Eigenvector-based point source localization applied to image restoration
In this paper we address the problem of resolving and localizing blurred point sources in intensity images. This problem is often encountered in restoration of long exposure astronomical star images in the presence of atmospheric turbulence. A new approach to image restoration is introduced which is a generalization of techniques originating from the field of direction of arrival estimation (DOA). It is shown that in the frequency domain, blurred point source images can be modeled with a structure analogous to the response of linear sensor arrays to fully correlated sources. Thus, the problem may be cast into the form of DOA estimation, and eigenstructure algorithms such as MUSIC may be adapted to search for these point sources. The new algorithm takes advantage of the benefits of these eigenvector based techniques, such as interpixel super-resolution, computational efficiency, and increased robustness in the presence of noise if multiple time samples are available. Application to single snapshot and multiple frame image cases are discussed. The duality between the frequency domain representation of blurred shifted point sources and the array response to sources at varying angles in the spatial domain is explained. A theoretical framework for extending the DOA algorithms to the 2-D case is developed, and a practical algorithm incorporating regularized 2-D smoothing is presented. Synthetic and actual photographic examples of star image deblurring using the new algorithm are included, along with a comparison to existing point source deblurring algorithms.
0984: Computer science