Orthogonal Hilbert transform filter banks and wavelets

Spaendonck, R. van; Blu, Thierry; Baraniuk, Richard G.; Vetterli, Martin

doi:10.1109/icassp.2003.1201729

Cited by 25 publications

(19 citation statements)

References 6 publications

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“…The first seeks a ψ c (t ) that forms an orthonormal or biorthogonal basis [9], [11], [37], [64], [108], [114]. As we show below, this strong constraint prevents the resulting CWT from overcoming most of the four DWT shortcomings outlined above.…”

Section: One Solution: Complex Waveletsmentioning

confidence: 99%

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The dual-tree complex wavelet transform

Selesnick

Baraniuk

Kingsbury³

2005

IEEE Signal Process. Mag.

2,178

1,202

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[ A coherent framework for multiscale signal and image processing ] T he dual-tree complex wavelet transform (CWT) is a relatively recent enhancement to the discrete wavelet transform (DWT), with important additional properties: It is nearly shift invariant and directionally selective in two and higher dimensions. It achieves this with a redundancy factor of only 2 d for d-dimensional signals, which is substantially lower than the undecimated DWT. The multidimensional (M-D) dual-tree CWT is nonseparable but is based on a computationally efficient, separable filter bank (FB). This tutorial discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing. We use the complex number symbol C in CWT to avoid confusion with the often-used acronym CWT for the (different) continuous wavelet transform. BACKGROUNDThis article aims to reach two different audiences. The first is the wavelet community, many members of which are unfamiliar with the utility, convenience, and unique properties of complex wavelets. The second is the broader class of signal processing folk who work with applications where the DWT has proven somewhat disappointing, such as those involving complex or modulat-

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Section: One Solution: Complex Waveletsmentioning

confidence: 99%

“…A natural and straightforward approach towards an invertible analytic CWT splits each output of the FB [see Figure 24(a)] into its positive and negative frequency components using a complex PR FB acting as a Hilbert transformer [9], [36]- [39], [108], [109], [114]. But this approach turns out to have a basic limitation.…”

Section: Cwt Via Dwt Post-processingmentioning

confidence: 99%

The dual-tree complex wavelet transform

Selesnick

Baraniuk

Kingsbury³

2005

IEEE Signal Process. Mag.

2,178

1,202

View full text Add to dashboard Cite

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“…According to Eqs. (12), (14) and (15), ψ H 0 (ω) = e −ıβ(ω) ψ 0 (ω). Whenθ 0 takes the form (20), the expression of β is given by Eq.…”

Section: B Sufficient Conditions For Obtaining Dual Decompositionsmentioning

confidence: 99%

“…The phaselet extension of the dualtree DWT has been recently introduced by R. Gopinath in [12]. More recently, several authors have also proposed a projection scheme with an explicit control of the redundancy or with specific filter bank structures [13], [14]. Finally, other works on the blending of analytic signals and wavelets must be mentioned [15], [16], in the context of denoising or higher dimension signal processing.…”

Section: Introductionmentioning

confidence: 99%

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

Chaux

Duval

Pesquet

2006

IEEE Trans. on Image Process.

116

110

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Abstract-We propose a 2D generalization to the M -band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (i) the construction of the dual basis and (ii) the resulting directional analysis. We also revisit the necessary pre-processing stage in the M -band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed Mband decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various M -band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.

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“…Although SWT improves the power of wavelet in image denoising considerably, it suffers from the cost of very high redundancy which makes it computationally expensive [37]. Recently, many mathematical algorithms have been proposed to solve the DWT problems by using different forms of Complex Wavelet Transforms (CWT) [38][39][40][41][42][43]. Dual-Tree Complex Wavelet Transform (DT-CWT) is considered as one of the most efficient forms of CWT as reported in [44,45].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Image Denoising Method for Wireless Multimedia Sensor Networks Based on DT-CWT

Sammouda

Al-Salman

Gumaei

et al. 2015

International Journal of Distributed Sensor Networks

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Wireless multimedia sensor network (WMSN) is a developed technology of wireless sensor networks and includes a set of nodes equipped with cameras and other sensors to detect ambient environment and produce multimedia data content. In this context, many types of noises occur due to sensors problems, change of illumination, fog, rain, and other weather conditions. These noises usually degrade the digital images acquired by camera sensors. Image denoising in spatial domain is more difficult and timeconsuming for real-time processing of WMSNs applications. In this study, an efficient method based on Dual-Tree Complex Wavelet Transform (DT-CWT) is developed to enhance the image denosing in WMSNs. This method is designed to reduce the image noises by selecting an optimal threshold value estimated from the approximation of wavelet coefficients. In our experiment, the proposed method was tested and compared with standard Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT) on a set of natural scene images. Better results were achieved by using the DT-CWT in terms of image quality metrics and processing time.

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Orthogonal Hilbert transform filter banks and wavelets

Cited by 25 publications

References 6 publications

The dual-tree complex wavelet transform

The dual-tree complex wavelet transform

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

An Efficient Image Denoising Method for Wireless Multimedia Sensor Networks Based on DT-CWT

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