The proximal alternating iterative hard thresholding method for l0 minimization, with complexity O (1/√k)

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:311

Article

Yang, Fan¹  Shen, Yi¹  Liu, Zhi Song² 

[1] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310028, Zhejiang, Peoples R China

[2] Zhejiang Ocean Univ, Sch Math Phys & Informat Sci, Zhoushan 316004, Peoples R China

关键词: Sparse approximation;    Alternating minimization;    Hard thresholding;    Tight wavelet frame;    Kurdyka-Lojasiewicz property;   

DOI  :  10.1016/j.cam.2016.07.013

来源: Elsevier

【 摘 要 】

Since digital images are usually sparse in the wavelet frame domain, some nonconvex minimization models based on wavelet frame have been proposed and sparse approximations have been widely used in image restoration in recent years. Among them, the proximal alternating iterative hard thresholding method is proposed in this paper to solve the nonconvex model based on wavelet frame. Through combining the proposed algorithm with the iterative hard thresholding algorithm which is well studied in compressed sensing theory, this paper proves that the complexity of the proposed method is O (1 / root k). On the other hand, a more general nonconvex-nonsmooth model is adopted and the pseudo proximal alternating linearized minimization method is developed to solve the above problem. With the Kurdyka-Lojasiewicz (KL) property, it is proved that the sequence generated by the proposed algorithm converges to some critical points of the corresponding model. Finally, the proposed method is applied to restore the blurred noisy gray images. As the numerical results reveal, the performance of the proposed method is comparable or better than some well-known convex image restoration methods. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free