# Improved Imaging by Invex Regularizers with Global Optima Guarantees

arXiv: https://arxiv.org/abs/2211.10112 · HTML: https://mlsanity.com/paper/2211.10112/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2022.

## Built on by (most cited first, 6 of 6)

- [Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation](https://mlsanity.com/paper/2402.01052/) (2024)
- [Outlier-robust Estimation of a Sparse Linear Model Using Invexity](https://mlsanity.com/paper/2306.12678/) (2023)
- [Invex Programs: First Order Algorithms and Their Convergence](https://mlsanity.com/paper/2307.04456/) (2023)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Deep Learning Evidence for Global Optimality of Gerver's Sofa](https://mlsanity.com/paper/2407.11106/) (2024)
- [Cauchy-Schwarz Regularizers](https://mlsanity.com/paper/2503.01639/) (2025)

## Abstract (arXiv)

Image reconstruction enhanced by regularizers, e.g., to enforce sparsity, low rank or smoothness priors on images, has many successful applications in vision tasks such as computer photography, biomedical and spectral imaging. It has been well accepted that non-convex regularizers normally perform better than convex ones in terms of the reconstruction quality. But their convergence analysis is only established to a critical point, rather than the global optima. To mitigate the loss of guarantees for global optima, we propose to apply the concept of textitinvexity and provide the first list of proved invex regularizers for improving image reconstruction. Moreover, we establish convergence guarantees to global optima for various advanced image reconstruction techniques after being improved by such invex regularization. To the best of our knowledge, this is the first practical work applying invex regularization to improve imaging with global optima guarantees. To demonstrate the effectiveness of invex regularization, numerical experiments are conducted for various imaging tasks using benchmark datasets.