We develop multicomponent AM--FM models for multidimensional signals. The analysis is cast in a general-dimensional framework where the component modulating functions are assumed to lie in certain Sobolev spaces. For both continuous and discrete 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 provide an automated method to repair broken, occluded oriented image textures. Our approach is based on partial differential equations (PDEs) and AM--FM image modeling. Reconstruction of the texture occurs via simultaneous PDE-generated diffusion and reaction. In the diffusion process, the image is adaptively smoothed, preserving important boundaries and features. The reaction process produces the reconstructed textural information in the occluded image regions. Gabor filters are designed and used in the reaction process using an AM--FM dominant component analysis. An AM--FM model of the texture image is constructed, making it possible to localize the reaction filters spatio--spectrally. In contrast to previous disocclusion techniques that depend on interpolation, on continuity of the connected components within the image level sets, or on texture estimation, the reaction--diffusion process proposed here yields a seamless transition between the recreated region and the unoccluded image regions. Using AM--FM dominant component analysis, we avoid the ad hoc parameter selection typified with other reaction--diffusion approaches. As a useful example, we focus on the repair of broken, occluded fingerprints. We also treat several exemplary natural textures to demonstrate the technique's generality.

We compute joint AM-FM models that characterize infrared targets and backgrounds in the modulation domain. We consider spatially localized structures within an IR image as sums of nonstationary, quasi-sinusoidal functions admitting locally narrowband amplitude and frequency modulations. By quantitatively estimating the modulations that dominate the signal spectrum on a spatially local basis, we obtain a new modulation domain feature vector that can augment the more traditional pixel domain, Fourier spectrum, and multispectral color features that have been used in IR target detection and tracking systems for a long time. Our preliminary studies, based primarily on midwave and longwave missile approach sequences, suggest that IR targets and backgrounds do typically possess sufficient spatially local modulated structure (i.e., texture) for modulation domain techniques to be meaningfully applied. We also present qualitative results strongly indicating that the modulation domain feature vector is a powerful tool for discriminating infrared targets and backgrounds.

From a perceptual view, audio signals are composed of low bandwidth and low frequency sub-processes, which modulate much higher carrier frequencies. • Modulation decomposition?

The decomposition of audio signals into perceptually meaningful modulation components is highly desirable for the development of new audio effects on the one hand and as a building block for future efficient audio compression algorithms on the other hand. In the past, there has always been a distinction between parametric coding methods and waveform coding: While waveform coding methods scale easily up to transparency (provided the necessary bit rate is available), parametric coding schemes are subjected to the limitations of the underlying source models. Otherwise, parametric methods usually offer a wealth of manipulation possibilities which can be exploited for application of audio effects, while waveform coding is strictly limited to the best as possible reproduction of the original signal. The analysis/synthesis approach presented in this paper is an attempt to show a way to bridge this gap by enabling a seamless transition between both approaches. 1.