Atomic Norm Denoising In Blind Two-Dimensional Super-Resolution

In this work, we develop a new framework for denoising in blind two-dimensional (2D) super-resolution that recovers a set of 2D continuous parameters as well as unknown waveforms from noisy samples. We apply the atomic norm to denoise a weighted sum of time-delayed and frequency-shifted unknown waveforms. Moreover, we derive the theoretical mean-squared error of the estimator, and we show that it depends on the noise level and other system parameters. Then, we prove that when the number of samples satisfies certain bound, we can recover all the unknowns with high probability. Finally, we verify our theoretical findings using simulations.