We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the translation invariance of the Fourier transform, followed by a removal step to estimate the solution's support. The superset method is always successful in the noiseless regime (unlike L1-minimization) and generalizes to higher dimensions (unlike the matrix pencil method). Relative robustness to noise is demonstrated numerically.
© 2013 SAMPTA
Demanet, L., Needell, D., Nguyen, N., "Super-resolution via superset selection and pruning", Proc. 10th International Conf. on Sampling Theory and Applications (SAMPTA) 2013. http://arxiv.org/abs/1302.6288