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：我们调查在只有间接数据的情况下检测本地信号或此类信号的线性组合的小型最大测试。 当然,在有噪音的情况下,无法可靠地检测到太小的信号。在高西亚白色噪音模型中,我们讨论信号最小尺寸的上下界限,这样就有可能进行小误差概率测试。在某些情况下,我们能够描述微量信号探测边界的特征。我们的结果被用于反向的问题,如数字差异、分变和拉登变异。