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Related Concept Videos

Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Downsampling01:20

Downsampling

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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...

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Related Experiment Video

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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Separate magnitude and phase regularization via compressed sensing.

Feng Zhao1, Douglas C Noll, Jon-Fredrik Nielsen

  • 1Biomedical Engineering Department, The University of Michigan, Ann Arbor, MI 48109, USA. zhaofll@umich.edu

IEEE Transactions on Medical Imaging
|May 4, 2012
PubMed
Summary

Compressed sensing MRI accelerates imaging, even with rapid phase variations. New methods accurately reconstruct magnitude and phase images from undersampled data for applications like thermometry and velocity mapping.

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Area of Science:

  • Magnetic Resonance Imaging (MRI) Physics
  • Medical Imaging Reconstruction Algorithms
  • Biomedical Signal Processing

Background:

  • Compressed sensing (CS) accelerates MRI but struggles with rapid spatial phase variations common in applications like proton resonance frequency shift (PRF-shift) thermometry and velocity mapping.
  • Existing iterative MRI reconstruction methods require fully sampled data and unwrapped phase maps, limiting their applicability.
  • Accurate reconstruction of both magnitude and phase information is crucial for quantitative MRI techniques.

Purpose of the Study:

  • To integrate compressed sensing (CS) into an iterative MRI reconstruction framework for accurate magnitude and phase imaging from undersampled data.
  • To develop novel phase regularization techniques capable of handling phase wrapping and reconstructing images with encoded phase variations.
  • To validate the proposed method for challenging applications such as PRF-shift thermometry and velocity mapping.

Main Methods:

  • Combined compressed sensing (CS) with an iterative MRI reconstruction framework.
  • Introduced new phase regularization terms to address phase wrapping and reconstruct complex phase variations.
  • Validated the method using simulated thermometry data and in vivo velocity mapping data.

Main Results:

  • The proposed CS-integrated method accurately reconstructs magnitude and phase images from undersampled MRI data.
  • The novel phase regularization effectively handles phase wrapping and reconstructs encoded phase variations.
  • Demonstrated superior performance compared to conventional phase-corrected CS in simulated and in vivo experiments.

Conclusions:

  • The developed CS-based reconstruction method overcomes limitations of previous approaches for accelerated MRI with rapid phase variations.
  • This technique enables accurate quantitative imaging in applications like PRF-shift thermometry and velocity mapping using undersampled data.
  • The findings pave the way for faster and more robust quantitative MRI acquisitions.