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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 back projects 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 X 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 X N are thus determined. Their value varies with window size. The filters are applied to image reconstructions of SPECT.(ABSTRACT TRUNCATED AT 250 WORDS)

An improvement on the two-dimensional convolution method of image reconstruction and its application to SPECT.