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Improving the signal-to-noise-ratio (SNR) of magnetic resonance imaging (MRI) using denoising techniques could enhance their value, provided that signal statistics and image resolution are not compromised. Here, a new denoising method based on spectral subtraction of the measured noise power from each signal acquisition is presented. Spectral subtraction denoising (SSD) assumes no prior knowledge of the acquired signal and does not increase acquisition time. Whereas conventional denoising/filtering methods are compromised in parallel imaging by spatially dependent noise statistics, SSD is performed on signals acquired from each coil separately, prior to reconstruction. Using numerical simulations, we show that SSD can improve SNR by up to ~45% in MRI reconstructed from both single and array coils, without compromising image resolution. Application of SSD to phantom, human heart, and brain MRI achieved SNR improvements of ~40% compared to conventional reconstruction. Comparison of SSD with anisotropic diffusion filtering showed comparable SNR enhancement at low-SNR levels (SNR = 5-15) but improved accuracy and retention of structural detail at a reduced computational load.