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In this paper, morphological operations on hexagonal lattices and regular hexagonal regions are applied to 2D parallel beam computerized tomography (CT) image denoising. To show some denoising effects of the morphological operations, for an input image, we add certain amount of noise to get the noised image; and perform Radon transform and inverse Radon transform on the noised image to obtain a CT image. To compare hexagonal lattices with square lattices fairly, the CT image is resampled to an image defined on a certain randomized grid, which is in turn resampled to an image defined on a hexagonal lattice and an image defined on the corresponding square lattice (with the same sampling rate), respectively. For the morphological operations, we use a structuring element defined on a hexagonal lattice and a structuring element defined on a square lattice such that those two structuring elements have the same number of ones. Each of those two images performs an erosion with the corresponding structuring element. Then use those two images as masks and use the two corresponding eroded images as makers to perform morphological image reconstructions to obtain the two reconstructed images. Finally, both usual and Phantom images are used as test images. For many different tested noise levels, the output data show that the image reconstructed on the hexagonal lattice is usually more similar to the input image than the one reconstructed on the square lattice.
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