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MRI, FBP and phase encoding. Spins. Precession. RF pulse. T1 and T2. Bloch Equations. Receiver. T1 and T2. Effect of tissue. Slice selection. Slice selection. FBP. Filtered Back Projection. Filtered B a ck Projection. Filtered Back Projection. Filtered backprojection.
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Filtered backprojection • Filter the measured projection data at different projection • angles with a special function. • Backproject the filtered projection data to form the • reconstructed image. • Filtering can be implemented in 2 ways, in the spatial domain, the filter operation is • equivalent to to convolving the measured projection data using a special convolving • function h(t) • More efficient multiplication will be in the spatial frequency domain. • FFT the measured projection data into the frequency domain: • p(,)=FT {p(t, ) • Multiply the the fourier transform projections with the special function. • Inverse Fourier transform the product p’(,).