# Fast Inexact Bilevel Optimization for Analytical Deep Image Priors

arXiv: https://arxiv.org/abs/2502.09758 · HTML: https://mlsanity.com/paper/2502.09758/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2025.

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

- [Bilevel Learning via Inexact Stochastic Gradient Descent](https://mlsanity.com/paper/2511.06774/) (2025)

## Abstract (arXiv)

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.