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

MRI, FBP and phase encoding


Spins

Spins


Precession

Precession


Rf pulse

RF pulse


T1 and t2

T1 and T2


Bloch equations

Bloch Equations


Receiver

Receiver


T1 and t21

T1 and T2


Effect of tissue

Effect of tissue


Slice selection

Slice selection


Slice selection1

Slice selection


Mri fbp and phase encoding

FBP


Filtered back projection

Filtered Back Projection


Filtered b a ck projection

Filtered Back Projection


Filtered back projection1

Filtered Back Projection


Mri fbp and phase encoding

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


Phase encoding1

Phase encoding


K space

K space


K space1

K Space


Partial k space reconstruction

Partial K space reconstruction


Partial k space reconstruction1

Partial K space reconstruction


Partial k space reconstruction2

Partial K space reconstruction


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