A system and method for reconstructing a series of images of a subject includes acquiring medical image data from the subject with a medical imaging system and reconstructing a series of images of the subject from the acquired medical image data set. The reconstructing includes enforcing general adherence to a non-patient-specific signal model that describes a dependency of image intensity values on at least one variable that is associated with a physical or physiological property by constraining reconstruction of individual images in the series of images using the non-patient-specific model. The reconstructing also includes preserving information in the series of images that deviate from the non-patient-specific model by controlling a requirement of consistency with the non-patient-specific model.