Updated: July 5th, 2023 15:58

2009 journal article

A Shearlet Approach to Edge Analysis and Detection

*IEEE TRANSACTIONS ON IMAGE PROCESSING*, *18*(5), 929–941.

author keywords: Curvelets; edge detection; feature extraction; shearlets; singularities; wavelets

TL;DR:
This paper proposes a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges, which is useful to design simple and effective algorithms for the detection of corners and junctions.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2009 journal article

Edge analysis and identification using the continuous shearlet transform

*APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS*, *27*(1), 24–46.

author keywords: Analysis of singularities; Continuous wavelets; Curvelets; Directional wavelets; Edge detection; Shearlets; Wavelets

TL;DR:
The continuous shearlet transform is considered, which is the mapping of the wavelet transform to identify the set of singularities of a function or distribution f.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2009 journal article

Resolution of the wavefront set using continuous shearlets

*Transactions of the American Mathematical Society*, *361*(5), 2719–2754.

Source: NC State University Libraries

Added: August 6, 2018

2009 journal article

Shearlet-Based Total Variation Diffusion for Denoising

*IEEE TRANSACTIONS ON IMAGE PROCESSING*, *18*(2), 260–268.

author keywords: Curvelets; denoising; diffusion; regularization; shearlets; total variation

MeSH headings : Algorithms; Artifacts; Image Enhancement / methods; Image Interpretation, Computer-Assisted / methods; Reproducibility of Results; Sensitivity and Specificity

TL;DR:
It is shown that it is possible to obtain much better estimates from aShearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2008 journal article

Representation of Fourier integral operators using shearlets

*JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS*, *14*(3), 327–371.

author keywords: curvelets; Fourier integral operators; pseudo differential operators; shearlets; sparsity; wavelets

TL;DR:
The shearlets are shown to provide very efficient representations for a large class of Fourier Integral Operators, an affine-like system of well-localized waveforms at various scales, locations and orientations, which are particularly efficient in representing anisotropic functions.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2008 journal article

Sparse directional image representations using the discrete shearlet transform

*APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS*, *25*(1), 25–46.

author keywords: curvelets; denoising; image processing; shearlets; sparse representation; wavelets

TL;DR:
The numerical experiments presented in this paper demonstrate that the discrete shearlet transform is very competitive in denoising applications both in terms of performance and computational efficiency.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2007 journal article

Construction of regular and irregular shearlet frames

*Journal of Wavelet Theory and Applications*, *1*(1), 1–12.

Source: NC State University Libraries

Added: August 6, 2018

2007 journal article

Optimally sparse multidimensional representation using shearlets

*SIAM JOURNAL ON MATHEMATICAL ANALYSIS*, *39*(1), 298–318.

author keywords: affine systems; curvelets; geometric image processing; shearlets; sparse representation; wavelets

TL;DR:
It is shown that shearlets, an affine-like system of functions recently introduced by the authors and their collaborators, are essentially optimal in representing 2-dimensional functions f which are C^2 except for discontinuities along $C^2$ curves.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2007 journal article

Sparse shearlet representation of Fourier integral operators

*Electronic Research Announcements in Mathematical Sciences*, *14*, 7–19.

Source: NC State University Libraries

Added: August 6, 2018

2006 journal article

Some remarks on the unified characterization of reproducing systems

*Collectanea Mathematica (Barcelona, Spain)*, *57*(3), 295–307.

Source: NC State University Libraries

Added: August 6, 2018

2006 chapter

The theory of wavelets with composite dilations

In *Harmonic analysis and applications* (pp. 231–249).

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(OpenAlex)

Source: NC State University Libraries

Added: August 6, 2018

2006 journal article

Theory of reproducing systems on locally compact Abelian groups

*Colloquium Mathematicum*, *106*, 197–220.

Source: NC State University Libraries

Added: August 6, 2018

2006 journal article

Wavelets with composite dilations and their MRA properties

*APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS*, *20*(2), 202–236.

author keywords: affine systems; frames; multiwavelets; wavelets

Source: Web Of Science

Added: August 6, 2018

2005 journal article

Connectivity in the set of Gabor frames

*APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS*, *18*(1), 123–136.

author keywords: connectivity; frames; Gabor systems

TL;DR:
It is shown exactly how to modify a Gabor frame or Parseval frame to obtain a new one with the same property, and this construction is a modification of a method used in [Glas. 38 (58) (2003) 75–98] to study the connectivity of affineParseval frames.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

9. Industry, Innovation and Infrastructure
(Web of Science)

11. Sustainable Cities and Communities
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2005 conference paper

Sparse multidimensional representation using shearlets

In A. F. L. M. Papadakis & M. A. Unser (Eds.), *Wavelets XI: 31 July-3 August, 2005, San Diego, California, USA* (pp. 254–262).

Ed(s): A. M. Papadakis & M. Unser

Source: NC State University Libraries

Added: August 6, 2018

2004 journal article

Oversampling, quasi-affine frames, and wave packets

*Applied and Computational Harmonic Analysis*, *16*(2), 111–147.

Source: NC State University Libraries

Added: August 6, 2018

2004 journal article

Wavelets with composite dilations

*ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY*, *10*, 78–87.

author keywords: affine systems; frames; multiresolution analysis (MRA); multiwavelets; wavelets

Source: Web Of Science

Added: August 6, 2018

2003 chapter

Affine, quasi-affine and co-affine wavelets

In *Beyond wavelets* (pp. 215–224).

Source: NC State University Libraries

Added: August 6, 2018

2002 journal article

A unified characterization of reproducing systems generated by a finite family

*Journal of Geometric Analysis*, *12*(3), 469–491.

Source: NC State University Libraries

Added: August 6, 2018

2002 journal article

A unified characterization of reproducing systems generated by a finite family. II

*Journal of Geometric Analysis*, *12*(4), 615–622.

Source: NC State University Libraries

Added: August 6, 2018

2001 journal article

Pseudodifferential operators on modulation spaces

*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*, *262*(1), 242–255.

Source: Web Of Science

Added: August 6, 2018

2001 journal article

Time-frequency analysis of pseudodifferential operators

*MONATSHEFTE FUR MATHEMATIK*, *133*(2), 143–156.

Source: Web Of Science

Added: August 6, 2018

1994 personal communication

A COMPARISON OF FRACTAL DIMENSION AND SPECTRUM COEFFICIENT CHARACTERIZATION OF 1/F-ALPHA NOISE

LABATE, D., CANAVERO, F., & DEMARCHI, A. (1994, April).

Source: Web Of Science

Added: August 6, 2018

1994 conference paper

Exact SPICE model of field coupling to multiconductor transmission lines

*1994 International Symposium on Electromagnetic Compatibility, Hotel Sendai Plaza, Sendai, Japan, May 16-20, 1994*, 12–15. Tokyo: Institute of Electronics, Information and Communication Engineers; Institute of Electrical Engineers of Japan.

Source: NC State University Libraries

Added: August 6, 2018

1994 journal article

FRACTAL APPROACH TO LIGHTNING RADIATION ON A TORTUOUS CHANNEL

*RADIO SCIENCE*, *29*(4), 691–704.

Source: Web Of Science

Added: August 6, 2018

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