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MRI, FBP and phase encoding - PowerPoint PPT Presentation

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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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MRI, FBP and phase encoding

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MRI, FBP and phase encoding



RF pulse

T1 and T2

Bloch Equations


T1 and T2

Effect of tissue

Slice selection

Slice selection


Filtered Back Projection

Filtered Back 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)

  • 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

Phase encoding

K space

K Space

Partial K space reconstruction

Partial K space reconstruction

Partial K space reconstruction

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