Solving total-variation image super-resolution problems via proximal symmetric alternating direction methods

• Published in: Journal of inequalities and applications Vol. 2016; no. 1; pp. 1 - 18
• Main Authors: Gao, Bin, Sun, Fenggang, Tong, Ying, Xu, Shiming
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 15.08.2016; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Computational efficiency; Convergence; convex minimization; Exact solutions; Image resolution; Inequalities; linearized Peaceman-Rechford splitting method; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; proximal symmetric alternating direction method of multipliers; single image super-resolution; strictly contractive; Symmetry; single image super-resolution; proximal symmetric alternating direction method of multipliers; convex minimization; linearized Peaceman-Rechford splitting method; strictly contractive
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-016-1136-7

The single image super-resolution (SISR) problem represents a class of efficient models appealing in many computer vision applications. In this paper, we focus on designing a proximal symmetric alternating direction method of multipliers (SADMM) for the SISR problem. By taking full exploitation of the special structure, the method enjoys the advantage of being easily implementable by linearizing the quadratic term of subproblems in the SISR problem. With this linearization, the resulting subproblems easily achieve closed-form solutions. A global convergence result is established for the proposed method. Preliminary numerical results demonstrate that the proposed method is efficient and the computing time is saved by nearly 40% compared with several state-of-the-art methods.