Abstract: The research status of non-axismetrical arc spectrum diagnosis was reviewed, and the spectral diagnosis method of arc plasma and three-dimensional temperature field reconstruction algorithm were summarized.The applicability, advantages and disadvantages of Algebraic Reconstruction Technique (ART), Maximum Likelihood Maximization(MLEM), Total variation-projection Onto Convex Subsets(TV-POCS), and its derivative algorithms were analyzed, and the key research directions of the reconstruction algorithm in the future were prospected.It provides theoretical basis and technical support for subsequent research of arc plasma spectrum diagnosis in non-axisymmetric welding.