We investigate minimax testing for detecting local signals or linear combinations of such signals when only indirect data is available. Naturally, in the presence of noise, signals that are too small cannot be reliably detected. In a Gaussian white noise model, we discuss upper and lower bounds for the minimal size of the signal such that testing with small error probabilities is possible. In certain situations we are able to characterize the asymptotic minimax detection boundary. Our results are applied to inverse problems such as numerical differentiation, deconvolution and the inversion of the Radon transform.

翻译：本文研究在仅能获取间接数据时，检测局部信号或此类信号线性组合的极小极大检验问题。在噪声存在的情况下，过小的信号自然无法被可靠检测。针对高斯白噪声模型，我们探讨了信号最小规模的上下界，使得在此条件下能以较小误差概率进行检验。在某些情形下，我们能够刻画渐近极小极大检测边界。所得结果应用于数值微分、反卷积及拉东变换逆变换等逆问题。