 Figueiredo is best known for his work developing novel mathematical foundations for the solution of fundamentally nonlinear problems, with applications in pattern recognition, signal processing, image processing, and neural networks.His work supported a variety of NASA space exploration projects, assisted the Department of Defense in weapons detection systems, helped companies identify credit card fraud, assisted the Environmental Protection Agency in oil spill detection and source matching, developed algorithms for more efficient transmission of mobile telecommunications signals, enhanced geophysical images for well-logging, and improved the early detection of brain and neural diseases, like Alzheimer's disease.In the early 1970s, Figueiredo introduced approaches for generalised splines for optimal signal based recovery to the field of signal processing.