## 3 Results and Discussion  
The IR test images used in the experiment were downloaded from the publicly available datasets found at [[http://adas.cvc.uab.es/elektra/datasets/far-infra-red/](http://adas.cvc.uab.es/elektra/datasets/far-infra-red/)]([http://adas.cvc.uab.es/elektra/datasets/far-infra-red/](http://adas.cvc.uab.es/elektra/datasets/far-infra-red/)) (accessed on 5 January 2022) and [[http://www.dgp.toronto.edu/](http://www.dgp.toronto.edu/)]([http://www.dgp.toronto.edu/](http://www.dgp.toronto.edu/))\(\sim\backslash\backslash\backslash\backslash\)nmorris/data/IRData/ (accessed on 5 January 2022). This study evaluated the quality of the denoised images from subjective and objective aspects. The objective evaluation metrics used in this study are PSNR, SSIM, and GMSD, which are defined using Equations (30)-(32), respectively:  
\[\text{PSNR}=10\log_{10}(\frac{255^{2}}{\frac{1}{MN}\sum\limits_{i=1}^{M}\sum \limits_{j=1}^{N}\left\|\mathbf{x}_{ij}-y_{ij}\right\|_{1}^{2}})\quad(\text{dB}), \tag{30}\]  
\[\text{SSIM}=\frac{\left(2u_{X}u_{Y}+\left(255k_{1}\right)^{2}\right)\left(2 \sigma_{XY}+\left(255k_{2}\right)^{2}\right)}{\left(u_{X}^{2}+u_{Y}^{2}+\left( 255k_{1}\right)^{2}\right)\left(\sigma_{X}^{2}+\sigma_{Y}^{2}+\left(255k_{2} \right)^{2}\right)}, \tag{31}\]where \(\mathbf{X}\) and \(\mathbf{Y}\) are the original and the restored image, respectively. \(u_{X}\) and \(u_{Y}\) represent the mean values of \(\mathbf{X}\) and \(\mathbf{Y}\), respectively. \(\sigma_{X}^{2}\) and \(\sigma_{Y}^{2}\) represent the variances of \(\mathbf{X}\) and \(\mathbf{Y}\), respectively. \(\sigma_{XY}\) represents the covariance of \(\mathbf{X}\) and \(\mathbf{Y}\). \(k_{1}\) and \(k_{2}\) are constants to ensure that SSIM is not zero.  
\[\text{GMSD}=\sqrt{\frac{1}{MN}\sum_{i=1}^{M}\sum_{j=1}^{N}\left\{\left[\text{ GMS}\right]_{i,j}-\frac{1}{MN}\sum_{i=1}^{M}\sum_{j=1}^{N}\left[\text{GMS} \right]_{i,j}\right\}^{2}}, \tag{32}\]  
where  
\[\left[\text{GMS}\right]_{i,j}=\frac{2\left[\mathbf{m_{X}}\right]_{i,j}\left[\mathbf{m _{Y}}\right]_{i,j}+c}{\left[\mathbf{m_{X}}\right]_{i,j}^{2}+\left[\mathbf{m_{Y}} \right]_{i,j}^{2}+c}. \tag{33}\]  
where \(c\) is a constant to ensure that the denominator is a non-zero number. \(\left[\mathbf{m_{X}}\right]_{i,j}\) and \(\left[\mathbf{m_{Y}}\right]_{i,j}\) refer to the gradient amplitude of the image in the horizontal and vertical directions, respectively.  
Larger PSNR, closer-to-1 SSIM, and smaller GMSD values indicate better deblurring performance.  
The variable parameters were preset before the experiment to focus on PSNR optimization before optimizing SSIM and GMSD. The variable parameters of the Lp_HOGS model were set as follows:  
The maximum number of iterations and the learning rate \(\gamma\) were set to 500 and 0.618, respectively.  
For each model, the balance coefficient \(\mu_{j}(j=1,2,\cdots,5)\), the quadratic penalty coefficient \(\beta_{i}(i=0,1,\cdots,5)\), and the Lp-pseudo-norm \(p\) were manually optimized to achieve the best deblurring effect on the IR image and ensure a fair experiment.  
A sensitivity experiment analysis revealed that \(K\) was essential and the image quality indicators were optimal when \(K=3\) was the size of the matrix. The structured information of the image could not be fully mined if the value of \(K\) was insignificant. Conversely, unstructured information could be introduced if the value was excessively large.