Foveated rendering is an optimization technique that leverages the characteristics of the human visual system, where sensitivity decreases from the fovea to the periphery. This method produces lossy peripheral images with reduced computational workload while preserving equivalent visual perception. The ultimate goal is to create a visual metamer-an image that elicits identical visual stimuli and perceptions as the full-resolution counterpart. However, common methods often introduce noticeable blur or aliasing, which limits further computational reduction. Our approach advances this reduction by enhancing the peripheral vision in foveated rendering to achieve closer metamerism. Unlike traditional methods that rely on full-resolution references and are time-consuming, our method uses a lightweight neural network and undersampled inputs in a novel shrunk-log-polar sampling space. This arrangement allows for more efficient rendering and compact neural network input. Employing a novel metamer loss, our network enhances peripheral content, improving perceived visual quality to levels indistinguishable from traditional metamers. As a post-rendering pass, this neural enhancement module can operate in real-time on modern graphics cards.