TY - GEN
T1 - Reconstructing image differences from tomographic Poisson data
AU - O'Sullivan, Joseph A.
AU - Chen, Yaqi
PY - 2013
Y1 - 2013
N2 - Given two measurements of an image and a modified version of the image, we seek reconstructions of both the original image and the difference of the images. The data are assumed to be Poisson, with known nonnegative forward operator and nonnegative images. A penalized likelihood is minimized with the penalty equal to the sum of the absolute difference between the images. An alternating minimization algorithm is developed by reformulating the penalized maximum likelihood problem as a double minimization of I-divergence plus the penalty. This algorithm guarantees monotonic decrease in the objective function for each iteration. Simulations with random images and tomographic data are presented to demonstrate properties of the algorithm. Convergence properties of the algorithm are studied both theoretically and in simulations.
AB - Given two measurements of an image and a modified version of the image, we seek reconstructions of both the original image and the difference of the images. The data are assumed to be Poisson, with known nonnegative forward operator and nonnegative images. A penalized likelihood is minimized with the penalty equal to the sum of the absolute difference between the images. An alternating minimization algorithm is developed by reformulating the penalized maximum likelihood problem as a double minimization of I-divergence plus the penalty. This algorithm guarantees monotonic decrease in the objective function for each iteration. Simulations with random images and tomographic data are presented to demonstrate properties of the algorithm. Convergence properties of the algorithm are studied both theoretically and in simulations.
KW - alternating minimization algorithm
KW - compressed sensing
KW - image reconstruction
KW - maximum likelihood estimation
UR - https://www.scopus.com/pages/publications/84890699007
U2 - 10.1109/DSP-SPE.2013.6642577
DO - 10.1109/DSP-SPE.2013.6642577
M3 - Conference contribution
AN - SCOPUS:84890699007
SN - 9781479916160
T3 - 2013 IEEE Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2013 - Proceedings
SP - 124
EP - 129
BT - 2013 IEEE Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2013 - Proceedings
PB - IEEE Computer Society
T2 - 2013 IEEE Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2013
Y2 - 11 August 2013 through 14 August 2013
ER -