My main interests are in numerical analysis and computational harmonic analysis. I investigate issues relating to the reconstruction of objects (images, signals, functions, etc) from data. Applications are broad, and range from image and signal processing to the numerical solution of PDEs. I am particularly interested in the development, analysis and application of compressed sensing techniques in these areas. I also have ongoing interests in sampling theory, high-order numerical methods, approximation theory, non-classical Fourier methods, and the resolution of the Gibbs phenomenon.