Data-driven thresholding in denoising with Spectral Graph Wavelet Transform

Loynes, Basile de; Navarro, Fabien; Olivier, Baptiste

doi:10.1016/j.cam.2020.113319

Cited by 12 publications

(9 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to performing denoising through heat kernel smoothing (i.e., lowpass filtering), the proposed WM graphs can be used to implement graph-wavelet denoising, similar to that implemented by Behjat et al (2015) for GM graphs, using novel data-driven GSP denoising schemes ( de Loynes et al, 2021 ) in combination with computationally efficient multi-scale spectral graph decomposition methods ( Li et al, 2019c ; Shuman, 2020) that can be tractably implemented on large graphs.…”

Section: Discussionmentioning

confidence: 99%

Diffusion-informed spatial smoothing of fMRI data in white matter using spectral graph filters

et al. 2021

View full text Add to dashboard Cite

Brain activation mapping using functional magnetic resonance imaging (fMRI) has been extensively studied in brain gray matter (GM), whereas in large disregarded for probing white matter (WM). This unbalanced treatment has been in part due to controversies in relation to the nature of the blood oxygenation level-dependent (BOLD) contrast in WM and its detectability. However, an accumulating body of studies has provided solid evidence of the functional significance of the BOLD signal in WM and has revealed that it exhibits anisotropic spatiotemporal correlations and structure-specific fluctuations concomitant with those of the cortical BOLD signal. In this work, we present an anisotropic spatial filtering scheme for smoothing fMRI data in WM that accounts for known spatial constraints on the BOLD signal in WM. In particular, the spatial correlation structure of the BOLD signal in WM is highly anisotropic and closely linked to local axonal structure in terms of shape and orientation, suggesting that isotropic Gaussian filters conventionally used for smoothing fMRI data are inadequate for denoising the BOLD signal in WM. The fundamental element in the proposed method is a graph-based description of WM that encodes the underlying anisotropy observed across WM, derived from diffusion-weighted MRI data. Based on this representation, and leveraging graph signal processing principles, we design subject-specific spatial filters that adapt to a subject’s unique WM structure at each position in the WM that they are applied at. We use the proposed filters to spatially smooth fMRI data in WM, as an alternative to the conventional practice of using isotropic Gaussian filters. We test the proposed filtering approach on two sets of simulated phantoms, showcasing its greater sensitivity and specificity for the detection of slender anisotropic activations, compared to that achieved with isotropic Gaussian filters. We also present WM activation mapping results on the Human Connectome Project’s 100-unrelated subject dataset, across seven functional tasks, showing that the proposed method enables the detection of streamline-like activations within axonal bundles.

show abstract

Section: Discussionmentioning

confidence: 99%

Diffusion-informed spatial smoothing of fMRI data in white matter using spectral graph filters

et al. 2021

View full text Add to dashboard Cite

show abstract

“…From [11], SURE for a general thresholding process h : R n(J+1) → R n(J+1) is given by the following identity…”

Section: Monte-carlo Estimation Of Weightsmentioning

confidence: 99%

“…In a denoising context, SGWT has recently been adapted by [21] to form a tight frame using the Littlewood-Paley decomposition inspired by [9]. Based on SGWT, [11] proposed an automatic calibration of the threshold parameter by adapting Stein's unbiased risk estimate (SURE) for a noisy signal defined on a graph and decomposed in a given wavelet tight frame. Even if this selection criterion produces efficient estimators of the unknown mean squared error (MSE), the main limitation is the need for a complete eigendecomposition of the Laplacian matrix, making it intractable for large-scale graphs.…”

