The locally stationary dual-tree complex wavelet model

Nelson, James; Gibberd, Alex; Naforniţa, Corina; Kingsbury, Nick

doi:10.1007/s11222-017-9784-0

Cited by 9 publications

(10 citation statements)

References 45 publications

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“…The transform scale in the DTCWT increases, as the size of the subbands decreases in octave steps, in accordance with classic wavelet transformations [13]. This gives each level a trade-off between resolution and redundancy.…”

Section: Lifting Dual Tree Complex Wavelet Transformmentioning

confidence: 64%

Lifting dual tree complex wavelets transform

Naimi

Adamou-Mitiche

Mitiche

2021

IJECE

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We describe the lifting dual tree complex wavelet transform (LDTCWT), a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). We describe a way to estimate the accuracy of this approximation and style appropriate filters to attain this. These benefits are often exploited among applications like denoising, segmentation, image fusion and compression. The results of applications shrinkage denoising demonstrate objective and subjective enhancements over the dual tree complex wavelet transform (DTCWT). The results of the shrinkage denoising example application indicate empirical and subjective enhancements over the DTCWT. The new transform with the DTCWT provide a trade-off between denoising computational competence of performance, and memory necessities. We tend to use the PSNR (peak signal to noise ratio) alongside the structural similarity index measure (SSIM) and the SSIM map to estimate denoised image quality.

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Section: Lifting Dual Tree Complex Wavelet Transformmentioning

confidence: 64%

Lifting dual tree complex wavelets transform

Naimi

Adamou-Mitiche

Mitiche

2021

IJECE

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“…This step mostly reduces the values of large-scale coefficients and re-distributes their energy to smaller scales. The theory was extended to the redundant DTCWT by Nelson et al (2018). Following Buschow et al (2019), any negative "energy" values introduced by the bias correction are set to zero.…”

Section: The Dual-tree Complex Wavelet Transformmentioning

confidence: 99%

SAD: Verifying the scale, anisotropy and direction of precipitation forecasts

Buschow

Friederichs

2021

Quart J Royal Meteoro Soc

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One important attribute of meteorological forecasts is their representation of spatial structures. While several existing verification methods explicitly measure a structure error, they mostly produce a single value with no simple interpretation. Extending a recently developed wavelet‐based verification method, this study separately evaluates the predicted spatial scale, orientation and degree of anisotropy. The scale component has been rigorously tested in previous work and is known to assess the quality of a forecast similar to other, established methods. However, directional aspects of spatial structure are less frequently considered in the verification literature. Since important weather phenomena related to fronts, coastlines and orography have distinctly anisotropic signatures, their representation in meteorological models is clearly of interest. The ability of the new wavelet approach to accurately evaluate directional properties is demonstrated using idealized and realistic test cases from the MesoVICT project. A comparison of precipitation forecasts from several forecasting systems reveals that errors in scale and direction can occur independently and should be treated as separate aspects of forecast quality. In a final step, we use the inverse wavelet transform to define a simple post‐processing algorithm that corrects the structural errors. The procedure improves visual similarity with the observations, as well as the objective scores.

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“…, J}, since we want to analyze the local degree of convective organization at each grid point. We denote the squared modulus of the corresponding complex coefficient as local spectral energy Nelson et al (2018) extended the theory of locally stationary wavelet processes (Eckley et al 2010) to the case of the DTCWT and formulated the necessary bias correction for the local energies, which removes unwanted overemphasis on the very large scales. The complete redundant DTCWT including the bias correction is implemented in the dualtrees R-package (Buschow et al 2020).…”

Section: A Dual-tree Complex Wavelet Transforms (Dtcwt)mentioning

confidence: 99%