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 de-noising algorithm. It is shown to be particularly successful in recovering weak signals that are practically drowned by the noise