By Oleg Portniaguine.
An interesting, but very challenging kind of imaging is to visualize the interior of a non-transparent object (such as a human body) using physical fields measured outside the body. This imaging is achieved through a mathematical engine known as "inverse problems solving" or "statistical optimization", one of the key research directions at the SCI Institute.
Another research direction being pursued at the SCI Institute is solving "ill-posed" imaging problems by constraining the solution with focusing criterion. This allows us to reconstruct sharp solutions out of smooth data. The process is made possible by selecting special stabilizing functions that permit sharp solutions. Applications of this technique range from bioelectric source localization utilizing magneto and electro -encephalography data for medical imaging, to geophysical inversions with gravity and magnetic fields.
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