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2D Adaptive Filters : ウィキペディア英語版 | 2D Adaptive Filters A two-dimensional (2D) adaptive filter is very much like an 1-dimensional adaptive filter in the sense that it is a linear system whose parameters are adaptively updated throughout the process, according to some optimization approach. The main difference between 1D and 2D adaptive filters is that the former usually takes as inputs signals with respect to time, what implies in causality constraints, while the latter handles signals with 2 dimensions, like x-y coordinates in the space domain, which are usually non-causal. Moreover, just like 1D filters, most 2D adaptive filters are digital filters, because of the complex and iterative nature of the algorithms. ==Motivation==
The topic of 2D adaptive filters is very important in electrical engineering and signal processing since these filters have the ability to take into account the nonstationary statistical properties of 2D signals. Adaptive filters find applications in areas such as Noise cancellation, Signal prediction, Equalization and Echo cancellation. Examples of applications of 2D adaptive filters include Image Denoising,〔Abadi, M. Shams Esfand, and S. Nikbakht. "Image denoising with two-dimensional adaptive filter algorithms." Iranian Journal of Electrical & Electronic Engineering 7.2 (2011).〕 Motion Tracking,〔Trimeche, Mejdi. "Hierarchical Motion Estimation Using Recursive LMS Filters." (2007).〕 OFDM channel estimation,〔Hou, Xiaolin, et al. "On two-dimensional adaptive channel estimation in OFDM systems." Vehicular Technology Conference, 2004. VTC2004-Fall. 2004 IEEE 60th. Vol. 1. IEEE, 2004.〕 magnetic recording equalization 〔Kumar, P. Sarath, and Sumit Roy. "Two-dimensional equalization: Theory and applications to high density magnetic recording." Communications, IEEE Transactions on 42.234 (1994): 386-395.〕
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