Parametric imaging of the cerebral metabolic rate for glucose (CMRGlc) using [(18)F]-fluoro deoxyglucose positron emission tomography is considered. Traditional imaging is hindered due to low signal-to-noise ratios at individual voxels. We propose to minimize the total variation of the tracer uptake rates while requiring good fit of traditional Patlak equations. This minimization guarantees spatial homogeneity within brain regions and good distinction between brain regions. Brain phantom simulations demonstrate significant improvement in quality of images by the proposed method as compared to Patlak images with post-filtering using Gaussian or median filters.