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Compressed sensing (CS) as a new data acquisition technique has been applied to monitor manufacturing processes. With a few measurements, sparse coefficient vectors can be recovered by solving an inverse problem and original signals can be reconstructed. Dictionary learning methods have been developed and applied in combination with CS to improve the sparsity level of the recovered coefficient vectors. In this work, a physics-constrained dictionary learning approach is proposed to solve both of reconstruction and classification problems by optimizing measurement, basis, and classification matrices simultaneously with the considerations of the application-specific restrictions. It is applied in image acquisitions in selective laser melting (SLM). The proposed approach includes the optimization in two steps. In the first stage, with the basis matrix fixed, the measurement matrix is optimized by determining the pixel locations for sampling in each image. The optimized measurement matrix only includes one non-zero entry in each row. The optimization of pixel locations is solved based on a constrained FrameSense algorithm. In the second stage, with the measurement matrix fixed, the basis and classification matrices are optimized based on the K-SVD algorithm. With the optimized basis matrix, the coefficient vector can be recovered with CS. The original signal can be reconstructed by the linear combination of the basis matrix and the recovered coefficient vector. The original signal can also be classified to identify different machine states by the linear combination of the classification matrix and the coefficient vector.