A tight threshold for noise eigenvalues in superresolution

Abstract

INTRODUCTION Identification of principal and noise eigenvalues in the eigenvalue/vector decomposition of a covariance matrix is an essential part of superresolution techniques such as MUSIC and PEGS (1). Target counting is decided directly by the number of principal eigenvalues chosen from the total set of eigenvalues. The resultant resolution pattern can be affected by the appearance of spurious peaks or the disappearance of real peaks if the eigenvalues are not properly identified. Curvefit methods customarily adopted to discriminate principal from noise eigenvalues fail when targets are so close that there is no significant slope change in the transition from noise eigenvalues to the least principal eigenvalue. Once the boundary between principal and noise eigenvalues is blurred, a superresolution technique based on the eigenvalue/vector decomposition of a covariance matrix loses its resolution capability.