  We study the interpolation capabilities of implicit neural representations
(INRs) of images. In principle, INRs promise a number of advantages, such as
continuous derivatives and arbitrary sampling, being freed from the
restrictions of a raster grid. However, empirically, INRs have been observed to
poorly interpolate between the pixels of the fit image; in other words, they do
not inherently possess a suitable prior for natural images. In this paper, we
propose to address and improve INRs' interpolation capabilities by explicitly
integrating image prior information into the INR architecture via deep decoder,
a specific implementation of the deep image prior (DIP). Our method, which we
call TITAN, leverages a residual connection from the input which enables
integrating the principles of the grid-based DIP into the grid-free INR.
Through super-resolution and computed tomography experiments, we demonstrate
that our method significantly improves upon classic INRs, thanks to the induced
natural image bias. We also find that by constraining the weights to be sparse,
image quality and sharpness are enhanced, increasing the Lipschitz constant.
