The current research on still image recognition has been very successful, but the study of action recognition for video classes is still a challenging topic. In this work, we propose a random projection-based human action recognition algorithm to address the lack of depth information in color information (RGB video frames) that is not easily affected by environmental factors such as illumination and the lack of ability to recognize actions along the direction of view. A network structure is designed to take the obvious advantage of long- and short-term memory networks for controlling and remembering long sequences of historical information. The network structure in this paper is constituted by multiple memory units. At the same time, this paper constructs the spatial features, temporal features, and depth features of the three recognition stream outputs into a feature matrix, whose feature matrix is divided into multiple temporal segments according to the temporal dimension, then inputs them into the network layer in order, and achieves the fusion of the feature matrix in this paper according to their correlation characteristics on the temporal axis. Here, we proposed the concept of random batch projection operators. This basically uses as much sublimitation information as possible to improve projection accuracy by randomly selecting several subdependencies as projections defined during projection. A compressed sensing design of human motion acceleration data for low-power body area networks is proposed, and the basic idea and implementation process of compressed sensing theory for human motion data compression and reconstruction in wireless body area networks are introduced in detail.