Sampling rates and image reconstruction from scattered fields

Cepstral filtering is reviewed as a suitable and efficient method to solve the inverse scattering problem in the case of strongly scattering permittivity distributions. The number and distribution of measured scattered field data required is discussed, as is the effective number of degrees of freedom available to describe the scattering structure. The latter is identified as a key parameter determining the performance of the cepstral method. This is of particular importance for strong scattering and nonlinear image processing methods since many data sets are compiled based on the sampling requirements of weakly scattering objects. We find that the domain of the object support and the maximum permittivity contrast are important prior information for determining the minimum number of data samples necessary while maximizing use of the available degrees of freedom; examples are presented.