This paper proposes a novel denoising method for polarimetric synthetic aperture radar (PolSAR) image preprocessing tasks with integration and applications for texture-like land images classification tasks. The method is developed using the partial differential equations framework and employs a multi-polarimetric tensor to capture the geometry of fully polarimetric PolSAR data. The filtering intensity is modulated by the multiplicative gradient norm computed on the total scattered power. The method has good texture preservation properties and it is integrated on a PolSAR image classification chain providing good recognition accuracy rates. Visual results on real PolSAR data of maritime pine forests stands are also provided for showing its effectiveness.