On the wavelet analysis of CMB time ordered data: application to Archeops

We present an alternative analysis of CMB time ordered data (TOD) using a wavelet-based representation of the data time-frequency plane. We demonstrate that the wavelet transform decorrelates $1/f$-type Gaussian stationary noise and permits a simple and functional description of locally stationary processes. In particular, this makes possible the generalization of the classical algorithms of map making and CMB power spectrum estimation to the case of locally stationary 1/f type noise. As an example, we present a wavelet based algorithm for the destriping of CMB-like maps. In addition, we describe a wavelet-based analysis of the Archeops data including time-frequency visualization, wavelet destriping and filtering of the TOD. These filtered data was used to produce polarized maps of Galactic dust diffuse emission. Finally, we describe the modeling of the non-stationarity on the Archeops noise for the estimation of the CMB power spectrum.