# Semi-Sparsity for Smoothing Filters

arXiv: https://arxiv.org/abs/2107.00627 · HTML: https://mlsanity.com/paper/2107.00627/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 91 references that are in the map.
- First posted on arXiv 1 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [NIMA: Neural Image Assessment](https://mlsanity.com/paper/1709.05424/) (2017)
- [The Fast Bilateral Solver](https://mlsanity.com/paper/1511.03296/) (2015)
- [Static/Dynamic Filtering for Mesh Geometry](https://mlsanity.com/paper/1712.03574/) (2017)
- [Sparse Regularization: Convergence Of Iterative Jumping Thresholding Algorithm](https://mlsanity.com/paper/1402.5744/) (2014)
- [Triangulated Surface Denoising using High Order Regularization with Dynamic Weights](https://mlsanity.com/paper/1711.08137/) (2017)
- [Sparse Norm Filtering](https://mlsanity.com/paper/1305.3971/) (2013)

## Built on by (most cited first, 3 of 3)

- [Bridging the Gap between Multi-focus and Multi-modal: A Focused Integration Framework for Multi-modal Image Fusion](https://mlsanity.com/paper/2311.01886/) (2023)
- [Semi-sparsity Priors for Image Structure Analysis and Extraction](https://mlsanity.com/paper/2308.09141/) (2023)
- [Deep Image Prior with L0 Gradient Regularizer for Image Smoothing](https://mlsanity.com/paper/2601.13400/) (2026)

## Abstract (arXiv)

In this paper, we propose an interesting semi-sparsity smoothing algorithm based on a novel sparsity-inducing optimization framework. This method is derived from the multiple observations that semi-sparsity prior knowledge is more universally applicable, especially in areas where sparsity is not fully admitted, such as polynomial-smoothing surfaces. We illustrate that this semi-sparsity can be identified into a generalized L0-norm minimization in higher-order gradient domains, thereby giving rise to a new "feature-aware" filtering method with a powerful simultaneous-fitting ability in both sparse features (singularities and sharpening edges) and non-sparse regions (polynomial-smoothing surfaces). Notice that a direct solver is always unavailable due to the non-convexity and combinatorial nature of L0-norm minimization. Instead, we solve the model based on an efficient half-quadratic splitting minimization with fast Fourier transforms (FFTs) for acceleration. We finally demonstrate its versatility and many benefits to a series of signal/image processing and computer vision applications.