Reconstruction of noisy signals by minimization of non-convex functionals |
| |
| Affiliation: | 1. Department of Atmospheric Science, Kongju National University, Shinkwan-dong, Kongju, Chungnam 314-701, South Korea;2. Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-0811, Japan;3. Physical Oceanography Division, Korea Institute of Ocean Science & Technology, Ansan 426-744, South Korea;4. Graduate School of Science, Kyoto University, Kyoto, Japan;1. Institute of Materials Physics, College of Science, Northeast Electric Power University, Jilin, Jilin 132012, China;2. State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130022, China;3. College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA |
| |
| Abstract: | Non-convex functionals have shown sharper results in signal reconstruction as compared to convex ones, although the existence of a minimum has not been established in general. This paper addresses the study of a general class of either convex or non-convex functionals for denoising signals which combines two general terms for fitting and smoothing purposes, respectively. The first one measures how close a signal is to the original noisy signal. The second term aims at removing noise while preserving some expected characteristics in the true signal such as edges and fine details. A theoretical proof of the existence of a minimum for functionals of this class is presented. The main merit of this result is to show the existence of minimizer for a large family of non-convex functionals. |
| |
| Keywords: | Non-convex functional Signal denoising Minimizer Calculus of variations |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
