Thank you in advance for your interest and efforts to celebrate the mathematical sciences with new and larger audiences this spring. Mathematics and Imaging Mathematics is an essential element of imaging in fields as diverse as medicine, computer science, and space exploration, and many other settings as well. For instance, medicine benefits from the techniques of tomography, including cutting-edge ideas like electrical impedance tomography that may greatly improve the detection of cancerous tumors, and from level set and marching methods that can extract images of beating hearts from MRI images. Computer imaging depends upon a whole range of mathematical tools. Familiar references like Microsoft's Encarta encyclopedia and its 7,000 color images fit on a single CD-ROM because of fractal image compression.
Image compression is also one of the essential tools of space exploration.
Compression routinely increases the effective transmission rate of image data by a factor of fifteen or twenty. New techniques are being developed that will raise compression ratios into the hundreds while still preserving essential features of the image. One of these new ideas, wavelet image compression , has already enabled electronic storage and retrieval of the FBI's vast archive of fingerprint records. Image restoration tools can extract additional detail otherwise hidden in images from a wide range of sources, including satellites, medical imaging devices, telescopes, and even amateur video pictures submitted as courtroom evidence. Images from astronomical telescopes are cleaner to begin with if they have benefited from the control strategies of active and adaptive optics that minimize degradation from atmospheric blur and mechanical tremors.