Coherent Spectral Analysis of Asynchronously Sampled Signals

We propose a joint sparse signal recovery approach to coherent spectral analysis of irregularly sampled signals. These signals share the same frequencies, and are sampled asynchronously. Two types of solution procedures are considered. First one is a convex optimization approach, which optimizes a mixed
l
_2,1
-norm. The other method minimizes an approximation of
l
_2,0
-norm and the resulting algorithm can be implemented using a few FFTs and IFFTs. We demonstrate the effectiveness of the sparse recovery approach using simulation experiments. In particular, the
l
_2,0
approximation approach is very fast. In addition, it offers increased resolution, improved robustness to noise, and works well with limited number of data samples.