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A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
, 2011
"... The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smoot ..."
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Cited by 19 (8 self)
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The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multiorientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to nonEuclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping “pictures”.
ResonanceBased Signal Decomposition: A New SparsityEnabled Signal Analysis Method
"... Numerous signals arising from physiological and physical processes, in addition to being nonstationary, are moreover a mixture of sustained oscillations and nonoscillatory transients that are difficult to disentangle by linear methods. Examples of such signals include speech, biomedical, and geoph ..."
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Cited by 14 (6 self)
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Numerous signals arising from physiological and physical processes, in addition to being nonstationary, are moreover a mixture of sustained oscillations and nonoscillatory transients that are difficult to disentangle by linear methods. Examples of such signals include speech, biomedical, and geophysical signals. Therefore, this paper describes a new nonlinear signal analysis method based on signal resonance, rather than on frequency or scale, as provided by the Fourier and wavelet transforms. This method expresses a signal as the sum of a ‘highresonance ’ and a ‘lowresonance ’ component — a highresonance component being a signal consisting of multiple simultaneous sustained oscillations; a lowresonance component being a signal consisting of nonoscillatory transients of unspecified shape and duration. The resonancebased signal decomposition algorithm presented in this paper utilizes sparse signal representations, morphological component analysis, and constantQ (wavelet) transforms with adjustable Qfactor. Keywords: sparse signal representation, constantQ transform, wavelet transform, morphological component analysis 1.
Sparse signal representations using the tunable Qfactor wavelet transform
"... The tunable Qfactor wavelet transform (TQWT) is a fullydiscrete wavelet transform for which the Qfactor, Q, of the underlying wavelet and the asymptotic redundancy (oversampling rate), r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can ..."
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Cited by 1 (1 self)
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The tunable Qfactor wavelet transform (TQWT) is a fullydiscrete wavelet transform for which the Qfactor, Q, of the underlying wavelet and the asymptotic redundancy (oversampling rate), r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be realvalued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsitybased inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented using radix2 FFTs. The TQWT can also be used as an easilyinvertible discrete approximation of the continuous wavelet transform.
Oscillatory + Transient Signal Decomposition using Overcomplete RationalDilation Wavelet
"... This paper describes an approach for decomposing a signal into the sum of an oscillatory component and a transient component. The method uses a newly developed rationaldilation wavelet transform (WT), a selfinverting constantQ transform with an adjustable Qfactor (qualityfactor). We propose that ..."
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This paper describes an approach for decomposing a signal into the sum of an oscillatory component and a transient component. The method uses a newly developed rationaldilation wavelet transform (WT), a selfinverting constantQ transform with an adjustable Qfactor (qualityfactor). We propose that the oscillatory component be modeled as signal that can be sparsely represented using a high Qfactor WT; likewise, we propose that the transient component be modeled as a piecewise smooth signal that can be sparsely represented using a low Qfactor WT. Because the low and high Qfactor wavelet transforms are highly distinct (having low coherence), morphological component analysis (MCA) successfully yields the desired decomposition of a signal into an oscillatory and nonoscillatory component. The method, being nonlinear, is not constrained by the limits of conventional LTI filtering. Keywords: wavelets, sparsity, morphological component analysis, constant Q, Qfactor 1.
TQWT Toolbox Guide
, 2011
"... The ‘Tunable QFactor Wavelet Transform ’ (TQWT) is a flexible fullydiscrete wavelet transform [5]. The TQWT toolbox is a set of Matlab programs implementing and illustrating the TQWT. The programs validate the properties of the transform, clarify how the transform can be implemented, and show how ..."
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The ‘Tunable QFactor Wavelet Transform ’ (TQWT) is a flexible fullydiscrete wavelet transform [5]. The TQWT toolbox is a set of Matlab programs implementing and illustrating the TQWT. The programs validate the properties of the transform, clarify how the transform can be implemented, and show how it can be used. The TQWT is similar to the rationaldilation wavelet transform (RADWT) [2], but the TQWT does not
1A DualTree RationalDilation Complex Wavelet Transform
"... Abstract—In this correspondence, we introduce a dualtree rationaldilation complex wavelet transform for oscillatory signal processing. Like the shorttime Fourier transform and the dyadic dualtree complex wavelet transform, the introduced transform employs quadrature pairs of timefrequency atoms ..."
