In this talk, I will present 3 different roles of total variation (TV) regularization in variational methods in image

segmentation and MR image reconstruction.  First, TV as a measure of the perimeter of a candidate partition

encoded by the indicator function of a set:  In unsupervised image segmentation, the total length of region

boundaries is often minimized to obtain a compact partition that likely matches the way humans perceive. 

A statistical distance between color distributions of distinctive regions in a candidate partition is maximized with

the minimization of TV for unsupervised image partitioning.  Second, TV as a measure of streaking artifacts in

QSM deconvolution: QSM is a noninvasive MRI method for a quantitative study of the tissue magnetic

susceptibility distribution by solving the magnetic field to susceptibility source inversion problem.  A major

challenge in the ill-posed inverse problem is streaking artifacts from noise in the field which propagates at the

complementary magic angle.  These artifacts can be selectively reduced by weighted TV regularization that

makes use of anatomical information of the corresponding magnitude image.  Lastly, TV as a measure of

undersampling artifacts in image reconstruction for multi-contrast MRI.  In clinical MRI, multiple contrasts such

as T1w, T2w, and FLAIR are sequentially acquired, consequently taking a long scan time.  To shorten the scan

time, structuralinformation shared between contrasts is extracted and can be incorporated into the TV term as

an orthogonalprojector in the model-based image reconstruction for the subsequent contrasts that are highly

undersampled.