Image reconstruction with a hexagonal grid

Conventional image reconstruction methods use a square grid for ease of calculation or display of the image. On a square grid there are two possible ways to define neighboring pixels. We can either regard pixels as neighbors when they have a common edge or when they have at least one common corner, so that four and eight neighbors exist (a 4-neighborhood and an 8-neighborhood) and the distance between adjacent pixels is different in the horizontal (or vertical) direction from that in the diagonal direction. The difference in the distance between the neighbors introduces inconsistency when we interpolate neighboring pixel values with a weighting (kernel) function such as a blob (overlapping spherical elements having bell-shaped radial profiles). On the other hand, they do not occur with a hexagonal grid. On the hexagonal grid, we can only define a 6-neighborhood. Neighboring pixels have always one common edge and two common corners. Moreover, the distances between the neighboring pixels are equal. This paper describes an attempt to reconstruct SPECT images with a hexagonal grid with blobs. In the image reconstruction we used the spherically symmetric volume element (blob) proposed by R.M. Lewitt. And we located the center of the blob at the center of the hexagonal grid. We compared this image with an image reconstructed on a square grid. Simulation results showed the advantage of the hexagonal grid over the square grid.