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Abstract—In this correspondence, we introduce a dualtree rationaldilation complex wavelet transform for oscillatory signal processing. Like the shorttime Fourier transform and the dyadic dualtree complex wavelet transform, the introduced transform employs quadrature pairs of timefrequency atoms which allow to work with the analytic signal. The introduced wavelet transform is a constantQ transform, a property lacked by the shorttime Fourier transform, which in turn makes the introduced transform more suitable for models that depend on scale. Also, the frequency resolution can be as high as desired, a property lacked by the dyadic dualtree complex wavelet transform, which makes the introduced transform more suitable for processing oscillatory signals like speech, audio and various biomedical signals. Index Terms—Rationaldilation wavelet transform, dualtree complex wavelet transform, shorttime Fourier transform, analytic signal, instantaneous freuency estimation. I.
IEEE TRANSACTIONS ON SIGNAL PROCESSING (2011) 1 Wavelet Transform with Tunable QFactor
"... Abstract—This paper describes a discretetime wavelet transform for which the Qfactor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a realvalued scaling factor (dilationfactor) and is i ..."
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Abstract—This paper describes a discretetime wavelet transform for which the Qfactor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a realvalued scaling factor (dilationfactor) and is implemented using a perfect reconstruction oversampled filter bank with realvalued sampling factors. Two forms of the transform are presented. The first form is defined for discretetime signals defined on all of Z. The second form is defined for discretetime signals of finitelength and can be implemented efficiently with FFTs. The transform is parameterized by its Qfactor and its oversampling rate (redundancy), with modest oversampling rates (e.g. 34 times overcomplete) being sufficient for the analysis/synthesis functions to be well localized. Index Terms—wavelet transform, constantQ transform, filter bank, Qfactor. I.
Enhancement of Ultrasound Images Using RADWT
"... Abstract — Feature preserved enhancements are necessary in medical ultrasound images. The quality and important information present in ultrasound images are affected by speckle which makes the post processing difficult. A technique based on rational dilation wavelet transform (RADWT) is applied on m ..."
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Abstract — Feature preserved enhancements are necessary in medical ultrasound images. The quality and important information present in ultrasound images are affected by speckle which makes the post processing difficult. A technique based on rational dilation wavelet transform (RADWT) is applied on medical images to enhance the quality of speckle noise affected images. A new family of wavelet transform is presented for which the frequency resolution can be varied to provide the effectiveness of noisy coefficients. Denoising efficiency is improved by applying bilateral filter and different threshold schemes to noisy RADWT coefficient and edge features are preserved effectively, blurring associated with speckle noise is less and important details are enhanced properly for better visual illustration of ultrasound images. This approach helps us to improve the quality of the ultrasound images. Experimental results are shown for noise suppression, feature and edge preservation in different measures.
Rationaldilation wavelet transform with translation invariance
, 2013
"... We propose a wavelet transform which offers a tunable Qfactor in each decomposition level and retains the translationinvariant property as well. Rationaldilation wavelet transform, whose Qfactor could be tuned before decomposition, has a finer timefrequency localization ability than common dyad ..."
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We propose a wavelet transform which offers a tunable Qfactor in each decomposition level and retains the translationinvariant property as well. Rationaldilation wavelet transform, whose Qfactor could be tuned before decomposition, has a finer timefrequency localization ability than common dyadic wavelet transform. However, the fixing of its Qfactor in every decomposition level restricts the freedom of frequencydomain partition, and also the upsampler and downsampler in its decomposition destroys translationinvariant property. We firstly analyze the decomposition and reconstruction of a kind of rationaldilation wavelet transform, and then discuss a transform that provides a tunable Qfactor in each decomposition level and keeps the translationinvariant property. Also, this method is expanded to twodimensional case. Finally, we show the advantages of the method in timefrequency localization via the application in DEM generalization. Key words: Qfactor, rationaldilation wavelet transform, PseudoGibbs phenomenon, stationary.
zur Erlangung des akademischen Grades
"... und Neurowissenschaft. So hat zum einen neurobiologische Forschung gezeigt, daß ..."
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und Neurowissenschaft. So hat zum einen neurobiologische Forschung gezeigt, daß