In this paper we are interested in the inverse problem of recovering a compact supported function from its truncated Fourier transform. We derive new Lipschitz stability estimates for the inversion in terms of the truncation parameter. The obtained results show that the Lipschitz constant is of order one when the truncation parameter is larger than the spatial frequency of the function, and it grows exponentially when the truncation parameter tends to zero. Finally, we present some numerical examples of reconstruction of a compactly supported function from its noisy truncated Fourier transform. The numerical illustrations validate our theoretical results.

翻译：本文研究从截断傅里叶变换重构紧支撑函数的反问题。我们依据截断参数推导了反演问题新的利普希茨稳定性估计。所得结果表明：当截断参数大于函数的空间频率时，利普希茨常数为阶一量级；而当截断参数趋于零时，该常数呈指数增长。最后，我们展示了从含噪截断傅里叶变换重构紧支撑函数的若干数值算例。数值算例验证了我们的理论结果。