# A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially-Varying Generalised Gaussian Models

arXiv: https://arxiv.org/abs/2209.01375 · HTML: https://mlsanity.com/paper/2209.01375/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 78 references that are in the map.
- First posted on arXiv 3 Sep 2022.

## Builds on (most cited first, 12 of 12)

- [Proximal Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/1306.0187/) (2013)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems](https://mlsanity.com/paper/1706.06461/) (2017)
- [Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems](https://mlsanity.com/paper/1406.5429/) (2014)
- [Fixed Point Strategies in Data Science](https://mlsanity.com/paper/2008.02260/) (2020)
- [A Three-stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT)](https://mlsanity.com/paper/1506.00060/) (2015)
- [Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization](https://mlsanity.com/paper/1908.01402/) (2019)
- [Preconditioned P-ULA for Joint Deconvolution-Segmentation of Ultrasound Images -- Extended Version](https://mlsanity.com/paper/1903.08111/) (2019)
- [Variable Metric Forward-Backward Algorithm for Composite Minimization Problems](https://mlsanity.com/paper/1907.11486/) (2019)
- [Joint Segmentation and Deconvolution of Ultrasound Images Using a Hierarchical Bayesian Model based on Generalized Gaussian Priors](https://mlsanity.com/paper/1412.2813/) (2014)
- [Automated data-driven selection of the hyperparameters for Total-Variation based texture segmentation](https://mlsanity.com/paper/2004.09434/) (2020)
- [Space-variant Generalized Gaussian Regularization for Image Restoration](https://mlsanity.com/paper/1906.10517/) (2019)

## Abstract (arXiv)

The joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly propose a novel nonsmooth and non-convex variational formulation of the problem. For this purpose, we introduce a versatile generalised Gaussian prior whose parameters, including its exponent, are space-variant. Secondly, we design an alternating proximal-based optimisation algorithm that efficiently exploits the structure of the proposed non-convex objective function. We also analyse the convergence of this algorithm. As shown in numerical experiments conducted on joint deblurring/segmentation tasks, the proposed method provides high-quality results.