Bounded variation regularization using line sections. (English) Zbl 1183.68688
Summary: Based on a theorem that expresses the Bounded Variation (BV)-norm via the one-dimensional BV-norm restricted to a line, we find a representation of the higher-dimensional Rudin-Osher-Fatemi functional via one-dimensional ones. Moreover, we find a new representation of the dual norm and the dual functional. We use these results to propose optimization algorithms for the ROF-functional-an Uzawa algorithm and a dual projection algorithm-which only use one-dimensional minimization. Furthermore, the dual projection method can be used to find the orientation of textures in images.
MSC:
| 68U10 | Computing methodologies for image processing |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 49M29 | Numerical methods involving duality |
| 65K10 | Numerical optimization and variational techniques |
| 49Q15 | Geometric measure and integration theory, integral and normal currents in optimization |
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