Exact Three-Dimensional Estimation in Blind Super-Resolution via Convex Optimization

Abstract

In this work, we propose a general mathematical framework for blind three-dimensional super-resolution theory that recovers the continuous shifts and the amplitudes in a mixture of unknown waveforms upon using the received signal. We prove that the three-dimensional shifts, the amplitudes, and the unknown waveforms can all be recovered precisely and with high probability via convex programming when the number of the observed samples obeys certain complexity bound. This exact recovery holds provided that the shifts are sufficiently separated and that the unknown waveforms lie in a common known low-dimensional subspace that satisfies certain assumptions.