We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We derive results on the uniqueness and stability of the inverse problem in the case of small boundary data based on the technique of first- and higher-order linearization. Numerical simulations are provided to illustrate the quality of reconstructions that can be expected from noisy data.

翻译：本文研究耦合的半线性亥姆霍兹方程组的反问题，旨在从热声成像等应用中测量的内部数据重建系统中的多个系数。基于一阶及高阶线性化技术，我们在小边界数据情形下推导了该反问题的唯一性和稳定性结果。通过数值模拟展示了在含噪数据下可预期的重建质量。