We develop multicomponent AM-FM models for multidimensional signals. The analysis is cast in a general n-dimensional framework where the component modulating functions are assumed to lie in certain Sobolev spaces. For both continuous and discrete linear shift invariant (LSI) systems with AM-FM inputs, powerful new approximations are introduced that provide closed form expressions for the responses in terms of the input modulations. The approximation errors are bounded by generalized energy variances quantifying the localization of the filter impulse response and by Sobolev norms quantifying the smoothness of the modulations. The approximations are then used to develop novel spatially localized demodulation algorithms that estimate the AM and FM functions for multiple signal components simultaneously from the channel responses of a multiband linear filterbank used to isolate components. Two discrete computational paradigms are presented. Dominant component analysis estimates the locally dominant modulations in a signal, which are useful in a variety of machine vision applications, while channelized components analysis delivers a true multidimensional multicomponent signal representation. We demonstrate the techniques on several images of general interest in practical applications, and obtain reconstructions that establish the validity of characterizing images of this type as sums of locally narrowband modulated components.

We introduce a multidimensional quasi-eigenfunction approximation useful for characterizing and analyzing the responses of discrete linear systems to inputs modeled as AM-FM image functions. A new theorem is presented which provides a global bound on the approximation error. We demonstrate how the approximation may be used to develop discrete AM-FM demodulation algorithms, and show dramatic demodulation examples where the essential structure of natural images is captured using only a small number of AM-FM components.

We compute AM-FM representations for multicomponent, nonstationary images using a statistical component model. Components are isolated with a filterbank comprising frequency and orientation selective channels. The modulating functions for each component are estimated from the channel responses using localized nonlinear operators followed by optimal MMSE estimators. We also demonstrate reconstruction from the representation.

We present powerful multi-component AM-FM image models capable of efficiently representing complicated nonstationary multi-partite images, and show how the representation can be computed in a practical implementation. With images of this type, important structural and perceptual information is often manifest in the nonstationarities. Highly localized nonlinear operators are used to simultaneously estimate the amplitude and frequency modulating functions associated with each of the multiple components on a pixel-by-pixel basis. For the first time, we also demonstrate image reconstruction from the AM-FM representation.