Blind image deblurring via L1-regularized second-order gradient prior

作者：Liu, Jing; Tan, Jieqing^*; Zhang, Li; Zhu, Xingchen; Ge, Xianyu

来源：MULTIMEDIA TOOLS AND APPLICATIONS, 2022, 81(27): 39121-39144.

DOI：10.1007/s11042-022-13010-y

• Image deblurring
• Image restoration
• Deconvolution
• Kernel estimation
• The second-order gradient prior

The blind image deblurring is to find the underlying true image and the blur kernel from a blurred observation. This is a well-known ill-conditional problem in image processing field. To obtain a pleasant deblurred result, additional assumptions and prior knowledge are required. Proposed in this work is a simple and efficient blind image deblurring method which utilizes L-1-regularized second-order gradient prior. The inspiration for this work comes from the fact that the absolute values of the second-order gradient elements decrease with motion blur. This change is an essential feature of the motion blur process, and we demonstrate it mathematically in this paper. By enforcing the L-1 norm constraint to the term involving second-order gradients and incorporating it into the traditional deblurring framework, an effective optimization scheme is explored. The half-quadratic splitting technique is adopted to handle the non-convex minimum problem. Experimental results illustrate that our algorithm outperforms the state-of-art image deblurring algorithms in both benchmark datasets and ground-truth scenes. Besides, this algorithm is simple since it does not require any heuristic edge selection steps or involves too many nonlinear operators.