Computing in the network (COIN) exploits the sparce computing power of network nodes to offload applications' computations. This paradigm benefits computation-demanding applications, such as source separation for acoustic anomaly detection. However, wider adoption of COIN has not occurred due to intertwined challenges. The monolithic design of the source separation algorithms and the lack of a flexible transport layer in COIN hinders its exploitation. This article presents network joint independent component analysis (NJICA), leveraging COIN to recover original acoustic sources from a mixture of raw sensory signals. NJICA redesigns the monolithic algorithm for source separation into a distributed one to unleash the offloading capability to an arbitrary number of network nodes. Furthermore, NJICA develops a message-based transport layer that allows aggregating application data at network nodes and differentiating message types. Extensive evaluations of the practical implementation of NJICA using a realistic dataset shows that NJICA significantly reduces both the computation and service latencies.