Biomedical Engineering Reference
In-Depth Information
Chapter 6
Wavelets in Medical Image Processing:
Denoising, Segmentation, and Registration
Yinpeng Jin
1
, Elsa Angelini
1
, and Andrew Laine
1
6.1 Introduction
Wavelets have been widely used in signal and image processing for the past 20
years. Although a milestone paper by Grossmann
et al.
[3] was considered the
beginning of modern wavelet analysis, similar ideas and theoretical bases can be
found back in the early twentieth century [4]. Following two important papers
in the late 1980s by Mallat [5] and Daubechies [6], more than 9000 journal papers
and 200 topics related to wavelets have been published [7].
Wavelets were first introduced to medical imaging research in 1991 in a jour-
nal paper describing the application of wavelet transforms for noise reduction in
MRI images [8]. Ever since, wavelet transforms have been successfully applied
to many topics including tomographic reconstruction, image compression, noise
reduction, image enhancement, texture analysis/segmentation, and multiscale
registration. Two review papers, in 1996 [9] and 2000 [10], provide a summary
and overview of research works related to wavelets in medical image processing
from the past few years. Many related works can also be found in the topic edited
by Aldroubi
et al.
[11]. More currently, a special issue of
IEEE Transactions on
Medical Imaging
[7] provides a large collection of most recent research works
using wavelets in medical image processing.
The purpose of this chapter is to summarize the usefulness of wavelets in vari-
ous problems of medical imaging. The chapter is organized as follows. Section 6.2
1
Department of Biomedical Engineering, Columbia University, New York, NY, USA
305
