Image reproductionImage reproduction

Slice selectionSlice selection

FBPFBP

Filtered Back ProjectionFiltered Back Projection

FilteredFiltered B Baack Projectionck Projection

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)

p t p t 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 EncodingPhase Encoding

Gradient

Slice Plane

Slice Phase Frequency

XY Z X or Y Y or X

XZ Y X or Z Z or X

YZ X Y or Z Z or Y

Phase encodingPhase encoding

K spaceK space

K SpaceK Space

Partial K Partial K space space

reconstrucreconstructiontion

Partial K space Partial K space reconstructionreconstruction

Partial K space Partial K space reconstructionreconstruction

Zero paddingZero padding

ConjugatConjugate e

symmetrysymmetry

Conjugate symmetryConjugate symmetry

Homodyne Homodyne reconstructionreconstruction

Homodyne Homodyne reconstructionreconstruction

Homodyne Homodyne reconstructionreconstruction

HomodyHomodyne ne

reconstrreconstructionuction