Compressed Dynamic Mode Decomposition for Background Modeling

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.