Video Teleconferencing Improvements Act of 2001 - Amends the Federal Rules of Criminal Procedure to authorize the use of video teleconferencing for a defendant's initial appearance (under Rule 4) or arraignment (under Rule 10) or for certain proceedings (under Rule 43) when the proceeding is the sentencing hearing, when the defendant waives the right to be present in court, or when the court finds that communication with a defendant by video teleconferencing is an adequate substitute for the defendant's presence.