Publication

The finite ridgelet transform for image representation

Martin Vetterli, Minh Do
2003
Journal Articles

Abstract

The ridgelet transform (Candès and Donoho, 1999) was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we propose an or- thonormal version of the ridgelet transform for discrete and fi- nite-size images. Our construction uses the finite Radon transform (FRAT) (Bolker, 1987:Matùs and Flusser, 1993) as a building block. To overcome the periodiza- tion effect of a finite transform, we introduce a novel ordering of the FRAT coefficients. We also analyze the FRAT as a frame operator and derive the exact frame bounds. The resulting finite ridgelet transform (FRIT) is invertible, nonredundant and computed via fast algorithms. Furthermore, this construction leads to a family of directional and orthonormal bases for images. Numerical results show that the FRIT is more effective than the wavelet transform in approximating and denoising images with straight edges.

Official source

https://infoscience.epfl.ch/entities/publication/123c583f-694c-4855-901c-63bdb82b2cc5

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Martin Vetterli, Minh Do
2003
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/123c583f-694c-4855-901c-63bdb82b2cc5

About this result

Related concepts (32)

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

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.

Related publications (13)

The finite ridgelet transform for image representation

Chat with Graph Search

Human Brain Excitation-Inhibition Balance Through Fmri Dynamics: Estimators and in-Vivo Validation

3-Query RLDCs Are Strictly Stronger Than 3-Query LDCs

An FFT-based Numerical Method for Elasto-Plastic Contact