminator theory to make full use of prior knowledge. At the same time, adding the self-attention mechanism in the upper layers of the generator can overcome the problem of limited convolution kernel size [23]. In 2021, Zhang et al. proposed a deep learning system for attention-guided dual-layer image compression (AGDL), which advanced the state of the art in perceptual image compression [24]. In the same year, Barranca formulated a new framework for learning improved sampling paradigms for compressed sensing in a bio motivated manner, significantly improving the quality of signal reconstruction across multiple connection weight penalty schemes and signal classes [25].

#### 2.2. Attention

## 3. The Proposed Method

#### 3.1. Overall Network Framework

#### 3.2. Coordinated Self-Attention Module

**Context extraction**is used to collect relevant feature information from the feature map of the internal relationship of the image. We assume that the feature map obtained by the previous convolution block is $x\in {\mathbb{R}}^{C\times H\times W}$. We perform one-dimensional average pooling in two directions, so the outputs of the $c$-th channel at height $h$ and width $w$ are expressed as [34]

- $Conv1$ is a convolutional layer with a convolution kernel size of $1\times 1$,
- $\left[\xb7,\xb7\right]$ represents the connection operation along one dimension,
- ${z}^{h}\in {\mathbb{R}}^{C\times H\times 1}$ and ${z}^{w}\in {\mathbb{R}}^{C\times 1\times W}$ are the input feature maps,
- $\delta $ is the nonlinear activation function $ReLu$,
- $f\in {\mathbb{R}}^{C/r\times \left(H+W\right)\times 1}$ is the output feature map,
- $r$ is a reduction ratio to reduce the amount of computation.

**Transformation**aims to capture the channel and space dependencies and transform the extracted features on the nonlinear attention space to obtain the attention map ${z}_{f}$. The output ${z}_{f}$ can be expressed as [31]

**Fusion**aims to combine the obtained attention map with the feature map of the original convolutional block. According to (2) to (7), the process of aggregating global context features into features of each location can be expressed as

#### 3.3. Adaptive Gaussian Filter Sub-Networks

#### 3.4. AMLoss (Attention MSE Loss)

## 4. Experiments and Results

#### 4.1. Comparison of Different Attention Mechanism Modules

#### 4.2. Optimization Comparison of the AMLoss in Different Attention Mechanism Networks

#### 4.3. Comparison of Different Compressed Sensing Networks

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**ACRM structure diagram. It contains 2 fully connected layers, 4 CSAMs, 12 convolutional layers, and an adaptive Gaussian filter. Each CSAM module and 3 convolutions make up the ACR submodule. The kernel sizes and channels of the three convolutional layers from left to right are 11 × 11 × 64, 7 × 7 × 32, and 3 × 3 × 1, respectively. In addition to sequential connections between each module, there are skip connections. The grab module generates the corresponding important area mask matrix ${M}_{I}$ and unimportant area mask matrix ${M}_{U}$. Then, we multiply the $\widehat{y}$ and $y$ with the ${M}_{I}$ and ${M}_{U}$ to obtain ${y}^{\prime}$, ${y}^{\u2033}$, $\widehat{{y}^{\prime}}$, and $\widehat{{y}^{\u2033}}$. Finally, the AMLoss for backpropagation optimization is obtained.

**Figure 2.**CSAM structure diagram. The module contains three parts: context extraction, transformation, and fusion. Among them, “H Average Pooling” and “W Average Pooling” refer to 1D horizontal average pooling and 1D vertical average pooling, respectively. “ReLu” is the nonlinear activation function ReLu; “r” is a reduction ratio to reduce the amount of computation.

**Figure 3.**The structure diagram of BC-Net. It contains 2 fully connected layers and 8 convolutional layers. The 8 convolutional layers form 4 BC modules. In addition to the sequential connections between each module, there are skip connections. After the first convolutional layer of each module, the attention mechanism modules can be connected sequentially to form an attention-compressed sensing network.

