Deep Spectral Prior

Yanqi Cheng
Tieyong Zeng
Pietro Lio
Carola-Bibiane Schönlieb
Angelica I. Aviles-Rivero

affiliations

Visualisation of What Our Proposed Deep Spectral Prior (DSP) Can Do
This is a website made for Deep Spectral Prior.

Abstract

We introduce Deep Spectral Prior (DSP), a new formulation of Deep Image Prior (DIP) that redefines image reconstruction as a frequency-domain alignment problem. Unlike traditional DIP, which relies on pixel-wise loss and early stopping to mitigate overfitting, DSP directly matches Fourier coefficients between the network output and observed measurements. This shift introduces an explicit inductive bias towards spectral coherence, aligning with the known frequency structure of images and the spectral bias of convolutional neural networks. We provide a rigorous theoretical framework demonstrating that DSP acts as an implicit spectral regulariser, suppressing high-frequency noise by design and eliminating the need for early stopping. Our analysis spans four core dimensions establishing smooth convergence dynamics, local stability, and favourable bias-variance tradeoffs. We further show that DSP naturally projects reconstructions onto a frequency-consistent manifold, enhancing interpretability and robustness. These theoretical guarantees are supported by empirical results across denoising, inpainting, and super-resolution tasks, where DSP consistently outperforms classical DIP and other unsupervised baselines.

Super-resolution
Inpainting
Restoration
Desnoising

Paper and Supplementary Material


Yanqi Cheng, Tieyong Zeng, Pietro Lio, Carola-Bibiane Schönlieb, Angelica I Aviles-Rivero.
Deep Spectral Prior


[arXiv]   [Bibtex]



Acknowledgements

YC is funded by an AstraZeneca studentship and a Google studentship. CBS acknowl- edges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC advanced career fellowship EP/V029428/1, EPSRC grants EP/S026045/1 and EP/T003553/1, EP/N014588/1, EP/T017961/1, the Wellcome Innovator Awards 215733/Z/19/Z and 221633/Z/20/Z, the European Union Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute. AIAR gratefully acknowledges the support from Yau Mathematical Sciences Center, Tsinghua University.