Noise reduction or denoising is the process of removing noise from a signal. If some signal properties are known linear filtering is often useful. Fourier, wavelet and similar transform approaches remove unwanted signal components in the codomain. For this, predefined eigen-functions, e.g. wavelets, are used. Here we use singular value decomposition in order to compute a signal driven re-presentation (eigendecompositon). By removing unwanted components of the representation the signal can be denoised. We introduce the new method, apply it to signals and discuss its properties.