**Figure 4.**(

**a**) Different attention mechanism algorithms test the PSNR of MNIST pictures at different measurement rates. (

**b**) Different attention mechanism algorithms test the PSNR of Fashion-MNIST pictures at different measurement rates.

**Figure 5.**Model images were reconstructed on the MNIST dataset, MR = 0.01. The top-down compressed sensing networks are (

**a**) BC + SE, (

**b**) BC + CBAM, (

**c**) BC + GC, (

**d**) BC + CA, and (

**e**) BC + CSAM.

**Figure 6.**(

**a**) PSNR of different algorithms at different measurement rates on the Fashion-MNIST dataset. (

**b**) Loss values of test images of different algorithms on the Fashion-MNIST dataset. (

**c**) PSNR of different algorithms at different measurement rates on the CelebA dataset. (

**d**) Loss values of test images of different algorithms on the CelebA dataset.

**Figure 7.**Model images are reconstructed on the CelebA dataset, MR = 0.1. From top to bottom are the (

**a**) original image, (

**b**) Recon-Net reconstructed image, (

**c**) DR2-Net reconstructed image, (

**d**) Bsr2-Net reconstructed image, and (

**e**) ACRM reconstructed image.

**Table 1.**PSNR and SSIM of algorithms embedded with different attention mechanisms on the MNIST dataset at different measurement rates.

Methods | MR = 0.1 | MR = 0.05 | MR = 0.03 | MR = 0.01 | MR = 0.005 | |||||
---|---|---|---|---|---|---|---|---|---|---|

PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | |

BC | 19.344 | 0.925 | 16.619 | 0.859 | 14.964 | 0.798 | 10.563 | 0.578 | 8.288 | 0.364 |

BC + SE | 19.591 | 0.932 | 16.894 | 0.882 | 15.195 | 0.821 | 10.332 | 0.561 | 8.412 | 0.381 |

BC + CBAM | 18.918 | 0.879 | 16.819 | 0.86 | 15.658 | 0.842 | 10.599 | 0.557 | 7.737 | 0.294 |

BC + GC | 21.091 | 0.953 | 18.043 | 0.912 | 15.652 | 0.844 | 10.679 | 0.584 | 8.499 | 0.382 |

BC + CA | 18.15 | 0.89 | 16.362 | 0.845 | 14.788 | 0.78 | 10.11 | 0.524 | 8.446 | 0.39 |

BC + CSAM | 21.448 | 0.953 | 18.199 | 0.92 | 15.836 | 0.856 | 10.789 | 0.595 | 8.592 | 0.416 |

**Table 2.**PSNR and SSIM of algorithms embedded with different attention mechanisms on the Fashion-MNIST dataset at different measurement rates.

Methods | MR = 0.1 | MR = 0.05 | MR = 0.03 | MR = 0.01 | MR = 0.005 | |||||
---|---|---|---|---|---|---|---|---|---|---|

PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | |

BC | 17.284 | 0.769 | 15.88 | 0.718 | 15.031 | 0.678 | 12.686 | 0.563 | 10.729 | 0.428 |

BC + SE | 17.412 | 0.782 | 15.857 | 0.723 | 14.947 | 0.685 | 12.584 | 0.551 | 10.493 | 0.409 |

BC + CBAM | 17.493 | 0.792 | 15.947 | 0.731 | 15.093 | 0.687 | 12.34 | 0.543 | 10.79 | 0.453 |

BC + GC | 17.481 | 0.787 | 16.053 | 0.729 | 15.137 | 0.689 | 12.653 | 0.568 | 10.665 | 0.42 |

BC + CA | 17.303 | 0.784 | 15.924 | 0.726 | 14.695 | 0.659 | 12.657 | 0.556 | 10.805 | 0.441 |

BC + CSAM | 17.636 | 0.791 | 16.151 | 0.739 | 15.183 | 0.689 | 12.885 | 0.656 | 10.821 | 0.45 |

Methods | MR = 0.1 | MR = 0.05 | MR = 0.03 | MR = 0.01 | MR = 0.005 | |||||
---|---|---|---|---|---|---|---|---|---|---|

PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | |

BC + CSAM | 17.636 | 0.791 | 16.151 | 0.739 | 15.183 | 0.689 | 12.885 | 0.656 | 10.821 | 0.45 |

BC + CSAM + AGF | 17.964 | 0.802 | 16.334 | 0.752 | 15.231 | 0.702 | 12.975 | 0.675 | 10.894 | 0.47 |

$\sigma =6$ | $\sigma =6$ | $\sigma =5$ | $\sigma =2.75$ | $\sigma =1$ |

**Table 4.**Performance comparison of the AMLoss and MSE-Loss acting on different attention compressed sensing networks in the MNIST dataset.

