This paper introduces a variational formulation for image denoising based on a quadratic function over kernels of variable bandwidth. These kernels are scale adaptive and reflect spatial and photometric similarities between pixels. The bandwidth of the kernels is observation-dependent towards improving the accuracy of the reconstruction process and is constrained to be locally smooth. We analyze the evolution of the noise model form the RAW space to the RGB one, by propagating it over the image formation process. The experimental results demonstrate that the use of a variable bandwidth approach and an image intensity dependent noise variance ensures better restoration quality.