Fast missing-data IAA with application to notched spectrum SAR

Recently, the spectral estimation method known as the iterative adaptive approach (IAA) has been shown to provide higher resolution and lower sidelobes than comparable spectral estimation methods. The computational complexity is higher than methods such as the periodogram (matched filter method). Fast algorithms have been developed that considerably reduce the computational complexity of IAA by using Toeplitz and Vandermonde structures. For the missing-data case, several of these structures are lost, and existing fast algorithms are only efficient when the number of available samples is small. In this work, we consider the case in which the number of missing samples is small. This allows us to use low-rank completion to transform the problem to the structured problem. We compare the computational speed of the algorithm with the state of the art and demonstrate the utility in a frequency-notched synthetic aperture radar imaging problem.