Publication

A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D

Michaël Unser, Thierry Blu
2003
Journal Articles

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 Hilbert 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.

Official source

https://infoscience.epfl.ch/entities/publication/2295ac5d-d010-4c7e-8d03-efd6062a796c

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Michaël Unser, Thierry Blu
2003
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/2295ac5d-d010-4c7e-8d03-efd6062a796c

About this result

Related concepts (32)

Wavelet transform

In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.

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