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Related Concept Videos

The Wave Nature of Light02:12

The Wave Nature of Light

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms and was able to demonstrate that white light consists of the individual colors of the rainbow combined together. Newton explained his optics findings in terms of a "corpuscular" view of light, in which light was composed of streams of extremely tiny particles traveling at high speeds according to Newton's laws of motion.
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
Equations of Wave Motion01:02

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...

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Related Experiment Video

Updated: Jul 12, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Published on: July 19, 2016

An introduction to wavelet theory and application for the radiological physicist

M D Harpen1

  • 1University of South Alabama, Department of Radiology, Mobile 36617, USA.

Medical Physics
|November 4, 1998
PubMed
Summary

This primer introduces wavelet transform theory for radiological physicists, focusing on practical applications in medical imaging like teleradiology and computer-aided diagnosis. It provides essential knowledge without complex mathematical rigor.

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Area of Science:

  • Mathematics
  • Medical Imaging
  • Radiology

Background:

  • Wavelet transform is a key mathematical technique for image processing.
  • Advancements in diagnostic radiology include teleradiology, PACS, and computer-aided diagnosis.
  • Radiological physicists need to understand wavelet theory for these evolving technologies.

Purpose of the Study:

  • To present a primer on wavelet theory tailored for radiological physicists.
  • To provide a working knowledge of wavelet theory relevant to medical imaging.
  • To simplify complex mathematical concepts for a physics audience.

Main Methods:

  • The study offers a simplified mathematical treatment of wavelet theory.
  • Focuses on concepts relevant to image compression, noise suppression, and feature extraction.
  • Avoids excessive mathematical rigor to enhance accessibility.

Main Results:

  • The primer equips radiological physicists with foundational wavelet theory knowledge.
  • It bridges the gap between advanced mathematics and practical radiological applications.
  • Readers gain a reasonably deep working knowledge of wavelet theory.

Conclusions:

  • Wavelet theory is crucial for the future of diagnostic radiology and medical imaging.
  • This primer serves as an accessible educational resource for physicists.
  • Understanding wavelets enhances capabilities in teleradiology and computer-aided diagnosis.