The Nonsubsampled Contourlet Transform: Theory, Design, and Applications

Cunha, A.L. da; Zhou, Jianping; Minh, N.

doi:10.1109/tip.2006.877507

Cited by 1,843 publications

(933 citation statements)

References 34 publications

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“…However, in most of these methods, the image is decomposed in a separable fashion, without taking full advantage of the geometric information associated with the edges [35,30]. By contrast, a multiscale decomposition which is able to take advantage of directional features, such as curvelets, shearlets or wavelets with composite dilations, is much more effective in dealing with the edges and other directional information [16,47,43,12].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…A standard method for designing nonsubsampled directional representations is to use critically sampled transformations based on 2D directional filters that satisfies Bezout's identity, as done in [12,22]. As will become clear below, this approach is frequently associated with filters that do not faithfully match with the desired theoretical frequency decomposition.…”

Section: Introductionmentioning

confidence: 99%

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Directional Multiscale Processing of Images Using Wavelets with Composite Dilations

2012

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Directional Multiscale Processing of Images Using Wavelets with Composite Dilations

2012

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“…The transform direction with the slope r = a + b (15) minimizes the width ∆ d (and, thereof, N (0) e (j)) on the unit square. In that case the number of the E-type coefficients is given by N (0) e (j) = O a 4 2 n 2 j .…”

Section: Appendix I Proof Of Theoremmentioning

confidence: 99%

Sparse Image Representation by Directionlets

Velisavljević¹,

Vetterli²,

Beferull-Lozano³

et al. 2010

Advances in Imaging and Electron Physics

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In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation is limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges or contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a non-sparse representation. To capture efficiently these elongated structures characterized by geometrical regularity along different directions (not only the horizontal and vertical), a more complex multi-directional (M-DIR) and asymmetric transform is required. We present a lattice-based perfect reconstruction and critically sampled asymmetric M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional (2-D) WT, unlike what is the case for some other directional transform constructions (e.g. curvelets, contourlets or edgelets). The corresponding asymmetric basis functions, called directionlets, have directional vanishing moments (DVM) along any two directions with rational slopes, which allows for a sparser representation of elongated and oriented features. As a consequence of the improved sparsity, directionlets provide an efficient tool for non-linear approximation (NLA) of images, significantly outperforming the standard 2-D WT. Furthermore, directionlets combined with wavelet-based image compression methods lead to a gain in the performance in terms of both the mean-square error and visual quality, especially at the low bit-rate compression, while having the same complexity. Finally, a shift-invariant non-subsampled version of directionlets is successfully implemented in image interpolation, where critical sampling is not a key requirement.

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“…Transformation domain-based methods decompose infrared image into a series of low-frequency and high-frequency sub-bands by transform image from spatial domain to other transform domains. Wavelet transform [9] , shearlet transform [10] and Butterworth high-frequency filter [11] based methods are some classical transformation domain-based methods. This kind of method perform well in target detection, however, there exist disadvantages of complex and time-consuming calculation.…”

Section: Introductionmentioning

confidence: 99%

Background Suppression for Infrared Dim and Small Target Detection Using Local Gradient Weighted Filtering

Li¹,

Li²,

Zhao³

et al. 2017

dtetr

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Abstract. In this paper, a temporal local gradient weighted filtering based infrared dim small target background suppression method has been proposed. The highlight of the proposed method is that it utilizes the local gradient weighted filtering to deal with the temporal profile, which separates the small target from strong background clutter according to the difference of profile among small target, stable background and the edge of cloud. In this paper, two real low signal-to-clutter ratio (SCR) infrared imagery sequences containing moving dim small target are applied to verify the efficiency of the proposed method. Compared with several classical methods, the experimental results show that the performance of proposed method is superior to several other methods both in aspects of subjective visual and objective evaluation index.

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The Nonsubsampled Contourlet Transform: Theory, Design, and Applications

Cited by 1,843 publications

References 34 publications

Directional Multiscale Processing of Images Using Wavelets with Composite Dilations

Directional Multiscale Processing of Images Using Wavelets with Composite Dilations

Sparse Image Representation by Directionlets

Background Suppression for Infrared Dim and Small Target Detection Using Local Gradient Weighted Filtering

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