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Reconstruction algorithms for clinical X-ray CT scanners have evolved over the year with emphasis on improving the noise properties of the reconstructed image especially for whole body imaging. With increasing regulations on X-ray radiation dose, approximate reconstruction algorithms are preferred over exact reconstruction algorithms for clinical applications due to their superior noise properties. In this thesis, we look into improving the image quality, measured in terms of noise, of exact reconstruction algorithms. Of all the exact reconstruction algorithms available in litterature, we choose the exact reconstruction algorithm developed be Katsevich because of its superior computation efficiency. The noise properties of the Katsevich algorithm is improved by modifying the algorithm to reconstruct the estimate of the attenuation density function over a small region in space. This small region is called a slice and we introduce five methods that allow Katsevich algorithm to reconstruct slices. The first method is called the sub-sampling filtering method and this method reconstructs an estimate of a slice by averaging estimates of sub- samples within the slice region.