His research interests are in statistical signal processing and machine learning, as it applies to adaptive array processing for radar, sonar, and communication; modal analysis for electric power monitoring; and image processing for classification.

He has made original contributions to matched and adaptive subspace detection, invariance theories for signal processing, and reduced-rank signal processing. He has co-authored the books, L.L. Scharf, “Statistical Signal Processing: Detection, Estimation, and Time Series Analysis,” Addison-Wesley, 1991, and P.J. Schreier and L.L. Scharf, “Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals,” Cambridge University Press, 2010.

Professor Scharf has received several awards for his professional service and his contributions to statistical signal processing, including the Technical Achievement and Society Awards from the IEEE Signal Processing Society (SPS); the Donald W. Tufts Award for Underwater Acoustic Signal Processing, the Diamond Award from the University of Washington, and the 2016 IEEE Jack S. Kilby Medal for Signal Processing. He is a Life Fellow of IEEE