Guo, Xiaoxia; Li, Fang; Ng, Michael K. A fast \(\ell_1\)-TV algorithm for image restoration. (English) Zbl 1191.65029 SIAM J. Sci. Comput. 31, No. 3, 2322-2341 (2009). Summary: Image restoration problems are often solved by finding the minimizer of a suitable objective function consisting of a data-fitting term and a regularization term. In this paper, we consider the data-fitting term measured in the \(\ell_1\) norm to handle non-Gaussian additive noise and the regularization term given by the total variation (TV) to restore image edges. We propose a new algorithm for this image restoration problem by making use of new variables to modify the data-fitting term and the TV regularization term. An alternating minimization method based on the new formulation is employed to restore blurred and noisy images. Our experimental results show that the quality of restored images by the proposed method is competitive with those restored by the other tested methods. We also show the convergence of the alternating minimization algorithm and demonstrate that the proposed algorithm is very efficient. Cited in 1 ReviewCited in 25 Documents MSC: 65F10 Iterative numerical methods for linear systems 65F22 Ill-posedness and regularization problems in numerical linear algebra 68U10 Computing methodologies for image processing Keywords:iterative algorithm; image restoration; deblurring; denoising; \(\ell_1\) norm; total variation PDFBibTeX XMLCite \textit{X. Guo} et al., SIAM J. Sci. Comput. 31, No. 3, 2322--2341 (2009; Zbl 1191.65029) Full Text: DOI