Achieving Super-Resolution in Multi-Rate Sampling Systems via Efficient   Semidefinite Programming
  Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral estimation in multi-rate sampling systems. It shows that, under the existence of a common supporting grid, and under a minimal separation constraint, the frequencies of a spectrally sparse signal can be exactly jointly recovered from the output of a semidefinite program (SDP). The algorithmic complexity of this approach is discussed, and an equivalent SDP of minimal dimension is derived by extending the Gram parametrization properties of sparse trigonometric polynomials. 
M. Ferreira Da Costa, W. Dai
cs.IT math.IT