# PIP: Positional-encoding Image Prior

arXiv: https://arxiv.org/abs/2211.14298 · HTML: https://mlsanity.com/paper/2211.14298/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 56 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [The 2017 DAVIS Challenge on Video Object Segmentation](https://mlsanity.com/paper/1704.00675/) (2017)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [NeRF in the Dark: High Dynamic Range View Synthesis from Noisy Raw Images](https://mlsanity.com/paper/2111.13679/) (2021)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- ["Double-DIP": Unsupervised Image Decomposition via Coupled Deep-Image-Priors](https://mlsanity.com/paper/1812.00467/) (2018)
- [Neural Blind Deconvolution Using Deep Priors](https://mlsanity.com/paper/1908.02197/) (2019)
- [Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding](https://mlsanity.com/paper/2106.02795/) (2021)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Blind Video Temporal Consistency via Deep Video Prior](https://mlsanity.com/paper/2010.11838/) (2020)
- [E-NeRV: Expedite Neural Video Representation with Disentangled Spatial-Temporal Context](https://mlsanity.com/paper/2207.08132/) (2022)
- [Real-world Noisy Image Denoising: A New Benchmark](https://mlsanity.com/paper/1804.02603/) (2018)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Positional Encoding as Spatial Inductive Bias in GANs](https://mlsanity.com/paper/2012.05217/) (2020)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Omnimatte: Associating Objects and Their Effects in Video](https://mlsanity.com/paper/2105.06993/) (2021)
- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)
- [A Robust Volumetric Transformer for Accurate 3D Tumor Segmentation](https://mlsanity.com/paper/2111.13300/) (2021)
- [On Measuring and Controlling the Spectral Bias of the Deep Image Prior](https://mlsanity.com/paper/2107.01125/) (2021)
- [An Internal Learning Approach to Video Inpainting](https://mlsanity.com/paper/1909.07957/) (2019)
- [The Spectral Bias of the Deep Image Prior](https://mlsanity.com/paper/1912.08905/) (2019)
- [NAS-DIP: Learning Deep Image Prior with Neural Architecture Search](https://mlsanity.com/paper/2008.11713/) (2020)

## Built on by (most cited first, 3 of 3)

- [Deep Internal Learning: Deep Learning from a Single Input](https://mlsanity.com/paper/2312.07425/) (2023)
- [Deep Phase Coded Image Prior](https://mlsanity.com/paper/2404.03906/) (2024)
- [WaterWave: Bridging Underwater Image Enhancement into Video Streams via Wavelet-based Temporal Consistency Field](https://mlsanity.com/paper/2512.05492/) (2025)

## Abstract (arXiv)

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 or learned latent with Fourier-Features (Positional Encoding). We show that thanks to the Fourier features properties, we can replace the convolution layers with simple pixel-level MLPs. We name this scheme ``Positional Encoding Image Prior" (PIP) and exhibit that it performs very similarly to DIP on various image-reconstruction tasks with much less parameters required. Additionally, we demonstrate that PIP can be easily extended to videos, where 3D-DIP struggles and suffers from instability. Code and additional examples for all tasks, including videos, are available on the project page https://nimrodshabtay.github.io/PIP/