# On the Empirical Effect of Gaussian Noise in Under-sampled MRI Reconstruction

arXiv: https://arxiv.org/abs/1610.00410 · HTML: https://mlsanity.com/paper/1610.00410/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2016.

## Built on by (most cited first, 5 of 5)

- [Uncertainty-aware GAN with Adaptive Loss for Robust MRI Image Enhancement](https://mlsanity.com/paper/2110.03343/) (2021)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [Tumor likelihood estimation on MRI prostate data by utilizing k-Space information](https://mlsanity.com/paper/2407.06165/) (2024)
- [Noise2Recon: Enabling Joint MRI Reconstruction and Denoising with Semi-Supervised and Self-Supervised Learning](https://mlsanity.com/paper/2110.00075/) (2021)
- [Tuning-free multi-coil compressed sensing MRI with Parallel Variable Density Approximate Message Passing (P-VDAMP)](https://mlsanity.com/paper/2203.04180/) (2022)

## Abstract (arXiv)

In Fourier-based medical imaging, sampling below the Nyquist rate results in an underdetermined system, in which linear reconstructions will exhibit artifacts. Another consequence of under-sampling is lower signal to noise ratio (SNR) due to fewer acquired measurements. Even if an oracle provided the information to perfectly disambiguate the underdetermined system, the reconstructed image could still have lower image quality than a corresponding fully sampled acquisition because of the reduced measurement time. The effects of lower SNR and the underdetermined system are coupled during reconstruction, making it difficult to isolate the impact of lower SNR on image quality. To this end, we present an image quality prediction process that reconstructs fully sampled, fully determined data with noise added to simulate the loss of SNR induced by a given under-sampling pattern. The resulting prediction image empirically shows the effect of noise in under-sampled image reconstruction without any effect from an underdetermined system. We discuss how our image quality prediction process can simulate the distribution of noise for a given under-sampling pattern, including variable density sampling that produces colored noise in the measurement data. An interesting consequence of our prediction model is that we can show that recovery from underdetermined non-uniform sampling is equivalent to a weighted least squares optimization that accounts for heterogeneous noise levels across measurements. Through a series of experiments with synthetic and in vivo datasets, we demonstrate the efficacy of the image quality prediction process and show that it provides a better estimation of reconstruction image quality than the corresponding fully-sampled reference image.