The advent of big data and AI has precipitated a demand for computational frameworks that ensure real-time performance, accuracy, and privacy. While edge computing mitigates latency and privacy concerns, its scalability is constrained by the resources of edge devices, thus prompting the adoption of split computing (SC) addresses these limitations. However, SC faces challenges in (1) efficient data transmission under bandwidth constraints and (2) balancing accuracy with real-time performance. To tackle these challenges, we propose a novel split computing architecture inspired by compressed sensing (CS) theory. At its core is the High-Efficiency Compressed Sensing Bottleneck (HECS-B), which incorporates an efficient compressed sensing autoencoder into the shallow layer of a deep neural network (DNN) to create a bottleneck layer using the knowledge distillation method. This bottleneck splits the DNN into a distributed model while efficiently compressing intermediate feature data, preserving critical information for seamless reconstruction in the cloud. Through rigorous theoretical analysis and extensive experimental validation in both simulated and real-world settings, we demonstrate the effectiveness of the proposed approach. Compared to state-of-the-art methods, our architecture reduces bandwidth utilization by 50%, maintains high accuracy, and achieves a 60% speed-up in computational efficiency. The results highlight significant improvements in bandwidth efficiency, processing speed, and model accuracy, underscoring the potential of HECS-B to bridge the gap between resource-constrained edge devices and computationally intensive cloud services.