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本文从最大后验概率密度观点出发，在数据噪音向量和待求模型向量为具有零均值的独立高斯随机过程的假设前提下，建立起了随机反演的非线性系统方程；给出了模型方差估计的函数表达式，并在文章最后，证明了反演解的稀疏性，即解释了随机反演的输出解的高分辨率特征。文章在最小二乘反演方法的基础上，发展并完善了随机反演方法的理论基础；揭示了随机反演方法与最小二乘反演方法之间的本质区别；阐述了随机反演方法的优越性，并指出了其广阔的应用前景。
Based on the assumption of maximum a posteriori probability density, a nonlinear system equation of stochastic inversion is established on the assumption that the data noise vector and the vector to be determined are independent Gaussian random processes with zero mean. The model variance At last, we prove the sparsity of inverse solution, that is, explain the high-resolution features of the output solution of stochastic inversion. Based on the least square inversion method, the paper develops and improves the theoretical basis of stochastic inversion method, reveals the essential difference between stochastic inversion method and least squares inversion method, and expounds the stochastic inversion method Superiority, and pointed out its broad application prospects.