The Monogenic Wavelet Transform

Olhede, Sofia C.; Metikas, Georgios

doi:10.1109/tsp.2009.2023397

Cited by 61 publications

(38 citation statements)

References 42 publications

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“…The last two in the list are closely related to the Riesz transform of classical harmonic analysis [37]. Design of directional wavelets based on these and other alternative extensions are a promising topic of research [38], [39].…”

Section: Discussionmentioning

confidence: 99%

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Chaudhury

Unser

2009

IEEE Trans. Signal Process.

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Abstract-We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of , we then discuss a methodology for constructing 2-D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1-D counterpart, we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the HT-the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient fast Fourier transform (FFT)-based filterbank algorithm for implementing the associated complex wavelet transform.

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Section: Discussionmentioning

confidence: 99%

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Chaudhury

Unser

2009

IEEE Trans. Signal Process.

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“…Of particular relevance is that the RT is norm-preserving, R f = f , and invertible, R −n {R n f }(z) = f (z), if f (z) has zero mean. These properties allow the generation of monogenic wavelets [17,36] in multiple dimensions [54] and for colour images [48], as well as monogenic versions of existing quadrature wavelets that give a directional decomposition into amplitude and phase components [50].…”

Section: Circular Harmonic Waveletsmentioning

confidence: 99%

A Sinusoidal Image Model Derived from the Circular Harmonic Vector

Marchant

Jackway²

2016

J Math Imaging Vis

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We introduce a sinusoidal image model consisting of an oriented sinusoid plus a residual component. The model parameters are derived from the circular harmonic vector, a representation of local image structure consisting of the responses to the higher-order Riesz transforms of an isotropic wavelet. The vector is split into sinusoidal and residual components. The sinusoidal component gives a phase-based description of the dominant local linear symmetry, with improved orientation estimation compared to previous sinusoidal models. The residual component describes the remaining parts of the local structure, from which a complex-valued representation of intrinsic dimension is derived. The usefulness of the model is demonstrated for corner and junction detection and parameter-driven image reconstruction.

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“…Then the row numbers of the measurement matrix is (3) In (3), || || p || p represents p norm . Seeking for the sparse representation of a signal from the random sensing matrix is a non-deterministic polynomial problem [10].…”

Section: Compressive Sensingmentioning

confidence: 99%

“…The transform domain interference detection algorithms are mainly based on the different domain characteristics of the signal, background noise and interference. The commonly transform domains include the frequency domain [2], the wavelet domain [3], the fractional Fourier transform domain [4], etc. These methods achieve interference detection successfully, but with the development of technologies, the signal bandwidth is growing, large bandwidth leads to a sharp increase of the sampling rate, the existing methods are confined to the high sampling rate.…”

Section: Introductionmentioning

confidence: 99%

Joint Interference Detection Method for DSSS Communications Based on the OMP Algorithm and CA-CFAR

Zhang

Xin

Song

2016

MATEC Web of Conferences

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Abstract. The existing direct sequence spread spectrum (DSSS) communications interference detection algorithms are confined to the high sampling rate. In order to solve this problem, algorithm for DSSS communications interference detection was designed based on compressive sensing (CS). First of all, the orthogonal matching pursuit (OMP) algorithm was applied to the interference detection in DSSS communications, the advantages and weaknesses of the algorithm were analyzed; Secondly, according to the weaknesses of the OMP algorithm, a joint interference detection method based on the OMP algorithm and cell average constant false alarm rate (CA-CFAR) was proposed. The theoretical analyze and computer simulation all proved the effectiveness of the new algorithm. The simulation results show that the new method not only could achieve the interference detection, but also could estimate the interference quantity effectively.

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The Monogenic Wavelet Transform

Cited by 61 publications

References 42 publications

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

A Sinusoidal Image Model Derived from the Circular Harmonic Vector

Joint Interference Detection Method for DSSS Communications Based on the OMP Algorithm and CA-CFAR

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