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

TL;DR

This paper introduces a method to predict the impact of Gaussian noise on MRI image quality under various under-sampling patterns, isolating noise effects from system underdetermination.

Contribution

We propose an image quality prediction process that simulates noise effects in fully sampled data to evaluate under-sampled MRI reconstructions independently of system artifacts.

Findings

The prediction process accurately estimates image quality degradation due to noise.

Recovery from non-uniform sampling can be modeled as weighted least squares with heterogeneous noise.

The method outperforms traditional fully sampled references in estimating image quality.

Abstract

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.