Abstract: This paper studies three aspects of compressive sensing theory, optimization algorithms, and their applications in system state reconstruction. In compressive sensing theory, the relationship between the sparse and low rank of the compressed signal is studied, together with signal measurement and their relationship with the optimization algorithm. We focus on the analysis of the sparse original signal and the relationship between low rank; the relationship between the measurement matrix and the matrix compression, the measurement matrix satisfied the restricted isometry property (RIP), and the minimum number of measurements provided by the compressive sensing theory. The convex optimization problem of kernel function is discussed with respect to optimization algorithms used in reconstruction of the compressed signal. Characteristics of traditional optimization algorithms, including the least squares (LS) method, maximum entropy method, maximum likelihood method, and bias method are summarized and analyzed in the process of solving the performance index, optimization goal, and solution conditions. The alternating direction multiplier method (ADMM) and iterative threshold shrinkage method (IST) are also used to estimate quantum states, and application examples of pure state estimations with 5, 6, and 7 qubits are assumed. In addition, the effects of parameter estimation performances with different measurement rates and different algorithms in different qubits are compared on different levels. Finally, the research process used in system parameter estimation is fully explained based on optimization and compressive sensing theory.