Marshall S., Sicuranza G.L. Advances in Nonlinear Signal and Image
Processing.
Издательство Hindawi, 2006, 367 c.
n recent years the area of nonlinear signal and image processing has emerged as a distinct research field in its own right. It has formed from a fusion of techniques which, whilst coming from very different sources, share many characteristics. These techniques have appeared for two main reasons:
(i) the availability of high-powered computing at modest cost which can allow many operations to be carried out in real time or near real time,
(ii) the emergence of new applications requiring complex solutions for which classical linear techniques simply do not work.
Whilst linear techniques have many advantages, they mainly arise in a mathematical framework based on orthogonal spaces. The problem is tackled by mapping the data into lower-order spaces. For example, in Fourier analysis the modeling of both signals and systems by a summation of complex sinusoids leads to an elegant analysis with all cross-terms conveniently vanishing from the calculation. Filters can in effect be designed one frequency at a time. Such powerful superposition properties result in neat closed-form solutions of optimal filters. In many branches of engineering, from circuit analysis to audio processing, these techniques have worked well. In transient and discrete systems, Laplace and z transforms have proved to be similarly invaluable. However, solutions are limited to those based on superposition of sinusoids. Relaxation of this constraint is the basis of nonlinear signal and image processing. It can lead to better solutions to problems at the price of increased mathematical complexity, particularly in operator design.
Nonstationary stochastic differential equations.
Aperture filters: theory, application, and multiresolution analysis.
Finite-set signal processing.
Nonlinear signal modeling and structure selection with applications to genomics.
Nonlinear methods for speech analysis and synthesis.
Communication system nonlinearities: challenges and some solutions.
Nonlinear multichannel active noise control.
Chaotic sequences for digital watermarking.
Modeling of evolving textures using granulometries.
Multichannel weighted medians.
Color image processing: problems, progress, and perspectives.
Nonlinear edge detection in color image.
Издательство Hindawi, 2006, 367 c.
n recent years the area of nonlinear signal and image processing has emerged as a distinct research field in its own right. It has formed from a fusion of techniques which, whilst coming from very different sources, share many characteristics. These techniques have appeared for two main reasons:
(i) the availability of high-powered computing at modest cost which can allow many operations to be carried out in real time or near real time,
(ii) the emergence of new applications requiring complex solutions for which classical linear techniques simply do not work.
Whilst linear techniques have many advantages, they mainly arise in a mathematical framework based on orthogonal spaces. The problem is tackled by mapping the data into lower-order spaces. For example, in Fourier analysis the modeling of both signals and systems by a summation of complex sinusoids leads to an elegant analysis with all cross-terms conveniently vanishing from the calculation. Filters can in effect be designed one frequency at a time. Such powerful superposition properties result in neat closed-form solutions of optimal filters. In many branches of engineering, from circuit analysis to audio processing, these techniques have worked well. In transient and discrete systems, Laplace and z transforms have proved to be similarly invaluable. However, solutions are limited to those based on superposition of sinusoids. Relaxation of this constraint is the basis of nonlinear signal and image processing. It can lead to better solutions to problems at the price of increased mathematical complexity, particularly in operator design.
Nonstationary stochastic differential equations.
Aperture filters: theory, application, and multiresolution analysis.
Finite-set signal processing.
Nonlinear signal modeling and structure selection with applications to genomics.
Nonlinear methods for speech analysis and synthesis.
Communication system nonlinearities: challenges and some solutions.
Nonlinear multichannel active noise control.
Chaotic sequences for digital watermarking.
Modeling of evolving textures using granulometries.
Multichannel weighted medians.
Color image processing: problems, progress, and perspectives.
Nonlinear edge detection in color image.