#### Huasong Chen, Qiansheng Feng, Hao Qiang, Yuanyuan Fan, Tingyu Sheng, An L1 image decomposition method based on framelet analysis prior with anisotropic total variation, Vol. 2022 (2022), Article ID 30, pp. 1-17

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DOI: 10.23952/jnfa.2022.30

Received August 11, 2021; Accepted June 22, 2022; Published July 26, 2022

Abstract Image decomposition is an important and challenging problem in image processing. This paper proposes an $L1$ cartoon-texture image decomposition method. To separate the cartoon, we use framelet analysis prior to regularize cartoon, and employ an anisotropic total variation to enhance the edges of the separated images while eliminate the annoying stair-casing often emerging in total variation based methods. In order to remove the high frequency part (such as noise and texture) in cartoon, a simple quadratic term is added in cartoon separation. The texture is then separated by using a common discrete cosine transform. Also, an $L1$ fidelity term is proposed to estimate the least absolute deviation between the ground truth and the measured images. An alternating Bregman algorithm is developed to solve the double-variable and multi-$L1$ minimization problem. The experiments show that the proposed method provides better image decomposition than other methods.

H. Chen, Q. Feng, H. Qiang, Y. Fan, T. Sheng, An $L1$ image decomposition method based on framelet analysis prior with anisotropic total variation, J. Nonlinear Funct. Anal. 2022 (2022) 30.