TY - CHAP
T1 - Regularization Techniques for Tomography Problems
AU - Dong, Yiqiu
PY - 2021
Y1 - 2021
N2 - Inverse problems are mathematical problems that arise when our goal is to recover “interior” or “hidden” information from “outside”—or otherwise available—noisy data [3], [8], [67], [71]. Tomographic reconstruction is a classical example of an ill-posed inverse problem, and we have already seen that reconstructions are sensitive to measurement noise. Therefore, we cannot expect to compute satisfactory results by simply solving the system of linear equations—in the form of either a square system or a least-squares problem. In this chapter, we will introduce regularization techniques to incorporate prior information on the objects in order to stabilize the solutions with respect to measurement noise.
AB - Inverse problems are mathematical problems that arise when our goal is to recover “interior” or “hidden” information from “outside”—or otherwise available—noisy data [3], [8], [67], [71]. Tomographic reconstruction is a classical example of an ill-posed inverse problem, and we have already seen that reconstructions are sensitive to measurement noise. Therefore, we cannot expect to compute satisfactory results by simply solving the system of linear equations—in the form of either a square system or a least-squares problem. In this chapter, we will introduce regularization techniques to incorporate prior information on the objects in order to stabilize the solutions with respect to measurement noise.
U2 - 10.1137/1.9781611976670.ch12
DO - 10.1137/1.9781611976670.ch12
M3 - Book chapter
SN - 978-1-61197-666-3
T3 - Fundamentals of Algorithms
SP - 251
EP - 273
BT - Computed Tomography: Algorithms, Insight, and Just Enough Theory
A2 - Hansen, Per Christian
A2 - Jørgensen, Jakob Sauer
A2 - Lionheart, William R. B.
PB - Society for Industrial and Applied Mathematics
ER -