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Recently, an iterative reconstruction-reprojection (IRR) algorithm has been suggested for application to limited view computed tomography (CT). In the IRR, the interpolation operation is performed in the object space during backprojection-reprojection. The errors associated with the interpolation degrade the reconstructed image and may cause divergence unless a large number of rays is used. In this paper, we propose a projection space iterative reconstruction-reprojection (PSIRR) algorithm based on backprojection-reprojection in the projection space. In the process of the backprojection-reprojection, iteration is performed with a single equation instead of multiple equations and interpolation is eliminated. Computer simulation results are presented, and image quality of the PSIRR algorithm shows a substantial improvement compared to the original IRR algorithm. In addition, the new algorithm was applied to ultrasonic attenuation CT using a sponge phantom.