Positional Encoding Image Prior

In Deep Image Prior (DIP), a Convolutional Neural Network (CNN) is fitted to map a latent space to a degraded (e.g. noisy) image but in the process learns to reconstruct the clean image. This phenomenon is attributed to CNN's internal image prior. We revisit the DIP framework, examining it from the perspective of a neural implicit representation. Motivated by this perspective, we replace the random latent with Fourier-Features (Positional Encoding). We empirically demonstrate that the convolution layers in DIP can be replaced with simple pixel-level MLPs thanks to the Fourier features properties. We also prove that they are equivalent in the case of linear networks. We name our scheme "Positional Encoding Image Prior" (PIP) and exhibit that it performs very similar to DIP on various image-reconstruction tasks with much fewer parameters. Furthermore, we demonstrate that PIP can be easily extended to videos, an area where methods based on image-priors and certain INR approaches face challenges with stability. Code and additional examples for all tasks, including videos, are available on the project page nimrodshabtay.github.io/PIP.