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A study is presented where the use of dielectric a priori data in the reconstruction algorithm for microwave tomography is investigated. A new algorithm has been developed that includes the a priori dielectric data in the reconstruction process. This development is made as an extension to a conventional conjugate-gradient reconstruction algorithm. This paper further contains a numerical study of the new algorithm where the results indicate that by taking the a priori data into account, the accuracy and ability to resolve small objects can significantly be improved. This study was motivated by the development of an application for biomedical microwave imaging where it is investigated how knowledge of the tissue properties being imaged potentially can be used to improve the accuracy in the reconstruction.