Grayscale image reconstruction from projections with linear noise response

This paper presents concisely two reconstruction algorithms that provide exact image reconstruction from its projections and then analyzes the performance of these algorithms when noisy projection data are present. In both the reconstruction methods the projection samples are stored in a 2-D accumulator array where each column corresponds to the projection data at a certain view angle. However, the second method uses a significantly smaller number of projection samples. The response of the reconstruction methods is examined when Gaussian noise is applied in the projection data stored in the accumulator array. Several cases are examined regarding the original image size, the level of the input noise and the rounding of the grayscale values in the reconstructed image. The experimental results show that the two reconstruction methods have the same noise response and that in both cases the reconstructed image is linearly related to the input noise.