# Infrared Image Deblurring via High-Order Total Variation and Lp-Pseudonorm Shrinkage  
[PERSON]  
1 College of Physics and Information Engineering, Fuzhou University, Fuzhou 350000, China; [EMAIL_ADDRESS]  
[PERSON]  
2 School of Physics and Information Engineering, Minnan Normal University, Zhangzhou 363000, China  
22  
group sparsity and Lp quasinorm model [5], and the quaternion fractional-order total variation with Lp quasinorm model [6]. The total variation (TV) [7] model is simple and effective for image deblurring. However, it assumes the images to be piecewise constants, thus resulting in staircase artifacts [8]. Several TV-based restoration methods have been proposed to address the issue of staircase artifacts. Generally, these extensions are mainly divided into two categories, local information-based TV extension and non-local based TV extension. The local information-based TV model relies on exploring the total variation in a limited local area. On the contrary, non-local information-based TV models explore patch similarity by searching in the entire image. Concerning local information-based TV extension, [PERSON] [9] proposed a new higher-order regularization for removing noise. [PERSON] et al., [10] proposed a non-convex hybrid TV (Hybrid TV) model by introducing high-order TV. Similarly, [PERSON] et al., [11] assumed the first-order and second-order gradients to be hyper-Laplacian distributions and proposed a constrained non-convex hybrid TV model for edge-preserving image restoration. Likewise, [PERSON] et al., [12] proposed an effective hybrid regularization model based on the second-order total generalized variation and wavelet frame. Recently, [PERSON] et al., [13] proved that non-convex regularizations can promote sparsity more effectively than convex regularizations. Thus, by considering non-convex tools for depicting sparsity, [PERSON] et al., [14] proposed blind image deblurring using the L0 gradient prior. [PERSON] et al., [15] proposed a weighted-l1-method noise regularization for image deblurring. Based on overlapping group sparsity, [PERSON] et al., [16], [PERSON] et al., [17], [PERSON] et al., [18, 19], [PERSON] et al., [20] and [PERSON] et al., [21] proposed image reconstruction schemes to further minimize staircase artifacts. [PERSON] et al., [22, 23] combined second-order non-convex TV and non-convex higher-order total variation with overlapping group sparse regularization to remove staircase artifacts. By taking advantage of neighbor information, [PERSON] et al., [24] proposed a four-directional TV denoising method. Combining the Lp-quasinorm shrinkage with four-directional TV, [PERSON] et al., [6] extended anisotropic total variation (ATV) to a quaternion fractional TV using the Lp-quasinorm (FTV4 Lp) model. The aforementioned models mainly rely on local image information. In contrast, by considering non-local information, [PERSON] et al., [25] used a non-local data fidelity term to build a denoising model. [PERSON] [26] adopted non-local TV models to regularize the solution to the image recovery optimization problem. [PERSON] et al., [27] combined the block-matching and 3D (BM3D) filtering with generalized TV to deblur images. By considering the similarity of nonlocal patches, [PERSON] et al., [28] proposed a block-matching TV regularization. The Lp-pseudonorm is an emerging tool that is used for depicting sparse variables and has been applied in several signal-processing applications. [PERSON] et al., [29] demonstrated that Lp shrinkage is superior to soft threshold shrinkage in recovering sparse signals. Recently, Lp shrinkage has been applied to numerous fields, for example, [PERSON] et al., [5] proposed a method using the Lp-quasinorm instead of the L1-norm for infrared image deblurring with the overlapping group sparse TV method. [PERSON] et al., [30] presented a sparse time-frequency representation model using the Lp-quasinorm constraint, this model is capable of fitting the sparsity prior to the frequency domain.