论文标题
削减Prony的稳定超分辨率的方法
Decimated Prony's Method for Stable Super-resolution
论文作者
论文摘要
我们研究了从嘈杂频率样品中的有限冲动列车的振幅和节点的恢复。这个问题被称为稀疏性约束下的超分辨率，并且具有许多应用。当Dirac脉冲之间的分离小于Nyquist-Shannon-Rayleigh限制时，就会发生一个特别具有挑战性的情况。尽管大量的研究和公认的最差循环恢复界限，但目前尚无已知的计算有效方法，可以实现这些界限。在这项工作中，我们将著名的Prony的指数拟合方法与最近建立的分解技术结合在一起，用于分析上述制度中的超分辨率问题。我们表明，我们的方法在存在噪声的情况下达到了最佳的渐近稳定性，并且计算复杂性低于当前方法的现状。
We study recovery of amplitudes and nodes of a finite impulse train from noisy frequency samples. This problem is known as super-resolution under sparsity constraints and has numerous applications. An especially challenging scenario occurs when the separation between Dirac pulses is smaller than the Nyquist-Shannon-Rayleigh limit. Despite large volumes of research and well-established worst-case recovery bounds, there is currently no known computationally efficient method which achieves these bounds in practice. In this work we combine the well-known Prony's method for exponential fitting with a recently established decimation technique for analyzing the super-resolution problem in the above mentioned regime. We show that our approach attains optimal asymptotic stability in the presence of noise, and has lower computational complexity than the current state of the art methods.
