Image reproduction. Slice selection FBP Filtered Back Projection.

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Presentation transcript:

Image reproduction

Slice selection

FBP

Filtered Back Projection

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 ’ (,  ).

Phase Encoding Gradient FrequencyPhaseSlice Slice Plane Y or XX or YZXY Z or XX or ZYXZ Z or YY or ZXYZ

Phase encoding

K space

K Space

Partial K space reconstruction

Zero padding

Conjugate symmetry

Homodyne reconstruction