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We develop an inverse scattering algorithm for imaging 3-D dielectric scatterers with microwaves. The algorithm uses the biconjugate gradient and fast Fourier transform method (BCG-FFT) for forward modeling and a conjugate gradient algorithm to solve the inverse problem, which is formulated as a nonlinear optimization problem. The BCG-FFT method reduces the computational complexity of forward modeling to order N log2N, where N is the number of unknowns used to represent the vector fields in 3-D space. The conjugate gradient method requires the computation of the Fréchet derivative (matrix of partial derivatives) operating on a vector of residuals, which is equivalent to solving another forward problem. Simulations show the efficiency of this algorithm, especially when the number of illumination angles is limited.

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