A New Implementation of the Hyperanalytic Wavelet Transform

Adam, Ipam Fuaddina; Naforniţa, Corina; Boucher, Jean‐Marc; Isar, Alexandru

doi:10.1109/isscs.2007.4292747

Cited by 13 publications

(7 citation statements)

References 15 publications

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“…It means that the DTCWT requires special mother wavelet function. To overcome this restraint, in [7], Firoiu has proposed a new shift invariant called HWT using Hilbert transform and a two-stage mapping-based complex wavelet transform (MBCWT) in soft space [9]. And she also gives the proof that HWT is equivalent to DTCWT.…”

Section: Hyperanalytic Shearlet Transformmentioning

confidence: 99%

“…This construction not only greatly increases the redundancy of the transform but also slows down the calculation sharply. From [7], we can know that hyperanalytic wavelet (HWT) just has limited redundancy to achieve multi-scale decomposition without shift sensitivity, which is similar to dual tree complex wavelet (DTCWT), but differently, this method is more easily achievable than dual tree complex wavelet. And the construction of hyperanalytic wavelet also greatly accelerates the computation.…”

Section: Introductionmentioning

confidence: 99%

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Apply hyperanalytic shearlet transform to geometric separation

Liu

Shi

et al. 2014

EURASIP J. Adv. Signal Process.

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This paper first proposes a novel image separation method based on the hyperanalytic shearlet. By combining the advantages of both the hyperanalytic wavelet transform and the shear operation, hyperanalytic shearlet is easy to implement and also has a low redundancy. By using such transform and the orthonormal wavelet, a new geometric separation dictionary is obtained which can sparsely represent points and curviline singularities, respectively. In order to get the different components of image faster and more accurate, a fast alternating direction method (FADM) is used to train the dictionary. Our algorithm can greatly improve the computational efficiency without causing damage to the accuracy of image separation. Furthermore, a proper measure to evaluate the separation performance called sep-degree is defined. The experimental results have demonstrated the proposed method's effectiveness and superiority.

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Section: Hyperanalytic Shearlet Transformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Apply hyperanalytic shearlet transform to geometric separation

Liu

Shi

et al. 2014

EURASIP J. Adv. Signal Process.

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“…The magnitude information returned by AWT describes the envelopes of signals which can be used for time-frequency analysis. The phase information encodes the time related characteristics of signals, for applications such as instantaneous frequency estimation [4].…”

Section: Analytic Wavelet Transform (Awt)mentioning

confidence: 99%

Atmospheric Radar Signal Processing using Complex Wavelet Transforms

Rani¹,

Varadarajan²,

Sadasiva³

2014

IJCA

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“…These disadvantages can be diminished using a complex wavelet transform (Kingsbury, 2000(Kingsbury, , 2001. A very simple implementation of the Hyperanalytic Wavelet Transform, (HWT), recently proposed (Adam et al, 2007) has a high shift0invariance degree versus other quasi0shift0 invariant wavelet transforms (WT) at same redundancy. It has also an enhanced directional selectivity.…”

mentioning

confidence: 99%

“…Another appealing particularity of those transforms, coming from their multiresolution capability, is the interscale dependency of the wavelet coefficients. We present in the next paragraphs a new implementation of HWT (Adam et al, 2007) and its application to watermarking . The watermark capacity was studied in Moulin & Mihcak, 2002, where an information0theoretic model for image watermarking and data hiding is presented.…”

mentioning

confidence: 99%