Fast Image Restoration Method Based on the L 0, L 1, and L 2 Gradient Minimization

Jin Wang, Qing Xia () and Binhu Xia
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Jin Wang: School of Humanities and Social Sciences, Xi’an Jiaotong University, Xi’an 710049, China
Qing Xia: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
Binhu Xia: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China

Mathematics, 2022, vol. 10, issue 17, 1-15

Abstract: In this paper, we propose a novel image denoising method by coupling with L 0 , L 1 and L 2 gradient minimization. Our proposed method smoothes the gradient difference between image pixels and noise pixels and sharpens the edges by increasing the steepness of transition. We focus on global noise processing rather than local features and adaptively process noise signals with different characteristics. Based on the half-quadratic splitting method, we perform a smoothing step realized by a Poisson approach and two edge-preserving steps through an optimization formulation. This iterative method is fast, simple, and easy to implement. The proposed numerical scheme can be performed to a discrete cosine transform implementation, which can be applied with parallel GPUs computing in a straightforward manner. Various tests are presented, including both qualitative and quantitative tests, to demonstrate that the proposed method is efficient and robust for producing image processing results with good quality.

Keywords: image restoration method; gradient minimization; soft threshold method; hard threshold method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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