Partial Fourier Factor
Audit actual asymmetric signed-line coverage, conjugate pairs and DC availability; coverage above half alone does not guarantee successful partial-Fourier phase reconstruction.
Description
Partial-Fourier coverage is asymmetric when only part of a signed k-space line set is acquired.
Partial-Fourier coverage is asymmetric when only part of a signed k-space line set is acquired. Symmetric partner availability and DC inclusion are separate checks.
The tool returns acquiredFraction (acquired fraction); symmetricPairedLineCount (symmetric paired line count); dcAcquired (dc acquired); aboveHalfCoverage (above half coverage). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Partial Fourier Factor
Use Partial Fourier Factor when you already have fullSignedLineIndexes, acquiredLineIndexes and want acquiredFraction, symmetricPairedLineCount, dcAcquired, aboveHalfCoverage. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Partial Fourier Factor and understand its results
- Enter fullSignedLineIndexes, acquiredLineIndexes using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read acquiredFraction, symmetricPairedLineCount, dcAcquired, aboveHalfCoverage. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| fullSignedLineIndexes | Full signed line indexes | list of number | Required |
| acquiredLineIndexes | Acquired line indexes | list of number | Required |
Use distinct signed integer full and acquired lists with acquired a subset of full. Count both members of each nonzero pair; DC counts once as its own partner.
coverage = acquiredCount/fullCount; symmetricCount = acquired lines whose negated index is also acquired The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"fullSignedLineIndexes": [
-4,
-3,
-2,
-1,
0,
1,
2,
3
],
"acquiredLineIndexes": [
-1,
0,
1,
2,
3
]
},
"output": {
"acquiredFraction": 0.625,
"symmetricPairedLineCount": 3,
"dcAcquired": true,
"aboveHalfCoverage": true
}
}Limitations and assumptions
Above-half coverage uses a strict >0.5 comparison. No phase estimation, conjugate-symmetry validation or reconstruction occurs.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Compressed Sensing Acceleration: Measure actual 2D sampling-mask acceleration and audit required calibration coverage; mask sparsity is not a compressed-sensing reconstructability guarantee. GRAPPA Acceleration: Count unique regularly subsampled phase lines plus a contiguous ACS interval, avoiding double counting; GRAPPA kernel fitting and reconstruction are not performed.
Methodological background: RAD229: MRI signal and sequence lecture notes.1
References
-
RAD229: MRI signal and sequence lecture notes — Brian Hargreaves and colleagues, Stanford University
Similar or alternative tools
- Compressed Sensing Acceleration
Measure actual 2D sampling-mask acceleration and audit required calibration coverage; mask sparsity is not a compressed-sensing reconstructability guarantee.
- GRAPPA Acceleration
Count unique regularly subsampled phase lines plus a contiguous ACS interval, avoiding double counting; GRAPPA kernel fitting and reconstruction are not performed.