K-Space Sampling Density
Screen uniformly distributed full radial spokes using ceil(πN/2) angular Nyquist coverage; golden-angle subsets and compressed-sensing reconstruction quality are not evaluated.
Description
A conventional two-dimensional radial angular criterion requires about πN/2 spokes for a matrix size N.
A conventional two-dimensional radial angular criterion requires about πN/2 spokes for a matrix size N. The integer plan rounds that estimate upward.
The tool returns nyquistSpokes (nyquist spokes); samplingFraction (sampling fraction); angularCriterionMet (angular criterion met). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use K-Space Sampling Density
Use K-Space Sampling Density when you already have readoutMatrixSize, acquiredSpokes and want nyquistSpokes, samplingFraction, angularCriterionMet. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use K-Space Sampling Density and understand its results
- Enter readoutMatrixSize, acquiredSpokes 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 nyquistSpokes, samplingFraction, angularCriterionMet. 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 |
|---|---|---|---|
| readoutMatrixSize | Readout matrix size | integer | Required |
| acquiredSpokes | Acquired spokes | integer | Required |
Use positive integer matrix size and spoke count. Equality meets the criterion; a sampling fraction above one is retained.
required spokes = ceil(π×readoutMatrixSize/2); fraction = acquired/required The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"readoutMatrixSize": 128,
"acquiredSpokes": 100
},
"output": {
"nyquistSpokes": 202,
"samplingFraction": 0.49504950495049505,
"angularCriterionMet": false
}
}Limitations and assumptions
This nominal criterion assumes the stated radial geometry. Variable density, half-spokes and reconstruction behavior are not assessed.
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
Radial K-Space Trajectory: Generate explicit radial k-space spoke coordinates from supplied angles and signed radial sample locations; no trajectory density compensation is inferred. Compressed Sensing Acceleration: Measure actual 2D sampling-mask acceleration and audit required calibration coverage; mask sparsity is not a compressed-sensing reconstructability guarantee.
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
- Radial K-Space Trajectory
Generate explicit radial k-space spoke coordinates from supplied angles and signed radial sample locations; no trajectory density compensation is inferred.
- Compressed Sensing Acceleration
Measure actual 2D sampling-mask acceleration and audit required calibration coverage; mask sparsity is not a compressed-sensing reconstructability guarantee.