Poisson noise removal has been implemented by several methods and several approaches. This type of noise generally affects several types of images and in the whole case medical images especially those rebuilt after an X radiation. About it, as tests images are CT ones, further, we will present two methods derived from two different approaches to Poisson noise removal. one that is variational, which is a restoring process that takes into account the actual appearance of this noise which is multiplicative, the other methods derived from wavelet approach which is among the growing methods for the Poisson noise removal mainly in medical dataset. This method is called PURE-LET, simply to say Poisson Unbiased Risk Estimation-Linear Expansion of thresholds. This latter is based on of an optimization of statistical tool Mean Square Error (MSE) using an unnormalized Haar decomposition wavelet transform (DWT) and exploiting the property of the orthogonality of these latter. An original comparison at the end of this paper allows us to assess the reliability and robustness of either the variational method or the PURE-LET one against the annoying factors in medical imaging such as artifact, spatial resolution, etc. Finally, we come to the conclusion that the Variational method excels at the Pure-Let wavelet method.