A New Approach to Interpolation in Computed Tomography

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Abstract
Most X-ray scanners presently in production use a method of image reconstruction called filtered back-projection. There are 2 limitations in data sampling which require that approximations be used during the back-projection operation, and hence result in error in the reconstructed image. In both cases the errors are associated with sharp edges such as bone interfaces. The first limitation is that each view, or projection, contains a finite number of data values, n. This is usually handled by using a piecewise-linear or nearest-neighbor approximation to the filtered projection. The result is a slight high frequency attenuation, similar to that of a smoothing filter, and also a spectrum replication, which produces a moire-type artifact. Both effects can be reduced by using a finer sampling interval or by high-order curvilinear approximations. The 2nd limitation is that there are a finite number of views, m. The conventional way of handling this problem is to replace the .vphi.-integral with a discrete sum containing 1 value from each view. This approach in a pattern of peripheral streaks whose intensity depends on the number of views. A new way to evaluate the integral is proposed in which the contribution from each view is computed as an average over an appropriate small segment of the view. When the number of views is limited (m < n .pi./2), the new method reduces the streak artifact with no loss in spatial resolution. For m .simeq. n .pi. 4, the new method requires approximately twice the computing time.

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