This paper studies the recovery of a superposition of point sources from
noisy bandlimited data. In the fewest possible words, we only have information
about the spectrum of an object in a low-frequency band bounded by a certain
cut-off frequency and seek to obtain a higher resolution estimate by
extrapolating the spectrum up to a higher frequency. We show that as long as
the sources are separated by twice the inverse of the cut-off frequency,
solving a simple convex program produces a stable estimate in the sense that
the approximation error between the higher-resolution reconstruction and the
truth is proportional to the noise level times the square of the
super-resolution factor (SRF), which is the ratio between the desired high
frequency and the cut-off frequency of the data.

本文研究从噪声带限数据中恢复点源的叠加。我们仅仅了解一个物体在由某个截止频率限制的低频段的频谱，通过将频谱外推到更高频率来获得更高分辨率的估计。我们证明只要源之间相隔大于截止频率的两倍的倒数，求解一个简单的凸优化问题就可以在稳定的意义下产生一个估计，其中高分辨重建与真实值之间的逼近误差与噪声水平乘以超分辨因子（SRF）的平方成比例。