# An adaptive algorithm for TV-based model of three norms Lq(q=12,1,2) in image restoration

An adaptive algorithm for TV-based model of three norms Lq(q=12,1,2) in image restoration In this paper, we present an adaptive method for the TV-based model of three norms Lq(q=12,1,2) for the image restoration problem. The algorithm with the L2 norm is used in the smooth regions, where the value of |∇u| is small. The algorithm with the L12 norm is applied for the jumps, where the value of |∇u| is large. When the value of |∇u| is moderate, the algorithm with the L1 norm is employed. Thus, the three algorithms are applied for different regions of a given image such that the advantages of each algorithm are adopted. The numerical experiments demonstrate that our adaptive algorithm can not only keep the original edge and original detailed information but also weaken the staircase phenomenon in the restored images. Specifically, in contrast to the L1 norm as in the Rudin–Osher–Fatemi model, the L2 norm yields better results in the smooth and flat regions, and the L12 norm is more suitable in regions with strong discontinuities. Therefore, our adaptive algorithm is efficient and robust even for images with large noises. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

# An adaptive algorithm for TV-based model of three norms Lq(q=12,1,2) in image restoration

, Volume 329 – Jul 15, 2018
15 pages

Publisher
Elsevier
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.040
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we present an adaptive method for the TV-based model of three norms Lq(q=12,1,2) for the image restoration problem. The algorithm with the L2 norm is used in the smooth regions, where the value of |∇u| is small. The algorithm with the L12 norm is applied for the jumps, where the value of |∇u| is large. When the value of |∇u| is moderate, the algorithm with the L1 norm is employed. Thus, the three algorithms are applied for different regions of a given image such that the advantages of each algorithm are adopted. The numerical experiments demonstrate that our adaptive algorithm can not only keep the original edge and original detailed information but also weaken the staircase phenomenon in the restored images. Specifically, in contrast to the L1 norm as in the Rudin–Osher–Fatemi model, the L2 norm yields better results in the smooth and flat regions, and the L12 norm is more suitable in regions with strong discontinuities. Therefore, our adaptive algorithm is efficient and robust even for images with large noises.

### Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

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