The problem of recovering a mixture of spike signals convolved with distinct point spread functions (PSFs) lying on a parametric manifold, under the assumption that the spike locations are known, is studied. The PSF unmixing problem is formulated as a projected non-linear least squares estimator. A lower bound on the radius of the region of strong convexity is established in the presence of noise as a function of the manifold coherence and Lipschitz properties, guaranteeing convergence and stability of the optimization program. Numerical experiments highlight the speed of decay of the PSF class in the problem's conditioning and confirm theoretical findings. Finally, the proposed estimator is deployed on real-world spectroscopic data from laser-induced breakdown spectroscopy (LIBS), removing the need for manual calibration and validating the method's practical relevance.

翻译：本文研究了在已知尖峰信号位置的前提下，从位于参数流形上的不同点扩散函数（PSF）与尖峰信号卷积的混合中恢复信号的问题。该PSF解混问题被表述为一个投影非线性最小二乘估计器。在噪声存在的情况下，本文建立了强凸区域半径的下界，该下界是流形相干性和Lipschitz性质的函数，从而保证了优化程序的收敛性和稳定性。数值实验揭示了PSF类别在问题条件数中的快速衰减特性，并验证了理论结果。最后，将所提出的估计器应用于激光诱导击穿光谱（LIBS）的真实光谱数据，无需手动校准，验证了该方法的实际应用价值。