Alternating minimization algorithm with iteratively reweighted quadratic penalties for compressive transmission tomography

Yan Kaganovsky; Soysal Degirmenci; Shaobo Han; Ikenna Odinaka; David G. Politte; David J. Brady; Joseph A. O'Sullivan; Lawrence Carin

doi:10.1117/12.2081986

20 March 2015 Alternating minimization algorithm with iteratively reweighted quadratic penalties for compressive transmission tomography

Yan Kaganovsky, Soysal Degirmenci, Shaobo Han, Ikenna Odinaka, David G. Politte, David J. Brady, Joseph A. O'Sullivan, Lawrence Carin

Author Affiliations +

Proceedings Volume 9413, Medical Imaging 2015: Image Processing; 94130J (2015) https://doi.org/10.1117/12.2081986
Event: SPIE Medical Imaging, 2015, Orlando, Florida, United States

Abstract

We propose an alternating minimization (AM) algorithm for estimating attenuation functions in x-ray transmission tomography using priors that promote sparsity in the pixel/voxel differences domain. As opposed to standard maximum-a-posteriori (MAP) estimation, we use the automatic relevance determination (ARD) framework. In the ARD approach, sparsity (or compressibility) is promoted by introducing latent variables which serve as the weights of quadratic penalties, with one weight for each pixel/voxel; these weights are then automatically learned from the data. This leads to an algorithm where the quadratic penalty is reweighted in order to effectively promote sparsity. In addition to the usual object estimate, ARD also provides measures of uncertainty (posterior variances) which are used at each iteration to automatically determine the trade-off between data fidelity and the prior, thus potentially circumventing the need for any tuning parameters. We apply the convex decomposition lemma in a novel way and derive a separable surrogate function that leads to a parallel algorithm. We propose an extension of branchless distance-driven forward/back-projections which allows us to considerably speed up the computations associated with the posterior variances. We also study the acceleration of the algorithm using ordered subsets.

Citation Download Citation

Yan Kaganovsky, Soysal Degirmenci, Shaobo Han, Ikenna Odinaka, David G. Politte, David J. Brady, Joseph A. O'Sullivan, and Lawrence Carin "Alternating minimization algorithm with iteratively reweighted quadratic penalties for compressive transmission tomography", Proc. SPIE 9413, Medical Imaging 2015: Image Processing, 94130J (20 March 2015); https://doi.org/10.1117/12.2081986

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available