Fast Inexact Bilevel Optimization for Analytical Deep Image Priors

TL;DR

This paper introduces an adaptive inexact bilevel optimization method to efficiently solve analytical deep image prior problems, enabling faster processing of large-scale image restoration tasks like 2D color image deblurring.

Contribution

It extends a recent inexact bilevel method to infinite-dimensional problems, significantly improving computational efficiency for ADP-based image restoration.

Findings

Achieves faster computation for ADP in large-scale problems

Enables application of ADP to 2D color image deblurring

Demonstrates effectiveness through numerical experiments

Abstract

The analytical deep image prior (ADP) introduced by Dittmer et al. (2020) establishes a link between deep image priors and classical regularization theory via bilevel optimization. While this is an elegant construction, it involves expensive computations if the lower-level problem is to be solved accurately. To overcome this issue, we propose to use adaptive inexact bilevel optimization to solve ADP problems. We discuss an extension of a recent inexact bilevel method called the method of adaptive inexact descent of Salehi et al.(2024) to an infinite-dimensional setting required by the ADP framework. In our numerical experiments we demonstrate that the computational speed-up achieved by adaptive inexact bilevel optimization allows one to use ADP on larger-scale problems than in the previous literature, e.g. in deblurring of 2D color images.