Yang Ting, Liu Lin, Xiang You, Liu Shujun, Zhang Wenli
School of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing, 400067, China.
School of Microelectronics and Communication Engineering, Chongqing University, Chongqing, 400044, China.
Heliyon. 2024 Jun 12;10(12):e32659. doi: 10.1016/j.heliyon.2024.e32659. eCollection 2024 Jun 30.
In this paper, on the premise that the prior probability is unknown, a noise enhanced binary hypothesis-testing is investigated under the Minimax criterion for a general nonlinear system. Firstly, for lowering the decision risk, an additive noise is intentionally injected to the input and a decision is made under Minimax criterion based on the noise modified output. Then an optimization problem for minimizing the maximum of Bayesian conditional risk under an equality constraint is formulated via analyzing the relationship between the additive noise and the optimal noise modified Minimax decision rule. Furthermore, lemma and theorem are proposed to prove that the optimal noise is a constant vector, which simplifies the optimization problem greatly. An algorithm is also developed to search the optimal constant and the key parameter of detector, and further to determine the decision rule and the Bayes risk. Finally, simulation results about the original (in the absence of additive noise) and the noise-modified optimal decision solutions under Minimax criterion for a sine transform system are provided to illustrate the theoretical results.
本文在先验概率未知的前提下，针对一般非线性系统，研究了基于极小极大准则的噪声增强二元假设检验。首先，为降低决策风险，有意向输入中注入加性噪声，并基于噪声修改后的输出在极小极大准则下进行决策。然后，通过分析加性噪声与最优噪声修改极小极大决策规则之间的关系，构建了一个在等式约束下使贝叶斯条件风险最大值最小化的优化问题。此外，提出引理和定理以证明最优噪声是一个常向量，这极大地简化了优化问题。还开发了一种算法来搜索最优常数和检测器的关键参数，并进一步确定决策规则和贝叶斯风险。最后，给出了关于正弦变换系统在极小极大准则下原始（无加性噪声时）和噪声修改最优决策解的仿真结果，以说明理论结果。
