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Ultrasound tomograph designed to reconstruct spatial distributions of sound speed and absorption coefficient in soft biological tissues (primarily in mammary gland) is presented. Distinctive feature of the tomograph is sparse annular antenna array with irregular arrangement of receiving-transmitting transducers. When an object is tomographed by its layers, 26 transducers in combination with antenna rotation allow providing the same data set as in case of nonrotating array with 256 transducers. Two-step processing algorithm uses both ray methods to reconstruct large-scale details of the required spatial distributions and wave methods to reconstruct small details. High degree of algorithm parallelism allows to reduce the time of experimental data processing by CUDA GPUs to several minutes per an image layer. Results of processing both model data and experimental data obtained for phantom objects are presented. Disadvantages of reconstruction at the first step of the algorithm with low resolution (0.5–1 cm) are analyzed. The high resolution (not worse than 1 mm), achieved at the second step of reconstructing the small details is illustrated. It is shown that these small details, which are the most informative for medical diagnostics at early stage of neoplasm, cannot be reconstructed without preliminary reconstruction of large-scale details.