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

[Display omitted] •CoSeM, a reference-less method for reducing k/t1-noise by ca. 3-fold, is introduced.•The approach operates on the basis of combined masking/compressed sensing fully sampled 2D sets.•The method is general, does not require a reference, improves SNR in 2D spectra/images, retains quantitativeness, and does not affect spectral/spatial resolution. 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.