Laustsen was born on June 15, 1954 in Aalborg, Denmark, to Aage Aarup Laustsen and Ellen Laustsen. He studied at the National Film School of Denmark from 1976 to 1979, to pursue a career of cinematography. Laustsen has been involved in the production of feature films, documentaries, and advertisements, and is a member of the Danish Society of Cinematographers.