Brief Summary: This clinical trial studies fluorine F 18 L-glutamate derivative BAY94-9392 (18F-FSPG) positron emission tomography (PET) in imaging patients with liver cancer before undergoing surgery or transplant. Diagnostic procedures, such as 18F-FSPG PET, may help find and diagnose liver cancer and find out how far the disease has spread.

Detailed Description: PRIMARY OBJECTIVES: I. To evaluate the relationship between 18F-FSPG PET/computed tomography (CT), pathology, and cancer metabolism in patients with suspected hepatocellular carcinoma (HCC) scheduled for liver resection surgery and orthotopic liver transplant (OLT). II. To compare 18F-FSPG PET/CT with standard-of-care (SOC) diagnostic MRI imaging in patients with suspected HCC scheduled for liver resection surgery or OLT. III. To compare the uptake of 18F-FSPG PET/CT with 11C-acetate PET/CT AND 18F-FDG PET/CT in suspected HCC and background liver in patients scheduled for liver resection surgery or OLT. IV. To evaluate uptake of 18F-FSPG PET/CT in benign liver lesions compared to background. V. To evaluate uptake of 18F-FSPG PET/CT in malignant non-HCC liver tumors. OUTLINE: Patients undergo 18F-FSPG PET and either carbon-11 (11C)-acetate PET or 18F-FDG PET scans within 4 weeks of surgery or OLT.