We propose two formulations to leverage the geometric properties of bivariate signals for dealing with the denoising problem. In doing so, we use the instantaneous Stokes parameters to incorporate the polarization state of the signal. While the first formulation exploits the statistics of the Stokes representation in a Bayesian setting, the second uses a kernel regression formulation to impose locally smooth time-varying polarization properties. In turn, we obtain two formulations that allow us to use both signal and polarization domain regularization for denoising a bivariate signal. The solutions to them exploit the polarization information efficiently as demonstrated in the numerical simulations