With increasing complexity of industrial processes, a number of variables are becoming increasingly large in modeling and monitoring steps, which is particularly prominent in dynamic processes. To address the issue of information redundancy in dynamic processes, this study proposes a sparse dynamic matrix estimation method (SDMEM) based on joint sparse constraints, which can effectively remove the irrelevant process variables and implement a more flexible structure for a dynamic process. Accordingly, the problem that dynamic features are difficult to extract owing to the high sampling rate is effectively solved by introducing differential information. Furthermore, a fast iterative optimization algorithm is designed for the proposed SDMEM with differential information (SDMEM-DI). A theoretical analysis shows the superiority of the proposed optimization algorithm in reducing computational complexity. Finally, experiments are conducted on a numerical example, a continuous stirred tank reactor (CSTR), and a catalytic cracking unit data of a refining and chemical plant, and the results show the effectiveness of the proposed SDMEM-DI.