DECAES - DEcomposition and Component Analysis of Exponential Signals

Jonathan Doucette1, Christian Kames1, Alexander Rauscher2

  • 1Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, V6T 1Z1 Vancouver, BC, Canada; UBC MRI Research Centre, 2221 Wesbrook Mall, V6T 2B5 Vancouver, BC, Canada.

Summary

This study introduces a rapid method for decomposing multi-exponential signals, significantly speeding up the analysis of magnetic resonance imaging (MRI) data for applications like myelin water mapping.

Related Concept Videos

Exponential and Sinusoidal Signals01:18

Exponential and Sinusoidal Signals

The exponential function is crucial for characterizing waveforms that rise and decay rapidly. This continuous-time exponential function is defined using exponential terms with constants α and A. When both constants are real, the function is represented as,
621
Exponential Fourier series01:24

Exponential Fourier series

In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
Euler's identity...
564
Even and Odd Signals01:17

Even and Odd Signals

An even signal, whether in continuous-time or discrete-time, is defined by its symmetry with its time-reversed version. Mathematically, this is represented as
1.9K
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
572
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at...
807
Exponential Functions with Base e01:30

Exponential Functions with Base e

Exponential functions with base e are essential for modeling continuous processes of growth and decay. The constant e, approximately 2.718, naturally arises in systems where change occurs proportionally to the current value. A positive exponent represents continuous growth, while a negative exponent represents continuous decay. These functions are especially useful for describing situations where change happens smoothly over time rather than in discrete steps.One clear example of exponential...
121