Direct reconstruction of single-photon emission computed tomography images using retained matrix elements

In clinical applications, two methods of single-photon emission computed tomography (SPECT) reconstruction are widely used. These are filtered backprojection and iterative reconstruction. Filtered backprojection is fast and produces acceptable images. Iterative reconstruction is slow, but produces images of greater accuracy than backprojection. The authors sought to develop a method of SPECT reconstruction that would have the advantages of both established methods: close in speed to backprojection and with the accuracy of iterative reconstruction. This was accomplished by computing a direct solution to the set of linear equations governing SPECT reconstruction. We tested this method of SPECT reconstruction using a set of projections from a cold rod and sphere phantom. Direct reconstruction produced images having equivalent resolution to backprojected images, but with double the contrast ratio. The direct method required 10 seconds of computation per slice on a Macintosh Quadra 950 (Apple Computer; Cupertin, CA), significantly faster than most iterative methods.