Methods | Loss | MR = 0.1 | MR = 0.05 | MR = 0.03 | MR = 0.01 | MR = 0.005 | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | ||

BC + SE | MSE-Loss | 19.591 | 0.932 | 16.894 | 0.882 | 15.195 | 0.821 | 10.332 | 0.561 | 8.412 | 0.381 |

AMLoss (2) | 20.814 | 0.943 | 17.601 | 0.894 | 15.223 | 0.821 | 10.503 | 0.564 | 8.529 | 0.382 | |

BC + CBAM | MSE-Loss | 18.918 | 0.879 | 16.819 | 0.86 | 15.658 | 0.842 | 10.599 | 0.557 | 7.737 | 0.294 |

AMLoss (1.1) | 21.042 | 0.953 | 17.512 | 0.894 | 15.824 | 0.845 | 10.721 | 0.559 | 8.32 | 0.404 | |

BC + GC | MSE-Loss | 21.091 | 0.953 | 18.043 | 0.912 | 15.652 | 0.844 | 10.679 | 0.584 | 8.499 | 0.382 |

AMLoss (1.2) | 21.210 | 0.955 | 18.244 | 0.92 | 15.739 | 0.845 | 10.758 | 0.588 | 8.553 | 0.386 | |

BC + CA | MSE-Loss | 18.15 | 0.89 | 16.362 | 0.845 | 14.788 | 0.78 | 10.11 | 0.524 | 8.446 | 0.39 |

AMLoss (1.2) | 20.395 | 0.944 | 17.6 | 0.909 | 15.042 | 0.822 | 10.24 | 0.571 | 8.521 | 0.41 | |

BC + CSAM | MSE-Loss | 21.448 | 0.953 | 18.199 | 0.92 | 15.836 | 0.856 | 10.789 | 0.595 | 8.592 | 0.416 |

AMLoss (1.15) | 22.182 | 0.959 | 18.485 | 0.931 | 16.12 | 0.86 | 10.847 | 0.605 | 8.646 | 0.418 |

**Table 5.**PSNR and SSIM of different algorithms are performed on the Fashion-MNIST dataset with different measurement rates.

Methods | MR = 0.1 | MR = 0.05 | MR = 0.03 | MR = 0.01 | ||||
---|---|---|---|---|---|---|---|---|

PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | |

Recon-Net | 17.601 | 0.796 | 15.039 | 0.693 | 14.37 | 0.639 | 12.094 | 0.519 |

DR2-Net | 17.784 | 0.804 | 15.956 | 0.72 | 15.046 | 0.683 | 12.741 | 0.56 |

Bsr2-Net | 17.885 | 0.796 | 16.304 | 0.749 | 15.357 | 0.695 | 13.261 | 0.598 |

ACRM (1.1) | 18.12 | 0.817 | 16.673 | 0.757 | 15.743 | 0.719 | 13.438 | 0.603 |

$\sigma =6$ | $\sigma =6$ | $\sigma =4.75$ | $\sigma =4$ |

**Table 6.**PSNR and SSIM of different algorithms are performed on the CelebA dataset with different measurement rates.

Methods | MR = 0.1 | MR = 0.05 | MR = 0.03 | MR = 0.01 | ||||
---|---|---|---|---|---|---|---|---|

PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | |

Recon-Net | 22.347 | 0.843 | 20.507 | 0.764 | 18.91 | 0.681 | 16.136 | 0.524 |

DR2-Net | 20.893 | 0.776 | 19.602 | 0.712 | 18.49 | 0.651 | 15.949 | 0.509 |

Bsr2-Net | 20.833 | 0.772 | 19.834 | 0.726 | 18.727 | 0.669 | 15.969 | 0.51 |

ACRM (1.2) | 22.38 | 0.843 | 20.543 | 0.767 | 19.027 | 0.69 | 16.188 | 0.535 |

$\sigma =7$ | $\sigma =6$ | $\sigma =5.75$ | $\sigma =2$ |

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**MDPI and ACS Style**

Wei, Z.; Yan, Q.; Lu, X.; Zheng, Y.; Sun, S.; Lin, J.
Compression Reconstruction Network with Coordinated Self-Attention and Adaptive Gaussian Filtering Module. *Mathematics* **2023**, *11*, 847.
https://doi.org/10.3390/math11040847

**AMA Style**

Wei Z, Yan Q, Lu X, Zheng Y, Sun S, Lin J.
Compression Reconstruction Network with Coordinated Self-Attention and Adaptive Gaussian Filtering Module. *Mathematics*. 2023; 11(4):847.
https://doi.org/10.3390/math11040847

**Chicago/Turabian Style**

Wei, Zhen, Qiurong Yan, Xiaoqiang Lu, Yongjian Zheng, Shida Sun, and Jian Lin.
2023. "Compression Reconstruction Network with Coordinated Self-Attention and Adaptive Gaussian Filtering Module" *Mathematics* 11, no. 4: 847.
https://doi.org/10.3390/math11040847