In many practical applications such as direction-of-arrival (DOA) estimationand line spectral estimation, the sparsifying dictionary is usuallycharacterized by a set of unknown parameters in a continuous domain. To applythe conventional compressed sensing to such applications, the continuousparameter space has to be discretized to a finite set of grid points.Discretization, however, incurs errors and leads to deteriorated recoveryperformance. To address this issue, we propose an iterative reweighted methodwhich jointly estimates the unknown parameters and the sparse signals.Specifically, the proposed algorithm is developed by iteratively decreasing asurrogate function majorizing a given objective function, which results in agradual and interweaved iterative process to refine the unknown parameters andthe sparse signal. Numerical results show that the algorithm provides superiorperformance in resolving closely-spaced frequency components.
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