In passive polarization imaging, the degree and the angle of linear polarization images are representations of the polarization content in the scene that can be used to detect small polarized objects in a largely randomly polarized surrounding. The polarized signal is often near the noise limit of a photon detector (as in CCD and CMOS cameras) and sensitivity to polarization deteriorates further when the source imagery is under-exposed. This work aims to increase the robustness to sensor noise by estimating the Cartesian coordinates of the degree and angle of linear polarization-a notion we refer to as "Stokes simplex." The proposed Stokes Simplex Polarimetric Image Denoising (SSPID) algorithm is the minimum mean squared error estimation of the noise-free Stokes simplex vectors in the wavelet domain from the Poisson corrupted analyzer images. Benchmarking against the state-of-the-art polarization image denoising methods on a newly acquired division-of-time (DoT) polarimetric data shows superior performance.