We are using the Fast Fourier rather than the Discrete Fourier Transform.The Radon Transform changes the projection information into polar values, and each line of an angle is a slice of the Transform. We weight each of these values with a weighting filter, something similiar to the sinc function (the transform of the absolute value function). We filter with a low and high frequency filter, using the scaling and wavelet coefficients of a wave function. Using wavelet coefficients we were not able to adjust the segregation point between high and low frequency values. We were able to separate the frequency values in half, though it seems that a 1/3 separation provides better results. This is because, as this is local tomography, the low frequency values must be interpolated. The values that are processed as low frequency should corespond more directly to Choices scaling functions differ in conditions.

Shannon Scaling Function

smooth, with a complete set of continuous derivatives; a support that is all R

Haar Scaling Function

discontinuous ; compactly supported

Daubecheis Scaling Function

fullfills the following requirements

• Compact support condition
• Orthogonality condition
• Regularity condition

This is the Shepp and Logan head phantom,
often used in testing reconstructinos.