Robust blind spikes deconvolution

Abstract

Blind spikes deconvolution, or blind super-resolution, deals with the problem of estimating the delays and amplitudes of spikes from its convolution with an unknown low-pass point spread function. By constraining the point spread function in a known low-dimensional subspace, a convex optimization algorithm called AtomicLift has been proposed to exactly recover the spikes up to an unavoidable scaling ambiguity in the noiseless setting. This paper analyzes the performance of AtomicLift in the presence of bounded noise, and shows that the spikes are localized in a stable manner where the localization inaccuracy is proportional to the noise level. Moreover, we show AtomicLift is also capable to handle sparse outliers in the frequency domain.