Mri fbp and phase encoding
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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


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 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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