This paper presents a fast and effective electromagnetic reconstruction algorithm with phaseless data under weak scattering conditions. The proposed algorithm is based on the phaseless data multiplicative regularized contrast sources inversion method (PD-MRCSI). We recast the weak scattering problem as an optimization problem in terms of the undetermined contrast and contrast sources. Using the conjugate gradient iterative method, the problem is solved by alternately updating the contrast sources and the contrast. Additionally, this method can combine with the PD-MRCSI method. Taking advantage of the properties of fast convergence of this algorithm and stable convergence of PD-MRCSI method, the combined technique makes image reconstructions more fast and effective. Although the method is derived from weak scattering situation, it is also useful for the case which weak scattering approximation is not satisfied. The synthetic numerical reconstruction results, as well as experimental reconstruction results, presented that the proposed method is a very fast and effective reconstruction algorithm.
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