Design of 2-band orthogonal near-symmetric CQF

Abdelnour, A. Farras; Selesnick, Ivan

doi:10.1109/icassp.2001.940644

Cited by 28 publications

(22 citation statements)

References 7 publications

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“…For the MC simulations, the input signal is transformed to the complex wavelet domain, using the nearly symmetric Farras filters for 2-channel perfect reconstruction [27] in the first scale and the 6-tap Q-shift filters Gray corresponds to 0, white to positive correlations and black to negative correlations.…”

Section: Resultsmentioning

confidence: 99%

A Recursive Scheme for Computing Autocorrelation Functions of Decimated Complex Wavelet Subbands

Goossens

Aelterman

Pižurica

et al. 2010

IEEE Trans. Signal Process.

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Abstract-This correspondence deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function or alternatively the power spectral density (PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of "blind" wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem.

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Section: Resultsmentioning

confidence: 99%

A Recursive Scheme for Computing Autocorrelation Functions of Decimated Complex Wavelet Subbands

Goossens

Aelterman

Pižurica

et al. 2010

IEEE Trans. Signal Process.

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“…2. Six complex wavelets from the 2-D dual-tree CWT frame generated from orthogonal near-symmetric filters [23] in the first stage and Q-filters [24] in subsequent stages. (a) Real parts, with approximate even symmetry; (b) imaginary parts, with approximate odd symmetry.…”

Section: Introductionmentioning

confidence: 99%

Coherent Multiscale Image Processing Using Dual-Tree Quaternion Wavelets

Chan

Choi

Baraniuk

2008

IEEE Trans. on Image Process.

109

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The dual-tree quaternion wavelet transform (QWT) is a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant tight frame representation whose coefficients sport a magnitude and three phases: two phases encode local image shifts while the third contains image texture information. The QWT is based on an alternative theory for the 2-D Hilbert transform and can be computed using a dual-tree filter bank with linear computational complexity. To demonstrate the properties of the QWT's coherent magnitude/phase representation, we develop an efficient and accurate procedure for estimating the local geometrical structure of an image. We also develop a new multiscale algorithm for estimating the disparity between a pair of images that is promising for image registration and flow estimation applications. The algorithm features multiscale phase unwrapping, linear complexity, and sub-pixel estimation accuracy.

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“…The denoised image is obtained applying the inverse wavelet transform after this thresholding. The reader is referred to [15]- [17] for further details.…”

Section: Wavelet Shrinkage For Image Denoisingmentioning

confidence: 99%

“…The two trees are in fact real and use two different sets of perfect reconstruction filters. In the particular implementation we used in this paper, we considered Farras filters [15] for the first decomposition stage, and Kingsburry's Q-shift filters [16] for the remaining stages. Farras filters were designed to have two particular important properties for the complex wavelet transforms, i. e., (1) be orthogonal, and (2) have a subset of exactly symmetric coefficients (among all).…”

Section: Wavelet Shrinkage For Image Denoisingmentioning

confidence: 99%

Three-Dimensional Visualization of Long Range Scenes by Photon Counting Mid-Wave Infrared Integral Imaging

Carmona

Javidi

LeMaster

2015

J. Display Technol.

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Abstract-Integral Imaging under photon counting conditions has found different three-dimensional (3D) imaging applications, including 3D image reconstruction and recognition. In this letter, we present the application of the maximum likelihood (ML) estimation method for visualization of 3D scenes in photon starved environments using Mid-Wave Infrared 3D data of real scenes acquired at distances ranging from 50m to more than 2km. To the best of our knowledge, this is the first report on Mid-Wave Infrared 3D photon counting integral imaging of distant scenes.

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Design of 2-band orthogonal near-symmetric CQF

Cited by 28 publications

References 7 publications

A Recursive Scheme for Computing Autocorrelation Functions of Decimated Complex Wavelet Subbands

A Recursive Scheme for Computing Autocorrelation Functions of Decimated Complex Wavelet Subbands

Coherent Multiscale Image Processing Using Dual-Tree Quaternion Wavelets

Three-Dimensional Visualization of Long Range Scenes by Photon Counting Mid-Wave Infrared Integral Imaging

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