Image analysis using a dual-tree M-band wavelet transform

Chaux, Caroline; Duval, Laurent; Pesquet, Jean-Christophe

doi:10.1109/tip.2006.875178

Cited by 116 publications

(112 citation statements)

References 35 publications

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“…This idea can be pushed further. Other bases are possible such as the M-band extension of the dual-tree wavelets constructed by Chaux et al (2006), wavelet packets schemes such as Bayram and Selesnick (2008), and mixtures of wavelets such as Nelson (2015). Although these constructions offer useful additional functionality, their statistically properties have yet to be explored.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

The locally stationary dual-tree complex wavelet model

et al. 2017

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We here harmonise two significant contributions to the field of wavelet analysis in the past two decades, namely the locally stationary wavelet process and the family of dualtree complex wavelets. By combining these two components, we furnish a statistical model that can simultaneously access benefits from these two constructions. On the one hand, our model borrows the debiased spectrum and auto-covariance estimator from the locally stationary wavelet model. On the other hand, the enhanced directional selectivity is obtained from the dual-tree complex wavelets over the regular lattice. The resulting model allows for the description and identification of wavelet fields with significantly more directional fidelity than was previously possible. The corresponding estimation theory is established for the new model, and some stationarity detection experiments illustrate its practicality.

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Section: Conclusion and Further Workmentioning

confidence: 99%

The locally stationary dual-tree complex wavelet model

et al. 2017

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“…Denoising with wavelet transforms basically consists in cancelling noise related coefficients, while retaining contour information to prevent image over-smoothing, as proposed in [15]. In this work, we have used a slightly more efficient decomposition, called the dual-tree wavelet transform [16], which yields state-of-the-art performance for multichannel and especially colour image denoising [17]. …”

Section: Intake Valves Exhaust Valvesmentioning

confidence: 99%

Development of Specific Tools for Analysis and Quantification of Pre-ignition in a Boosted SI Engine

Zaccardi¹,

Duval²,

Pagot³

2009

SAE Int. J. Engines

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Recent developments on highly downsized spark ignition engines have been focused on knocking behaviour improvement and the most advanced technologies combination can face up to 2.5 MPa IMEP while maintaining acceptable fuel consumption. Unfortunately, knocking is not the only limit that strongly downsized engines have to confront. The improvement of low-end torque is limited by another abnormal combustion which appears as a random pre-ignition. This violent phenomenon which emits a sharp metallic noise is unacceptable even on modern supercharged gasoline engines because of the great pressure rise that it causes in the cylinder (up to 20 MPa).The phases of this abnormal combustion have been analysed and a global mechanism has been identified consisting of a local ignition before the spark, followed by a propagating phase and ended by a massive autoignition. This last step finally causes a steep pressure rise and pressure oscillations.One of our objectives was to evaluate the sensitivity of an engine to pre-ignition regarding its design and settings. Therefore, in addition to our comprehension work, we have developed a first methodology based upon robust statistics to define new reliable and repeatable criteria to quantify this stochastic pre-ignition but also to detect each of its occurrence, suggesting the possibility of an on-line detection during steady state and transient operation as well. The statistical approach also showed that the distributions of well chosen combustion indicators are strongly altered by pre-ignitions. A second methodology was then defined to evaluate the influence of different parameters on pre-ignition by quantifying this alteration. This analysis notably gives the opportunity to achieve a deeper analysis of pre-ignition during engine development on test bench.

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“…The design of dual-tree filters is addressed through a Hilbert pair formulation for the "dual" wavelets. Generalizations to 2D dual-tree M-band wavelet decompositions, proposed in [ChDuPe06], are briefly reviewed in the next section.…”

Section: Background Workmentioning

confidence: 99%

“…(1) Figure 2 shows the 1D basis functions obtained [ChDuPe06] with M = 8 bands. The primal and dual wavelets are in quadrature, as can be seen from their pairwise symmetry/antisymmetry.…”

Section: M-band Wavelets and Hilbert Pairsmentioning

confidence: 99%

Seismic data analysis with dual-tree M-band wavelet transforms

Duval¹,

Chaux²,

Ker³

2007

69th EAGE Conference and Exhibition - Workshop Package

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SummaryThe complexity of seismic data still challenges signal processing algorithms in several applications. The rediscovery of wavelet transforms by J. Morlet et al. has allowed improvements in addressing several data representation (local analysis, compression) and restoration problems. However, despites their achievements, traditional approaches based on discrete and separable (both for computational purposes) wavelets fail at efficiently representing directional or higher dimensional data features, such as line or plane singularities, especially in severe noise conditions. Subsequent extensions to wavelets (multiscale pyramids, curvelets [YaTrHe04][Do06], contourlets, bandlets) have recently generated tremendous theoretical and practical interests. They feature local and multiscale properties associated with a certain amount of redundancy, which may represent an issue for huge datasets processing.We propose here seismic data processing based on dual-tree M-band wavelet transforms [ChDuPe06]. They combine:• orthogonal M-band filter banks which better separate frequency bands in seismic data than wavelets, due to the increased degrees of freedom in the filter design,• Hilbert transform and complex representation of seismic signals which have been effective, especially for attributes definition, with a relatively low redundancy (a factor of two). These transforms have been successfully applied to random noise removal in traditional and remote sensing imagery.We apply them to seismic data and address their potential for local slope analysis and coherent noise (ground-roll) filtering.

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Image analysis using a dual-tree M-band wavelet transform

Cited by 116 publications

References 35 publications

The locally stationary dual-tree complex wavelet model

The locally stationary dual-tree complex wavelet model

Development of Specific Tools for Analysis and Quantification of Pre-ignition in a Boosted SI Engine

Seismic data analysis with dual-tree M-band wavelet transforms

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