A unified variational approach to denoising and bias correction in MR.
We propose a novel bias correction method for magnetic resonance (MR) imaging that uses complementary body coil and surface coil images. The former are spatially homogeneous but have low signal intensity; the latter provide excellent signal response but have large bias fields. We present a variational framework where we optimize an energy functional to estimate the bias field and the underlying image using both observed images. The energy functional contains smoothness-enforcing regularization for both the image and the bias field. We present extensions of our basic framework to a variety of imaging protocols. We solve the optimization problem using a computationally efficient numerical algorithm based on coordinate descent, preconditioned conjugate gradient, half-quadratic regularization, and multigrid techniques. We show qualitative and quantitative results demonstrating the effectiveness of the proposed method in producing debiased and denoised MR images.
Fan
Ayres
A
Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA. fan@mit.edu
Wells
William M
WM
Fisher
John W
JW
Cetin
Müjdat
M
Haker
Steven
S
Mulkern
Robert
R
Tempany
Clare
C
Willsky
Alan S
AS
D000465:Algorithms; D016477:Artifacts; D001921:Brain / Q000033:anatomy & histology; D003198:Computer Simulation; D006321:Heart / Q000033:anatomy & histology; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D011467:Prostate / Q000033:anatomy & histology; D011786:Quality Control; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity