"肖像研究" can be translated into English as "Portrait Studies" or "Research on Portraits".
"Portrait Studies" is a more concise and commonly used term in academic or artistic contexts to refer to the systematic examination and analysis of portraits.
"Research on Portraits" is a more straightforward translation that clearly conveys the idea of conducting research specifically focused on portraits.
Both translations are acceptable, and the choice between them may depend on the specific context or the preference of the speaker/writer.