Noise reduction in astronomical spectra using wavelet packets

The wavelet representation of a signal offers greater flexibility in de-noising astronomical spectra than classical Fourier smoothing due to the additional wavelength resolution of the decomposed signal. We present here a new wavelet-based approach to noise reduction. It is similar to an application of the splitting algorithm of a wavelet packets analysis using non-orthogonal wavelets. It clearly separates the signal from the noise, in particular also at the noise-dominated highest frequencies. This allows a better suppression of the noise, so that the spectrum de-noised in this manner provides a closer approximation of the uncorrupted signal than in the case of a single wavelet transformation or a Fourier transform. We test this method on intensity and circularly polarized spectra of the sun and compare with Fourier and other wavelet-based de-noising algorithms. Our technique is found to give better results than any other tested denoising algorithm. It is shown to be particularly successful in recovering weak signals that are practically drowned by the noise.