Many existing Natural Scene Statistics-based no reference image quality assessment (NR IQA) algorithms employ parametric distributions to capture the statistical inconsistencies of bandpass distorted image coefficients. Here we propose a model of natural image coefficients expressed in the bandpass spatial domain that has the potential to capture higher-order correlations that may be induced by the presence of distortions. We analyze how the parameters of the multivariate model are affected by different distortion types, and we show their ability to capture distortion-sensitive image quality information. We also demonstrate the violation of Gaussianity assumptions that occur when locally estimating the energies of image coefficients. Thus we propose a generalized Gaussian-based local contrast estimator as a way to implement non-linear local gain control, that facilitates the accurate modeling of both pristine and distorted images. We integrate the novel approach of generalized contrast normalization with multivariate modeling of bandpass image coefficients into a holistic NR IQA model, which we refer to as multivariate generalized contrast normalization (MVGCN). We demonstrate the improved performance of MVGCN on quality relevant tasks on multiple imaging modalities, including visible light image quality prediction and task success prediction on distorted X-ray images.