# Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

arXiv: https://arxiv.org/abs/1810.12249 · HTML: https://mlsanity.com/paper/1810.12249/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2018.

## Built on by (most cited first, 4 of 4)

- [Robust Hyperspectral Image Fusion with Simultaneous Guide Image Denoising via Constrained Convex Optimization](https://mlsanity.com/paper/2209.11979/) (2022)
- [Robust Foreground-Background Separation for Severely-Degraded Videos Using Convolutional Sparse Representation Modeling](https://mlsanity.com/paper/2506.17838/) (2025)
- [Graph Spatio-Spectral Total Variation Model for Hyperspectral Image Denoising](https://mlsanity.com/paper/2207.11050/) (2022)
- [Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction](https://mlsanity.com/paper/2601.11116/) (2026)

## Abstract (arXiv)

This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective function to be minimized. Such formulation facilitates the selection of regularization terms and hyperparameters, but due to the non-separability of the data-fidelity constraint, it does not suit block-coordinate-wise randomization as is. To resolve this, we give another expression of the data-fidelity constraint via epigraphs, which enables to design a randomized solver based on a stochastic proximal algorithm with randomized epigraphical projection. Our method is very efficient especially when the problem involves non-structured large matrices. We apply our method to CT image reconstruction, where the advantage of our method over the deterministic counterpart is demonstrated.