Sensor plays an important role in modern manufacturing systems to monitor the manufacturing processes and machine health conditions. Especially for complex systems, multiple sensors need to be applied concurrently to collect different information. In recent decades, data fusion techniques have been developed to process data collected from multiple sensors simultaneously. Common data fusion techniques are based on traditional machine learning or deep learning algorithms such as support vector machines, deep random forest, k-nearest neighbours, and deep neural network. These methods are applied to process either original signals or features extracted from signals. The performance of existing data fusion methods depends on the resolution of signals. Signals with higher resolutions can provide more details of patterns. However, the challenges of using high-resolution signals in process monitoring are bandwidth limitation of data communication, increasing life-cycle cost of sensors, and physical limitations of data collection in practice. To address the above limitations of the existing data fusion methods, we propose a physics-constrained dictionary learning (PCDL) method to enable data fusion while reducing the volume of data collection. Thus, the proposed method can classify and reconstruct original signals with the low-resolution ones. The sensing efficiency can be significantly improved.