Magnetic resonance spectroscopy imaging (MRSI) is a powerful non-invasive tool for characterising markers of biological processes. This technique extends conventional MRI by providing an additional dimension of spectral information describing the abnormal presence or concentration of metabolites of interest. Unfortunately, in vivo MRSI suffers from poor signal-to-noise ratio limiting its clinical use for treatment purposes. This is due to the combination of a weak MR signal and low metabolite concentrations, in addition to the acquisition noise. We propose a new method that handles this challenge by efficiently denoising MRSI signals without constraining the spectral or spatial profiles. The proposed denoising approach is based on wavelet transforms and exploits the sparsity of the MRSI signals both in the spatial and frequency domains. A fast proximal optimization algorithm is then used to recover the optimal solution. Experiments on synthetic and real MRSI data showed that the proposed scheme achieves superior noise suppression (SNR increase up to 60%). In addition, this method is computationally efficient and preserves data features better than existing methods.