A denoising method for multidimensional magnetic resonance spectroscopy and imaging based on compressed sensing

Both in spectroscopy and imaging, t1-noise arising from instabilities such as temperature alterations, field-related frequency drifts, electronic and sample-spinning instabilities, or motions in in vivo experiments, affects many 2D Magnetic Resonance experiments. This work introduces a post-processing method that aims to attenuate t1-noise, by suitably averaging multiple signals/representations that have been reconstructed from the sampled data. The ensuing Compressed Sensing Multiplicative (CoSeM) denoising starts from a fully sampled 2D MR data set, discards random indirect-domain points, and makes up for these missing, masked data, by a compressed sensing reconstruction of the now incompletely sampled 2D data set. This procedure is repeated for multiple renditions of the masked data -some of which will have been more strongly affected by t1-noise than others. This leads to a large set of 2D NMR spectra/images compatible with the collected data; CoSeM chooses out of these those renditions that reduce the noise according to a suitable criterion, and then sums up their spectra/images leading to a reduction in t1-noise. The performance of the method was assessed in synthetic data, as well as in numerous different experiments: 2D solid and solution state NMR, 2D localized MRS of live brains, and 2D abdominal MRI. Throughout all these data, CoSeM processing evidenced 2-3 fold increases in SNR, without introducing biases, false peaks, or spectral/image blurring. CoSeM also retains a quantitative linearity in the information -allowing, for instance, reliable T1 inversion-recovery MRI mapping experiments.