Sparse solution to an underdetermined linear integral equation is
the central problem for a broad range of applications - scattering,
sensing, imaging, machine learning, signal and image processing, data
analysis and compression, model reduction, optimal control and
design. We will introduce a weak formulation of the problem and
construct its sparse solution by a nonlinear process - the design
of a Gaussian quadrature for the kernel of the integral equation.
We will present a systematic method to solve the resulting quadrature