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Quiz: Physics & Engineering: Reconstruction Methods for Undersampled Data

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Quiz: Physics & Engineering: Reconstruction Methods for Undersampled Data

Quiz: Physics & Engineering: Reconstruction Methods for Undersampled DataMegan Kravitz2021-08-06T16:17:36-07:00

Physics & Engineering:
Reconstruction Methods for Undersampled Data
by Jeff Fessler, Ph.D.

In routine “fully sampled” Cartesian MRI, one typically generates an image from the set of collected k-space samples using an inverse discrete Fourier transform (DFT). Since imaged object are continuous, what assumption enables this operation?
- Computers can only do DFTs
- The imaged object lies in a finite-dimensional subspace
- Nothing is being implicitly assumed when a DFT is used
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Following discretization, data acquisition can often be modeled as a simple affine system y=Ax+n, where y is k-space, A is the known system model, x is the discrete image, and n is noise. When undersampling is performed, A has fewer rows than columns. Why is least squares not an appropriate reconstruction objective in this scenario?
- Least squares sounds fine to me
- Least squares corresponds to maximum likelihood estimation
- Least squares does not provide unique solutions for underdetermined systems
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What is the tradeoff being made when regularization is used during image reconstruction?
- How closely the reconstructed image matches the observed data versus how well it fits some general presumption about its structure
- Whether the image will be smooth versus have a large dynamic range
- The accuracy of the system model versus the accuracy of the prior information
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What assumption underlies synthesis-type sparse reconstruction methods?
- The reconstructed image can be represented as a linear combination of only a few coefficient
- The image cannot be reconstructed with an analysis-type method
- The image is synthesized from training data using machine learning
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How do patch-based methods differ from conventional regularized reconstruction methods?
- Patch based methods are not guaranteed to converge to a unique solution
- Patch based methods utilize assumptions about the local structure of images whereas conventional methods utilize global assumptions
- Patch based methods only work for non-Cartesian data
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