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Continuous wave (CW) tomosynthesis provides many theoretical advantages over traditional breast imaging techniques, like mammography. These theoretical advantages include improved spatial resolution, better information weighting, and the ability to resolve structures hidden by tissue overlap. However, unlike mammography, tomosynthesis is a three-dimensional imaging modality and it will require a complex reconstruction algorithm to process its projection data and recreate the object planes. This paper details a reconstruction algorithm proposed for continuous wave tomosynthesis which is based on the filtered backprojection reconstruction algorithm used in computed tomography. The algorithm for tomosynthesis requires modifications to the filtered backprojection algorithm in order to account for the lack of complete data which is generated by a tomosynthesis scan. In order to demonstrate the potential viability of a CW tomosynthesis reconstruction algorithm, the modified reconstruction algorithm is applied to several simulated phantom images and analyzed for reconstructed image quality.