Inverse problems are mathematical problems set up to determine the cause from the effects. Scattering problems arise from the physical phenomenon of wave–matter interaction in which the wavelength is comparable to the typical dimension of the inhomogeneity. An inverse scattering problem is to the recover the unknown/inaccessible physical objects by the measurement of wave as the result of the interaction between the object with a given input field. Applications include nano-optics, super-resolution imaging, medical imaging, nondestructive testing, geophysical exploration, radar and sonar.