The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of AM–FM images

Clausel, Marianne; Oberlin, Thomas; Perrier, Valérie

doi:10.1016/j.acha.2014.10.003

Cited by 27 publications

(16 citation statements)

References 44 publications

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“…The disadvantage of such solution is first to require the whole knowledge of the 2D function, then to use a nonlocal filter. In image processing or for video applications, the Riesz transform is often applied on some bandpass filtered version of the image (by wavelets or pyramid decomposition), leading to approximate and faster implementations, even in the physical space [21,22,4]. Alternative approaches involve the Radon transform.…”

Section: Introductionmentioning

confidence: 99%

“…The Riesz transform is also the way to construct the monogenic signal in several dimensions, which is the natural extension of the one dimensional analytic signal [9,7,8]. The monogenic signal, as well as the Riesz transform, have many applications in image processing or computer vision, like the demodulation of 2D fringe patterns [11], the extraction of local features in 2D signals [23,16,21,10,4], the demodulation of holograms [17], or the analysis of color images [19].…”

Section: Introductionmentioning

confidence: 99%

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On locality of Radon to Riesz transform

Desbat

Perrier

2016

Signal Processing

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On locality of Radon to Riesz transform

Desbat

Perrier

2016

Signal Processing

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“…Finally, our results should also be compared against the results obtained with the 2D Prony-Huang transform reported in [60], 9 and partially reproduced in Fig. 3.…”

Section: Synthetic Overlapping Texture Decompositionmentioning

confidence: 99%

“…All these methods, however, are not adaptive relative to the signal, and can attribute principal components of the image to different bands, as well as contain several different image components in the same band. Adaptivity and tuned sparsity concerns have been addressed through synchrosqueezed wavelet transforms [9,14,72,74], where unimportant wavelet coefficients are removed by thresholding based on energy content. In pursuit of the same goal, the 2D empirical wavelet transform (EWT) [29,30] decomposes an image by creating a more adaptive wavelet basis.…”

Section: Recent and Related Workmentioning

confidence: 99%

Two-Dimensional Compact Variational Mode Decomposition

et al. 2017

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Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis. This decomposition enables space-frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting, or curvature estimation. Our model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image recomposition. L 1 and TV terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function, we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman-Bence-Osher-like threshold dynamics to handle efficiently the motion by mean curvature of the support function boundaries under the sparsity promoting terms. The versatility and effectiveness of our proposed model is demonstrated on a broad variety of example images from different modalities. These demonstrations include the decomposition of images into overlapping modes with smooth or sharp boundaries, segmentation of images of crystal grains, and inpainting of damaged image regions through artifact detection.

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“…Recently, this framework has been extended to the case of superimposed patterns. An extension of the synchrosqueezing method to the bidimensionnal setting, based on wavelet analysis, has been proposed in [7].…”

Section: Introductionmentioning

confidence: 99%

Riesz-based orientation of localizable Gaussian fields

Polisano

Clausel

Perrier

et al. 2021

Applied and Computational Harmonic Analysis

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In this work we give a sense to the notion of orientation for self-similar Gaussian fields with stationary increments, based on a Riesz analysis of these fields, with isotropic zero-mean analysis functions. We propose a structure tensor formulation and provide an intrinsic definition of the orientation vector as eigenvector of this tensor. That is, we show that the orientation vector does not depend on the analysis function, but only on the anisotropy encoded in the spectral density of the field. Then, we generalize this definition to a larger class of random fields called localizable Gaussian fields, whose orientation is derived from the orientation of their tangent fields. Two classes of Gaussian models with prescribed orientation are studied in the light of these new analysis tools.such that for any x, y ∈ R 2 , the covariance reads:The measure σ X is called the spectral measure of the Gaussian field with stationary increments X.

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The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of AM–FM images

Cited by 27 publications

References 44 publications

On locality of Radon to Riesz transform

On locality of Radon to Riesz transform

Two-Dimensional Compact Variational Mode Decomposition

Riesz-based orientation of localizable Gaussian fields

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