Deep Spectral Prior
Journal:
arXiv
Published Date:
May 26, 2025
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.
