An overview of image restoration based on variational regularization

doi:10.3868/s140-DDD-024-0010-x

Front. Math. China

2024, Vol. 19

Issue (3) : 157-180 https://doi.org/10.3868/s140-DDD-024-0010-x

An overview of image restoration based on variational regularization

Qibin FAN(

), Yuling JIAO

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

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Abstract

Image restoration is a complicated process in which the original information can be recovered from the degraded image model caused by lots of factors. Mathematically, image restoration problems are ill-posed inverse problems. In this paper image restoration models and algorithms based on variational regularization are surveyed. First, we review and analyze the typical models for denoising, deblurring and inpainting. Second, we construct a unified restoration model based on variational regularization and summarize the typical numerical methods for the model. At last, we point out eight diffcult problems which remain open in this field.

Keywords Regularization image restoration inverse problem total variation wavelet

Corresponding Author(s): Qibin FAN

Online First Date: 18 June 2024 Issue Date: 01 July 2024

Cite this article:

Qibin FAN,Yuling JIAO. An overview of image restoration based on variational regularization[J]. Front. Math. China, 2024, 19(3): 157-180.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-024-0010-x
https://academic.hep.com.cn/fmc/EN/Y2024/V19/I3/157

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