Apex Method in Image Sharpening and the Use of Low Exponent Levy Stable Laws

摘要

The APEX method is an FFT-based direct blind deconvolution technique that canprocess complex high resolution imagery in a few minutes of cpu time on current desktop platforms. The method is predicated on a restricted class of shift-invariant blurs that can be expressed as finite convolution products of two-dimensional radially symmetric Levy stable probability density function. This class generalizes Gaussian and Lorentzian densities but excludes defocus and motion blurs. Not all images can be enhanced with the APEX method. However, it is shown that the method can be usefully applied to a wide variety of real blurred images, including astronomical, Landsat and aerial images, MRI and PET brain scans, and scanning electron microscope images. APEX processing of these images enhances contrast and sharpens structural detail, leading to very noticeable improvements in visual quality. The discussion includes a documented example of non uniqueness where distinct point spread functions produce high-quality restorations of the same blurred image. Significantly, low exponent Levy point spread functions were detected and used in all the above examples. Such low exponents are exceptional in physical applications where symmetric stable laws appear. In the present case, the physical meaning of these Levy exponents is uncertain.