# Deep Spectral Prior

arXiv: https://arxiv.org/abs/2505.19873 · HTML: https://mlsanity.com/paper/2505.19873/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 53 references that are in the map.
- First posted on arXiv 26 May 2025.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Free-Form Image Inpainting with Gated Convolution](https://mlsanity.com/paper/1806.03589/) (2018)
- [ResShift: Efficient Diffusion Model for Image Super-resolution by Residual Shifting](https://mlsanity.com/paper/2307.12348/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [SinSR: Diffusion-Based Image Super-Resolution in a Single Step](https://mlsanity.com/paper/2311.14760/) (2023)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Image Restoration using Total Variation Regularized Deep Image Prior](https://mlsanity.com/paper/1810.12864/) (2018)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [Compressed Sensing with Deep Image Prior and Learned Regularization](https://mlsanity.com/paper/1806.06438/) (2018)
- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)
- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Rethinking Deep Image Prior for Denoising](https://mlsanity.com/paper/2108.12841/) (2021)
- [NAS-DIP: Learning Deep Image Prior with Neural Architecture Search](https://mlsanity.com/paper/2008.11713/) (2020)
- [Region-wise Generative Adversarial ImageInpainting for Large Missing Areas](https://mlsanity.com/paper/1909.12507/) (2019)
- [Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting](https://mlsanity.com/paper/2011.01748/) (2020)
- [PrefPaint: Aligning Image Inpainting Diffusion Model with Human Preference](https://mlsanity.com/paper/2410.21966/) (2024)
- [An Educated Warm Start For Deep Image Prior-Based Micro CT Reconstruction](https://mlsanity.com/paper/2111.11926/) (2021)
- [Diffraction tomography with a deep image prior](https://mlsanity.com/paper/1912.05330/) (2019)
- [Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstruction](https://mlsanity.com/paper/2402.04097/) (2024)
- [Efficient Attention-Sharing Information Distillation Transformer for Lightweight Single Image Super-Resolution](https://mlsanity.com/paper/2501.15774/) (2025)
- [Single-Shot Plug-and-Play Methods for Inverse Problems](https://mlsanity.com/paper/2311.13682/) (2023)
- [Sequential Diffusion-Guided Deep Image Prior For Medical Image Reconstruction](https://mlsanity.com/paper/2410.04482/) (2024)
- [You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors](https://mlsanity.com/paper/2412.06204/) (2024)

## Built on by (most cited first, 1 of 1)

- [DNA-Prior: Unsupervised Denoise Anything via Dual-Domain Prior](https://mlsanity.com/paper/2511.23124/) (2025)

## Abstract (arXiv)

We introduce the Deep Spectral Prior (DSP), a new framework for unsupervised image reconstruction that operates entirely in the complex frequency domain. Unlike the Deep Image Prior (DIP), which optimises pixel-level errors and is highly sensitive to overfitting, DSP performs joint learning of amplitude and phase to capture the full spectral structure of images. We derive a rigorous theoretical characterisation of DSP's optimisation dynamics, proving that it follows frequency-dependent descent trajectories that separate informative low-frequency modes from stochastic high-frequency noise. This spectral mode separation explains DSP's self-regularising behaviour and, for the first time, formally establishes the elimination of DIP's major limitation-its reliance on manual early stopping. Moreover, DSP induces an implicit projection onto a frequency-consistent manifold, ensuring convergence to stable, physically plausible reconstructions without explicit priors or supervision. Extensive experiments on denoising, inpainting, and deblurring demonstrate that DSP consistently surpasses DIP and other unsupervised baselines, achieving superior fidelity, robustness, and theoretical interpretability within a unified, unsupervised data-free framework.