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Non-linear multi-dimensional signal processing
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Non-linear multi-dimensional signal processing : ウィキペディア英語版
Non-linear multi-dimensional signal processing

== Nonlinear multi-dimensional signal processing ==
In signal processing, nonlinear multidimensional signal processing (NMSP) covers all signal processing using nonlinear multidimensional signals and systems. While nonlinear multidimensional signal processing is a subset of signal processing (multidimensional signal processing). Nonlinear multi-dimensional systems can be use in a broad range such as imaging,〔 teletraffic, communications, hydrology, geology, and economics. Nonlinear systems cannot be treated as linear system, using Fourier transformation and wavelet analysis. Nonlinear systems will have chaotic behavior, limit circle, steady state, bifurcation, multi-stability and so on. As the complicated of real nonlinear system, there didn't have canonical representation, like impulse response for linear systems.But there are some efforts to representation nonlinear system. Volterra and Wiener series using polynomial integral instead of linear convolution to representation nonlinear systems as the using of this methods naturally extended the signal into multi-dimensional. Empirical mode decomposition method using Hilbert transform instead of Fourier Transform apply to nonlinear multi-dimensional system. This method is an empirical method and directly apply to data sets. Multi-dimensional nonlinear filter (MDNF) is also an important part of NMSP, MDNF is always be used to filter noise in real data.There are nonlinear-type hybrid filters using in color image, Multidimensional nonlinear edge-preserving filter using in magnetic resonance image restoration. This filter using both temporal and spatial information combines the maximum likelihood estimate, spatial smoothing algorithm.

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