Nonparametric Blind Super-Resolution Using Adaptive Heavy-Tailed Priors

Abstract

Single-image nonparametric blind super-resolution is a fundamental image restoration problem yet largely ignored in the past decades among the computational photography and computer vision communities. An interesting phenomenon is observed that learning-based single-image super-resolution (SR) has been experiencing a rapid development since the boom of the sparse representation in 2005s and especially the representation learning in 2010s, wherein the high-res image is generally blurred by a supposed bicubic or Gaussian blur kernel. However, the parametric assumption on the form of blur kernels does not hold in most practical applications because in real low-res imaging a high-res image can undergo complex blur processes, e.g., Gaussian-shaped kernels of varying sizes, ellipse-shaped kernels of varying orientations, curvilinear kernels of varying trajectories. The paper is mainly motivated by one of our previous works: Shao and Elad (in: Zhang (ed) ICIG 2015, Part III, Lecture notes in computer science, Springer, Cham, 2015). Specifically, we take one step further in this paper and present a type of adaptive heavy-tailed image priors, which result in a new regularized formulation for nonparametric blind superresolution. The new image priors can be expressed and understood as a generalized integration of the normalized sparsity measure and relative total variation. Although it seems that the proposed priors are simple, the core merit of the priors is their practical capability for the challenging task of nonparametric blur kernel estimation for both super-resolution and deblurring. Harnessing the priors, a higher-quality intermediate high-res image becomes possible and therefore more accurate blur kernel estimation can be accomplished. A great many experiments are performed on both synthetic and real-world blurred low-res images, demonstrating the comparative or even superior performance of the proposed algorithm convincingly. Meanwhile, the proposed priors are demonstrated quite applicable to blind image deblurring which is a degenerated problem of nonparametric blind SR.

Blur Kernel Estimation and Non-Blind Super-Resolution for Power Equipment Infrared Images by Compressed Sensing and Adaptive Regularization

“…In order to make the experimental results more convincing, in addition to comparing our method with the classical blind SR method, we also design comparative experiments for the blur kernel estimation and non-blind SR reconstruction in our method. In the blind SR comparison experiment, we compared our method with the methods proposed by Keys [ 31 ], Shao [ 20 ], Michaeli [ 23 ], and Kim [ 22 ]. Since the actual infrared image of the power equipment did not have the original, clear HR image, we adopted two other objective evaluation indicators: average gradient (AG) and information entropy (IE).…”

“…In addition, in order to prove the effectiveness of the blur kernel estimation method in this paper, we compared the blur kernels estimated by our method and the algorithms proposed in [ 20 , 23 , 32 ]. We used the sum of the squared differences error (SSDE) to evaluate the accuracy of the estimated blur kernel: where represents the estimated blur kernel and represents the true blur kernel of the image.…”

“… Reconstruction results of different methods: ( a ) LR infrared image; ( b ) reconstruction results using the method in [ 31 ] (AG = 32.169; IE = 5.932); ( c ) reconstruction results using the method in [ 20 ] (AG = 35.921; IE = 5.991); ( d ) reconstruction results using the method in [ 23 ] (AG = 40.862; IE = 6.073); ( e ) reconstruction results using the method in [ 22 ] (AG = 38.910; IE = 6.040); ( f ) reconstruction results using our method (AG = 43.280; IE = 6.161). …”

“…However, the joint restoration of blur kernel and HR image is usually difficult, and it is easy to produce sub-optimal reconstruction results [ 19 ]. Therefore, there are few studies on blind SR methods [ 20 , 21 , 22 , 23 ]. Shao et al [ 20 ] proposed a non-parametric blind SR method based on an adaptive heavy-tail prior.…”

“…Therefore, there are few studies on blind SR methods [ 20 , 21 , 22 , 23 ]. Shao et al [ 20 ] proposed a non-parametric blind SR method based on an adaptive heavy-tail prior. Qian et al [ 21 ] proposed a blind SR restoration method based on frame-by-frame non-parametric blur estimation.…”