# Deep Image Prior with L0 Gradient Regularizer for Image Smoothing

arXiv: https://arxiv.org/abs/2601.13400 · HTML: https://mlsanity.com/paper/2601.13400/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Image Restoration using Total Variation Regularized Deep Image Prior](https://mlsanity.com/paper/1810.12864/) (2018)
- [A Generalized Framework for Edge-preserving and Structure-preserving Image Smoothing](https://mlsanity.com/paper/1907.09642/) (2019)
- [Combining Weighted Total Variation and Deep Image Prior for natural and medical image restoration via ADMM](https://mlsanity.com/paper/2009.11380/) (2020)
- [A Benchmark for Edge-Preserving Image Smoothing](https://mlsanity.com/paper/1904.01579/) (2019)
- [Semi-Global Weighted Least Squares in Image Filtering](https://mlsanity.com/paper/1705.01674/) (2017)
- [Semi-Sparsity for Smoothing Filters](https://mlsanity.com/paper/2107.00627/) (2021)

## Abstract (arXiv)

Image smoothing is a fundamental image processing operation that preserves the underlying structure, such as strong edges and contours, and removes minor details and textures in an image. Many image smoothing algorithms rely on computing local window statistics or solving an optimization problem. Recent state-of-the-art methods leverage deep learning, but they require a carefully curated training dataset. Because constructing a proper training dataset for image smoothing is challenging, we propose DIP-ℓ0, a deep image prior framework that incorporates the ℓ0 gradient regularizer. This framework can perform high-quality image smoothing without any training data. To properly minimize the associated loss function that has the nonconvex, nonsmooth ℓ0 ``norm", we develop an alternating direction method of multipliers algorithm that utilizes an off-the-shelf ℓ0 gradient minimization solver. Numerical experiments demonstrate that the proposed DIP-ℓ0 outperforms many image smoothing algorithms in edge-preserving image smoothing and JPEG artifact removal.