APEX: Mathematical Solution to Imaging

Alfred Carasso (photo courtsey: NIST)

A common but serious issue in almost all kinds imaging, ranging from amateur snapshots to precise scientific instrumentation, is the problem of removing blur. Many factors contribute to the blur, such as the motion of the object, the motion of the imager, irregularities in the optics and atmospheric effects. Theoretically speaking, if the exact set of mathematical operations that govern the blurring is known, we can remove the blur by delicate numerical analysis. But because of those many degrees of freedom involved, the precise mathematical transformation, the ‘point spread function,’ usually remains unknown.

However, in 2001, Alfred Carasso, a mathematician from National Institute of Standard Technology (NIST), developed a technique – the Apex method (Apex is not an acronym) — as a general solution to a specific limited class of blur: blur that is symmetric and has certain other mathematical characteristics. Apex was originally applied to monochromatic images from scanning electron microscopes, and to some medical imaging with great success.

Recently, Carasso applied Apex to astronomical images, including colour images from the Hubble Advanced Camera for Surveys (ACS). Overcoming the increased difficulties of de-blurring color images, Apex successfully detected and corrected unusual optical blurring functions in several astronomical images and delivered strikingly enhanced versions of well-known Hubble images, including the Whirlpool and Tadpole galaxies.

‘There is an element of luck in scientific research,’ an elated Carasso says, ‘sometimes a simple formulation, based on the right intuition, works out a lot better than you ever expected.’

Reference:
A.S. Carasso. "APEX blind deconvolution of color Hubble space telescope imagery and other astronomical data". Optical Engineering. 45, Number 10, October 2006, 107004