ing at the problems of low precision and slow speed of the traditional reconstruction algorithms, we propose a regularization priori based fast all variation algebraic iteration (ARTTV) algorithm to improve the reconstruction precision of the symmetric and asymmetric flames. Further, to improve the reconstruction speed, we establish an extreme learning machine neural network based on the “ARTTV-particle swarm algorithm kernel”, which exhibits approximately the same reconstruction ability as that of the iterative algorithm. The construction speed of the proposed algorithm is approximately 300 times that of the iterative algorithm.