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