In MR spectroscopy it is often interesting to observe a dynamic system as it varies in time, for example phosphocreatine depletion and resynthesis in exercising muscle. To achieve an adequate signal-to-noise ratio (SNR), particularly at lower field strengths, sequential spectra are typically averaged, compromising the achievable temporal resolution. Previous studies have shown that applying denoising techniques in the indirect temporal domain can greatly improve the accuracy of metabolite quantification for individual spectra, reducing the need for averaging and improving resolution¹. This study forms the first comparison of a range of different denoising methods for dynamic MRS.

To assess the performance of any denoising technique, it is necessary to start with a "ground-truth" signal to which random noise can be added before the technique is applied. Synthetic timecourses often lack subtle features or use mathematically exact shapes which may be biased towards certain denoising methods. In order to accurately capture real-world nuances and variations, we chose to derive our ground truth signals from experimental data.

Six denoising methods were considered: SVD, wavelet, sliding window, sliding window with Gaussian weighting, spline and SIFT.

We selected four exams measuring 31P MRS in exercising muscle, covering a representative range of clinical cases: a young female, young male, middle-aged male (all healthy volunteers) and a male patient with peripheral artery disease. From these exams the noisy timecourses of the PhosphoCreatine (PCr) and inorganic Phosphate (Pi) peaks were extracted. In each case, our smooth ground truth was obtained by applying the SVD, Gaussian window, spline and SIFT de-noising methods and averaging the results. Combining these four methods produces a smooth timecourse which is not biased towards a particular model representation (sinusoids, splines etc.). An example of this process is shown in figure 1. It is important to remember that this derived ground truth is not required to exactly match the true underlying signal of the source data, but merely to create a timecourse with similar characteristics.

Randomly generated white Gaussian noise was added to each ground truth at four different SNRs (10, 20, 30, 40), covering the typical range observed experimentally. For each initial time course and noise level a Monte Carlo approach was adopted where 400 noisy signals were created and denoised by all six methods, in order to assess the average performance of each method.

It was determined that the averaging method for producing the ground truth did not introduce significant bias towards any model, by applying each method to the plain denoised signal.

The results of the denoising are shown in figure 2. For each set of 400 noisy signals the average standard deviation between the denoised signal and the ground truth was used to calculate the final SNR. This was then divided by the initial value to show the proportional improvement in SNR, enabling comparison of the results for different initial levels of noise.

The spline fitting method consistently performed best for input signals with low SNR, but its performance deteriorated as the input signal improved. By contrast the SIFT method performed relatively poorly on both low and high SNR inputs, but performed much better for intermediate values. Surprisingly the wavelet method consistently gave relatively poor results, only improving the SNR by a factor of around 2.

Both the SVD and Gaussian weighted sliding window give reliably high denoising across the range of input noise levels, but the Gaussian window is undoubtedly the most successful method for the forms of data considered here, offering an average 3.5 times improvement in SNR.