Prof. Berthold Horn
Professor
Massachusetts Institue of Technology(MIT)
C.V. of Berthold Horn

ABSTRACT:
Wherever computing is a significant and indispensable part of imaging we may speak of "Computational Imaging".
Since computing---unlike manufacture of precision physical apparatus--- is rapidly becoming faster and cheaper, it behooves us to consider systems where the emphasis is shifted towards more reliance on computing.
Also, for some types of radiation, refractive and reflective elements simply are not available so the usual optical systems are not applicable.
Further, some sensor modalities inherently create "coded" information, not images. Examples of "computational imaging" systems include:

(1) Coded Aperture Imaging.
One view of coded aperture imaging is that multiple pin-holes produce an "image" convolved with a mask.
The result can be de-convolved to obtain an image.
Well designed apertures have flat power spectrum (with essentially random phase).
Remarkably, interesting mathematics arises from a search for such patterns.
Coded aperture methods can also be extended to deal with time sequences obtained with a moving detector array---with application to three-d imaging and detection of radioactive material at a distance.

(2) Synthetic Aperture Microscopy.
Optical properties of a target can be probed using finely textured illumination. Images taken \ with many different textures can provide enough information to reconstruct a high resolution image from many of lower resolution (in the limit, "images" obtained by a single photo cell).
Very high resolution textures can be created by the interference of numerous coherent monochromatic beams of controlled amplitude and phase.
Interesting application may be found in deep UV imaging (where refractive elements are not available) and high resolution fluorescence imaging (where resolution now is determined by the wavelength of the stimulating radiation).

(3) Diaphanography or "Diffuse Optical Tomography".
Discovering the distribution of absorption and/or scattering in a turbid medium is difficult because measurements of light transmitted from one place on the surface to another is affected not just by material along the line connecting the source and the detector, but by the diffusion of photon flux throughout the object.
A three-dimensional resistive grid---with leakage from each node to ground---is a convenient model.
Biomedical applications abound, although the inverse problem becomes less well posed the thicker the material.

(4) Exact Cone Beam Reconstruction.
In the 1970's CT made the transition from parallel beam ray collection (one detector) to fan beams (linear array). New algorithms for reconstruction had to be found. Similarly, now we are in the process of going from fan beams to cone beams collected by area sensors.
Again, the mathematical underpinnings need to be revised.
While there are well known approximations, such as that of Feldkamp, there is a search for "exact" methods, preferably ones that have a reasonable order of growth of complexity with image resolution.
Even the question of what is the ideal "orbit" for the X-ray source has not been fully answered (hint: circles are not sufficient).