Background subtraction is an important task for visual surveillance systems. However, this task becomes more complex when the data size grows since the real-world scenario requires larger data to be processed in a more efficient way, and in some cases, in a continuous manner. Until now, most of background subtraction algorithms were designed for mono or trichromatic cameras within the visible spectrum or near infrared part. Recent advances in multispectral imaging technologies give the possibility to record multispectral videos for video surveillance applications. Due to the specific nature of these data, many of the bands within multispectral images are often strongly correlated. In addition, processing multispectral images with hundreds of bands can be computationally burdensome. In order to address these major difficulties of multispectral imaging for video surveillance, this paper propose an online stochastic framework for tensor decomposition of multispectral video sequences (OSTD). The source code is available only for academic/research purposes (non-commercial).