MRI g-factor & SNR efficiency maps for modern iterative recon

Code and notebooks for estimating spatially varying noise amplification (g-factor / 1/g SNR efficiency) in parallel MRI reconstructions, with an emphasis on iterative (CG-SENSE) and non-Cartesian settings.

The goal is practical: make voxel-wise noise/SNR maps easier to compute and compare across reconstruction choices.

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What’s in this repo

• Notebooks demonstrating g-factor / 1/g estimation in:
  • Cartesian CG-SENSE (knee) with an analytical reference for validation
  • Non-Cartesian spiral CG-SENSE (phantom) with a high-N PMR surrogate reference
• Core utilities for:
  • Operator-style recon code (forward/adjoint)
  • diagonal estimation via image-space probing
  • Baseline Pseudo Multiple Replica (PMR) comparisons

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Key idea (high-level)

Traditional PMR estimates noise by:

1. adding random noise to k-space many times,
2. reconstructing each replica,
3. measuring voxel-wise variance from the ensemble.

This is general but can be expensive because it repeats full reconstructions.

This project explores a complementary approach:

• estimate the diagonal of the reconstructed-image covariance using stochastic probing (Hutchinson-style estimators),
• implemented using matrix–vector products that reuse existing solver primitives (e.g., CG with (A) / (A^H)).

The notebooks focus on comparing convergence behavior and practical runtime/quality trade-offs against PMR.

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Demos (Jupyter notebooks)

1) Non-Cartesian spiral phantom (regularized CG-SENSE)

Notebook: notebooks/non_cartesian_phantom_gfactor_comparison.ipynb

• Multi-coil GRE spiral phantom + measured trajectory
• Retrospective shot subsampling (e.g., keep every (R)-th interleave)
• Regularized CG-SENSE with NUFFT/DCF and Toeplitz normal-op acceleration
• Reference: high-replica PMR surrogate (e.g., (N_\mathrm{ref}=10{,}000))

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2) Cartesian knee (unregularized CG-SENSE, analytical reference)

Notebook: notebooks/cartesian_knee_gfactor_comparison.ipynb

• Stanford knee dataset (multi-coil Cartesian)
• Retrospective uniform undersampling (e.g., (R=2) along phase-encode)
• Unregularized CG-SENSE
• Reference: closed-form analytical SENSE g-factor

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Quick start

Setup

git clone [https://github.com/<your-org-or-user>/<your-repo>.git](https://github.com/onat-dalmaz/fast_mri_gfactor.git)
cd <your-repo>

conda env create -f environment.yml
conda activate <env-name>

If needed:

pip install h5py einops

Run notebooks

jupyter notebook

Open:

• notebooks/non_cartesian_phantom_gfactor_comparison.ipynb
• notebooks/cartesian_knee_gfactor_comparison.ipynb

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Notes on metrics & visualization

• Many figures show (1/g) rather than (g), since (1/g) is directly interpretable as SNR efficiency.
• Convergence is typically evaluated vs:
  • an analytical reference (Cartesian), or
  • a high-N PMR surrogate reference (non-Cartesian / no closed form).

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References (background)

• Pruessmann et al., SENSE (parallel imaging / g-factor)
• Robson et al., SNR and g-factor quantification in parallel imaging
• Hutchinson (stochastic trace/diagonal estimation), and follow-on diagonal estimation work (e.g., Bekas)

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Citation / use

This is research code intended for reproducible demonstrations. If you use ideas or figures, please cite the associated manuscript / preprint and/or relevant prior work listed above.