Section: Introductionmentioning

confidence: 99%

Large Graph Signal Denoising With Application to Differential Privacy

Chedemail

Loynes

Navarro³

et al. 2022

IEEE Trans. on Signal and Inf. Process. over Networks

Self Cite

View full text Add to dashboard Cite

Over the last decade, signal processing on graphs has become a very active area of research. Specifically, the number of applications, for instance in statistical or deep learning, using frames built from graphs, such as wavelets on graphs, has increased significantly. We consider in particular the case of signal denoising on graphs via a data-driven wavelet tight frame methodology. This adaptive approach is based on a threshold calibrated using Stein's unbiased risk estimate adapted to a tight-frame representation. We make it scalable to large graphs using Chebyshev-Jackson polynomial approximations, which allow fast computation of the wavelet coefficients, without the need to compute the Laplacian eigendecomposition. However, the overcomplete nature of the tight-frame, transforms a white noise into a correlated one. As a result, the covariance of the transformed noise appears in the divergence term of the SURE, thus requiring the computation and storage of the frame, which leads to an impractical calculation for large graphs. To estimate such covariance, we develop and analyze a Monte-Carlo strategy, based on the fast transformation of zero mean and unit variance random variables. This new data-driven denoising methodology finds a natural application in differential privacy. A comprehensive performance analysis is carried out on graphs of varying size, from real and simulated data.

show abstract

“…Wavelet analysis has been applied in the field of radio [72] (such as noise reduction for acoustic or video signals), meteorological [73][74][75] and hydrological information analysis [76,77]., image enhancement [78] and image fusion [79]. Hyperspectral images have a very high spectral resolution with hundreds of bands forming an approximately continuous spectral curve [80].…”

Section: Wavelet Analysismentioning

confidence: 99%

Assessment of Poplar Looper (Apocheima cinerarius Erschoff) Infestation on Euphrates (Populus euphratica) Using Time-Series MODIS NDVI Data Based on the Wavelet Transform and Discriminant Analysis

et al. 2021

View full text Add to dashboard Cite

Poplar looper (Apocheima cinerarius Erschoff) is a destructive insect infesting Euphrates or desert poplars (Populus euphratica) in Xinjiang, China. Since the late 1950s, it has been plaguing desert poplars in the Tarim Basin in Xinjiang and caused widespread damages. This paper presents an approach to the detection of poplar looper infestations on desert poplars and the assessment of the severity of the infestations using time-series MODIS NDVI data via the wavelet transform and discriminant analysis, using the middle and lower reaches of the Yerqiang River as a case study. We first applied the wavelet transform to the NDVI time series data in the period of 2009–2014 for the study area, which decomposed the data into a representation that shows detailed NDVI changes and trends as a function of time. This representation captures both intra- and inter-annual changes in the data, some of which characterise transient events. The decomposed components were then used to filter out details of the changes to create a smoothed NDVI time series that represent the phenology of healthy desert poplars. Next the subset of the original NDVI time series spanning the time period when the pest was active was extracted and added to the smoothed time series to generate a blended time series. The wavelet transform was applied again to decompose the blended time series to enhance and identify the changes in the data that may represent the signals of the pest infestations. Based on the amplitude of the enhanced pest infestation signals, a predictive model was developed via discriminant analysis to detect the pest infestation and assess its severity. The predictive model achieved a severity classification accuracy of 91.7% and 94.37% accuracy in detecting the time of the outbreak. The methodology presented in this paper provides a fast, precise, and practical method for monitoring pest outbreak in dense desert poplar forests, which can be used to support the surveillance and control of poplar looper infestations on desert poplars. It is of great significance to the conservation of the desert ecological environment.

show abstract

Data-driven thresholding in denoising with Spectral Graph Wavelet Transform

Cited by 12 publications

References 30 publications

Diffusion-informed spatial smoothing of fMRI data in white matter using spectral graph filters

Diffusion-informed spatial smoothing of fMRI data in white matter using spectral graph filters

Large Graph Signal Denoising With Application to Differential Privacy

Assessment of Poplar Looper (Apocheima cinerarius Erschoff) Infestation on Euphrates (Populus euphratica) Using Time-Series MODIS NDVI Data Based on the Wavelet Transform and Discriminant Analysis

Contact Info

Product

Resources

About