Adaptive image restoration using a generalized Gaussian model for unknown noise.

A model adaptive method is proposed for restoring blurred and noise corrupted images. The generalized p-Gaussian family of probability density functions is used as the approximating parametric noise model. Distribution shape parameters are estimated from the image, and the resulting maximum likelihood optimization problem is solved. An iterative algorithm for data-directed restoration is presented and analyzed.

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.

Restoration of blurred star field images by maximally sparse optimization.

The problem of removing blur from, or sharpening, astronomical star field intensity images is discussed. An approach to image restoration that recovers image detail using a constrained optimization theoretic approach is introduced. Ideal star images may be modeled as a few point sources in a uniform background. It is argued that a direct measure of image sparseness is the appropriate optimization criterion for deconvolving the image blurring function. A sparseness criterion based on the l(p) is presented, and candidate algorithms for solving the ensuing nonlinear constrained optimization problem are presented and reviewed. Synthetic and actual star image reconstruction examples are presented to demonstrate the method's superior performance as compared with several image deconvolution methods.