Application of low-rank approximation using truncated singular value decomposition for noise reduction in...

Dissolution dynamic nuclear polarization allows in vivo studies of metabolic flux using ¹³ C-hyperpolarized tracers by enhancing signal intensity by up to four orders of magnitude. The T₁ for in vivo applications is typically in the range of 10-50 s for the different ¹³ C-enriched metabolic substrates; the exponential loss of polarization due to various relaxation mechanisms leads to a strong reduction of the signal-to-noise ratio (SNR). A common solution to the problem of low SNR is the accumulation/averaging of consecutive spectra. However, some limitations related to long delays between consecutive scans occur: in particular, following biochemical kinetics and estimate apparent enzymatic constants becomes time critical when measurement scans are repeated with the typical delay of about 3 T₁ . Here we propose a method to dramatically reduce the noise, and therefore also the acquisition times, by computing, via truncated singular value decomposition, a low-rank approximation to the individual complex time-domain signals. Moreover, this approach has the additional advantage that the phase correction can be applied to the spectra already denoised, thus greatly reducing phase correction errors. We have tested the method on (1) simulated data; (2) performing dissolution of hyperpolarized 1-¹³ C-pyruvate in standard conditions and (3) in vivo data sets, using a porcine model injected with hyperpolarized Na-1-¹³ C-acetate. It was shown that the presented method reduces the noise level in all the experimental data sets, allowing the retrieval of signals from highly noisy data without any prior phase correction pre-processing. The effects of the proposed approach on the quantification of metabolic kinetics parameters have to be shown by full quantification studies.