Scheduled System Maintenance:
On Wednesday, July 29th, IEEE Xplore will undergo scheduled maintenance from 7:00-9:00 AM ET (11:00-13:00 UTC). During this time there may be intermittent impact on performance. We apologize for any inconvenience.
By Topic

Tomographic reconstruction and estimation based on multiscale natural-pixel bases

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Bhatia, M. ; J.P. Morgan & Co. Inc., New York, NY, USA ; Karl, W.C. ; Willsky, A.S.

We use a natural pixel-type representation of an object, originally developed for incomplete data tomography problems, to construct nearly orthonormal multiscale basis functions. The nearly orthonormal behavior of the multiscale basis functions results in a system matrix, relating the input (the object coefficients) and the output (the projection data), which is extremely sparse. In addition, the coarsest scale elements of this matrix capture any ill conditioning in the system matrix arising from the geometry of the imaging system. We exploit this feature to partition the system matrix by scales and obtain a reconstruction procedure that requires inversion of only a well-conditioned and sparse matrix. This enables us to formulate a tomographic reconstruction technique from incomplete data wherein the object is reconstructed at multiple scales or resolutions. In case of noisy projection data we extend our multiscale reconstruction technique to explicitly account for noise by calculating maximum a posteriori probability (MAP) multiscale reconstruction estimates based on a certain self-similar prior on the multiscale object coefficients. The framework for multiscale reconstruction presented can find application in regularization of imaging problems where the projection data are incomplete, irregular, and noisy, and in object feature recognition directly from projection data

Published in:

Image Processing, IEEE Transactions on  (Volume:6 ,  Issue: 3 )