Work

Deep Spectral Prior

Year: 2025

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.19873

Authors: Cheng, Yanqi, Zhao, Xuxiang, Zeng, Tieyong, Lio, Pietro, Schönlieb, Carola-Bibiane, Aviles-Rivero, Angelica I

Institutions: University of Cambridge, Chinese University of Hong Kong, Tsinghua University

Language: English

Topic: Generative Adversarial Networks and Image Synthesis

Subfield: Computer Vision and Pattern Recognition

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: AstraZeneca, W. F. Albright Institute of Archaeological Research, Leverhulme Trust, European Commission, Tsinghua University, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: Nonlocal Methods for Arbitrary Data Sources, Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India, G434337789, Cambridge Mathematics of Information in Healthcare (CMIH), EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, Combining Knowledge And Data Driven Approaches to Inverse Imaging Problems, PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation

OpenAlex ID: W4414587374

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