1990 Volume 39 Issue 4 Pages 155-162
In single-photon emission computed tomography (SPECT) and X-ray CT one-dimensional (1-D) convolution method is used for their image reconstruction from projections. The method makes a 1-D convolution filtering on projection data with a 1-D filter in the space domain, and backprojects the filtered data for reconstruction. Images can also be reconstructed by first forming the 2-D backprojection images from projections and then convoluting them with a 2-D space-domain filter. This is the reconstruction by the 2-D convolution method, and it has the opposite reconstruction process to the 1-D convolution method. Since the 2-D convolution method is inferior to the 1-D convolution method in speed in reconstruction, it has no practical use.
In the actual reconstruction by the 2-D convolution method, convolution is made on a finite plane which is called convolution window. A convolution window of size N×N needs a 2-D discrete filter of the same size. If better reconstructions are achieved with small convolution windows, the reconstruction time for the 2-D convolution method can be reduced. For this purpose, 2-D filters of a simple function form are proposed which can give good reconstructions with small convolution windows. They are here defined on a finite plane, depending on the window size used, although a filter function is usually defined on the infinite plane. They are however set so that they better approximate the property of a 2-D filter function defined on the infinite plane. Filters of size N×N are thus determined. Their value varies with window size.
The filters are applied to image reconstructions of SPECT. The results show that the filters give good reconstructions almost comparable to the 1-D convolution method for small convolution windows such as 9×9. It can result in the reduction in the reconstruction time for the 2-D convolution method. Thus, with filters proposed in the present work, an appreciable improvement on the 2-D convolution method is achieved. It will encourage person to use the method.
