The aim of this project is to keep the x-ray exposure of the patient as low as reasonably achievable while improving the diagnostic image quality for the radiologist. The means to achieve these goals is to develop and evaluate an ecient adaptive ltering (denoising/image enhancement) method that fully explores true 4D image acquisition modes. The proposed prototype system uses a novel lter set having directional lter responses being monomials. The monomial lter concept is used both for estimation of local structure and for the anisotropic adaptive ltering. Initial tests on clinical 4D CT-heart data with ECG-gated exposure has resulted in a signicant reduction of the noise level and an increased detail compared to 2D and 3D methods. Another promising feature is that the reconstruction induced streak artifacts which generally occur in low dose CT are remarkably reduced in 4D.