The method for removing noise from nuclear magnetic resonance signals and images involves removing noise from NMR signals through the application of stable linear time-frequency (SLTF) transforms. According to the method, a noise variance for a particular NMR signal is calculated and the NMR signal is sampled and digitized. A set of analysis samples that vary in the number of samples in frequency is selected so that each member of the set has a compact signal/image representation for at least one component according to the differing component relaxation times of the signal/image. Each member of the set is then processed by the SLTF to determine the transform coefficients, the coefficients are subjected to threshold value criteria to denoise the coefficients, and the inverse SLTF transform is computed for each member of the set to obtain the denoised signal. The member signals are then averaged to obtain the denoised NMR signal.