SENSE Acceleration

Assess real-valued two-coil/two-alias SENSE conditioning through SᵀΨ⁻¹S and geometry factors; this is not general complex-coil image reconstruction.

Description

SENSE unfolding depends on coil sensitivities distinguishing aliased positions.

SENSE unfolding depends on coil sensitivities distinguishing aliased positions. A noise-weighted Gram matrix describes the local conditioning in this two-coil, two-alias model.

The tool returns sensitivityGramDeterminant (sensitivity gram determinant); diagonalGramValues (diagonal gram values); localGeometryFactors (local geometry factors). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use SENSE Acceleration

Use SENSE Acceleration when you already have realCoilSensitivities, noiseCovariance and want sensitivityGramDeterminant, diagonalGramValues, localGeometryFactors. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use SENSE Acceleration and understand its results

Enter realCoilSensitivities, noiseCovariance 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 sensitivityGramDeterminant, diagonalGramValues, localGeometryFactors. 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
realCoilSensitivities	Real coil sensitivities	list of list of number	Required
noiseCovariance	Noise covariance	list of list of number	Required

Use exactly 2×2 real sensitivities and a symmetric positive-definite noise covariance. Require a positive sensitivity Gram determinant; both returned geometry factors coincide in this case.

Gram = Sᵀ noiseCovariance⁻¹ S; gᵢ = sqrt(Gramᵢᵢ × inverseGramᵢᵢ)

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "realCoilSensitivities": [
      [
        1,
        0
      ],
      [
        0,
        1
      ]
    ],
    "noiseCovariance": [
      [
        1,
        0
      ],
      [
        0,
        1
      ]
    ]
  },
  "output": {
    "sensitivityGramDeterminant": 1,
    "diagonalGramValues": [
      1,
      1
    ],
    "localGeometryFactors": [
      1,
      1
    ]
  }
}

Limitations and assumptions

Complex sensitivities and larger coil systems are unsupported. No images are reconstructed or calibration is performed.

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

Parallel Imaging G-Factor: Infer empirical g from SNR_full/(SNR_accel·√R) using comparable scans; g below one is retained as evidence of measurement/model mismatch, not clamped. Simultaneous Multi-Slice Leakage: Audit leakage fractions from measured source-to-target slice transfer magnitudes; source rows require consistent calibration and this is not a slice-unmixing algorithm.

Methodological background: SENSE: sensitivity encoding for fast MRI.^[1]

References

SENSE: sensitivity encoding for fast MRI — Pruessmann et al.; Magnetic Resonance in Medicine

Similar or alternative tools

Parallel Imaging G-Factor
Infer empirical g from SNR_full/(SNR_accel·√R) using comparable scans; g below one is retained as evidence of measurement/model mismatch, not clamped.
Simultaneous Multi-Slice Leakage
Audit leakage fractions from measured source-to-target slice transfer magnitudes; source rows require consistent calibration and this is not a slice-unmixing algorithm.