Tensor decomposition can be used for denoising magnetic resonance spectroscopic imaging (MRSI) data by reconstructing the data from a small number of ranks. Selecting too low an order can remove data from the reconstruction and alter peak amplitudes. A condition for selection of rank order is proposed that removes only noise from the reconstructed data and, therefore, preserves signals from low amplitude resonances. Denoising algorithms that apply this condition are demonstrated for metabolic imaging data sets obtained with hyperpolarised [1-13C]pyruvate and [6,6-2H]glucose in preclinical cancer models, which improve signal-to-noise and reduce the Cramér-Rao lower bound errors in peak fitting.
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