# Compressed Dynamic Mode Decomposition for Background Modeling

arXiv: https://arxiv.org/abs/1512.04205 · HTML: https://mlsanity.com/paper/1512.04205/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2015.

## Built on by (most cited first, 17 of 17)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties](https://mlsanity.com/paper/2106.06033/) (2021)
- [Learning Temporal Distribution and Spatial Correlation Towards Universal Moving Object Segmentation](https://mlsanity.com/paper/2304.09949/) (2023)
- [Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations](https://mlsanity.com/paper/2104.14034/) (2021)
- [Quaternion-based dynamic mode decomposition for background modeling in color videos](https://mlsanity.com/paper/2112.13982/) (2021)
- [Physics-Informed Koopman Network](https://mlsanity.com/paper/2211.09419/) (2022)
- [Spatial-Temporal Map Vehicle Trajectory Detection Using Dynamic Mode Decomposition and Res-UNet+ Neural Networks](https://mlsanity.com/paper/2201.04755/) (2022)
- [Digital Twin Data Modelling by Randomized Orthogonal Decomposition and Deep Learning](https://mlsanity.com/paper/2206.08659/) (2022)
- [Geometric Change Detection in Digital Twins using 3D Machine Learning](https://mlsanity.com/paper/2103.08201/) (2021)
- [Deep Learning Based Object Tracking in Walking Droplet and Granular Intruder Experiments](https://mlsanity.com/paper/2302.05425/) (2023)
- [Featurizing Koopman Mode Decomposition For Robust Forecasting](https://mlsanity.com/paper/2312.09146/) (2023)
- [Real-Time Motion Detection Using Dynamic Mode Decomposition](https://mlsanity.com/paper/2405.05057/) (2024)
- [Self-Supervised Video Representation Learning in a Heuristic Decoupled Perspective](https://mlsanity.com/paper/2407.14069/) (2024)
- [Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures](https://mlsanity.com/paper/2507.19787/) (2025)
- [Koopman Regularized Deep Speech Disentanglement for Speaker Verification](https://mlsanity.com/paper/2603.05577/) (2026)
- [DMDIntel: Interpreting Large Language Models via Dynamic Mode Decomposition](https://mlsanity.com/paper/2608.13048/) (2026)

## Abstract (arXiv)

We introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling. The dynamic mode decomposition (DMD) is a regression technique that integrates two of the leading data analysis methods in use today: Fourier transforms and singular value decomposition. Borrowing ideas from compressed sensing and matrix sketching, cDMD eases the computational workload of high resolution video processing. The key principal of cDMD is to obtain the decomposition on a (small) compressed matrix representation of the video feed. Hence, the cDMD algorithm scales with the intrinsic rank of the matrix, rather then the size of the actual video (data) matrix. Selection of the optimal modes characterizing the background is formulated as a sparsity-constrained sparse coding problem. Our results show, that the quality of the resulting background model is competitive, quantified by the F-measure, Recall and Precision. A GPU (graphics processing unit) accelerated implementation is also presented which further boosts the computational efficiency of the algorithm.