Iterative Soft Thresholding Compressed Sensing Reconstruction For Nuclear Magnetic Resonance Spectroscopy And Imaging

Seven decades after magnetic resonance phenomena has been discovered, Magnetic Resonance Imaging (MRI) has become a main approach for clinical diagnosis. With the development of MRI technology, there is an ever-growing demand for increasing the speed of MRI scans. The newly-occurred compressed sensing theory can break the limit of Nyquist sampling theorem, saving acquisition time while maintaining the quality of the reconstructed images. In this work, we under-sampled k space data and reconstructed with two different coefficient shrinkage methods in the wavelet transform domain. Both methods can effectively suppress the artifacts incurred by undersampling.2D Nuclear Magnetic Resonance (NMR) spectrum is an effective approach to elucidate the molecular structures and movement of materials. However, it bears the same weakness of MRI. It often takes too long to acquire NMR data, which hinders the applications of multi-demensional spectroscopy to many situations. In this work, Iterative Soft Thresholding (IST) is applied to partially-acquired 2D solid-state NMR data to reconstruct 2D solid-state NMR spectra with broad peaks. It was proved that with IST, compressed sensing can be used to save acquisition time of multi-dimension NMR spectra.