This clinical trial studies how well 18F-fluoromisonidazole ([18F]FMISO) positron emission tomography (PET)/computed tomography (CT) works after transcatheter arterial embolization in imaging tumors in patients with liver cancer. Transcatheter arterial embolization blocks blood flow to tumor cells by inserting tiny foreign particles into an artery near the tumor. [18F]FMISO is a type of radioimaging agent that binds to large molecules in tumor cells that have a low level of oxygen, and the radiation given off by [18F]FMISO is picked up by a PET scan and this may help researchers learn whether changes occur in the tumors after treatment, which can help decide how well the treatment worked earlier than is currently possible