Point-source localization in blurred images by a frequency-domain eigenvector-based method

We address the problem of resolving and localizing blurred point sources in intensity images. Telescopic star-field images blurred by atmospheric turbulence or optical aberrations are typical examples of this class of images, a new approach to image restoration is introduced, which is a generalization of 2-D sensor array processing 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 coherent signal sources. Thus, the problem may be cast into the form of DOA estimation, and eigenvector based subspace decomposition algorithms, such as MUSIC, may be adapted to search for these point sources. For deterministic point images the signal subspace is degenerate, with rank one, so rank enhancement techniques are required before MUSIC or related algorithms may be used. The presence of blur prohibits the use of existing rank enhancement methods. A generalized array smoothing method is introduced for rank enhancement in the presence of blur, and to regularize the ill posed nature of the image restoration. The new algorithm achieves inter-pixel super-resolution and is computationally efficient. Examples of star image deblurring using the algorithm are presented.