A new family of complex rotation-covariant multiresolution bases in 2D

Brigitte Forster; Thierry Blu; Michael Unser

doi:10.1117/12.503696

A new family of complex rotation-covariant multiresolution bases in 2D

Brigitte Forster, Thierry Blu, Michael Unser

EPFL

Research output: Contribution to journal › Conference article › peer-review

4 Scopus citations

Abstract

We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis elements have nice properties in Hubert space such as smoothness of fractional order α ∈ ℝ⁺. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.

Original language	English
Pages (from-to)	475-479
Number of pages	5
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	5207
Issue number	1
DOIs	https://doi.org/10.1117/12.503696
State	Published - 2003
Externally published	Yes
Event	Wavelets: Applications in Signal and Image Processing X - San Diego, CA, United States Duration: 4 Aug 2003 → 8 Aug 2003

Keywords

Complex wavelets
Multiresolution
Riesz basis
Scaling functions
Two-scale relation

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10.1117/12.503696

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abstract = "We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis elements have nice properties in Hubert space such as smoothness of fractional order α ∈ ℝ+. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.",

keywords = "Complex wavelets, Multiresolution, Riesz basis, Scaling functions, Two-scale relation",

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AU - Blu, Thierry

AU - Unser, Michael

PY - 2003

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N2 - We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis elements have nice properties in Hubert space such as smoothness of fractional order α ∈ ℝ+. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.

AB - We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis elements have nice properties in Hubert space such as smoothness of fractional order α ∈ ℝ+. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.

KW - Complex wavelets

KW - Multiresolution

KW - Riesz basis

KW - Scaling functions

KW - Two-scale relation

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DO - 10.1117/12.503696

M3 - Conference article

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EP - 479

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

IS - 1

T2 - Wavelets: Applications in Signal and Image Processing X

Y2 - 4 August 2003 through 8 August 2003

ER -

A new family of complex rotation-covariant multiresolution bases in 2D

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