Compressed Sensing Acceleration
Measure actual 2D sampling-mask acceleration and audit required calibration coverage; mask sparsity is not a compressed-sensing reconstructability guarantee.
Description
Sampling-mask coverage counts acquired k-space positions and checks whether every required calibration position was included.
Sampling-mask coverage counts acquired k-space positions and checks whether every required calibration position was included. Coverage alone does not determine reconstruction quality.
The tool returns acquiredSamples (acquired samples); nominalAcceleration (nominal acceleration); calibrationCoverageComplete (calibration coverage complete). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Compressed Sensing Acceleration
Use Compressed Sensing Acceleration when you already have samplingMask, fullySampledCalibrationMask and want acquiredSamples, nominalAcceleration, calibrationCoverageComplete. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Compressed Sensing Acceleration and understand its results
- Enter samplingMask, fullySampledCalibrationMask 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 acquiredSamples, nominalAcceleration, calibrationCoverageComplete. 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 |
|---|---|---|---|
| samplingMask | Sampling mask | list of list of number | Required |
| fullySampledCalibrationMask | Fully sampled calibration mask | list of list of number | Required |
Use aligned nonempty rectangular binary masks and at least one acquired sample. Return count, nominal acceleration and a calibration-coverage boolean.
acceleration = fullMaskSize/acquiredOnes; calibrationComplete = all required calibration ones are acquired The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"samplingMask": [
[
1,
0,
1
],
[
0,
1,
0
]
],
"fullySampledCalibrationMask": [
[
1,
0,
0
],
[
0,
1,
0
]
]
},
"output": {
"acquiredSamples": 3,
"nominalAcceleration": 2,
"calibrationCoverageComplete": true
}
}Limitations and assumptions
No incoherence, reconstruction, sparsity or image quality is evaluated. An all-zero calibration mask passes vacuously.
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
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. 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: Sparse MRI: The application of compressed sensing for rapid MR imaging.1
References
-
Sparse MRI: The application of compressed sensing for rapid MR imaging — Lustig, Donoho and Pauly; Magnetic Resonance in Medicine
Similar or alternative tools
- 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.
- GRAPPA Acceleration
Count unique regularly subsampled phase lines plus a contiguous ACS interval, avoiding double counting; GRAPPA kernel fitting and reconstruction are not performed.