MRI Reconstruction

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MRI Reconstruction

• Athaur Rahman Najeeb
• G0129603
• Department of Electrical and Computer Engineering

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Content

• MRI Principles
• K-space and Image Formation
• Image Reconstruction Technique
• Conclusion and summary

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Overview of Image Acquisition and Processing
Transformation 1 MRI Physics ( Pre- Processing )
Spin Processing
Data Processing
Transformation 2 Post Processing Image
Reconstruction
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MRI Basics

• MRI means Magnetic Resonance Imaging. It is an
  interaction between an external
• magnetic field, radio waves and hydrogen nuclei
  in the body. When placed in a
• magnetic field , the body temporarily becomes
  magnetized , that is the hydrogen
• nuclei align with the magnetic field creating
  magnetization. At equilibrium, net
• magnetization is parallel to the z axis of the
  external magnetic field. This is
• LONGITIDINAL MAGNETIZATION. A transverse
  magnetization is
• created when LM is tipped with an RF pulse ( at
  Larmor frequency ). LM recover
• partially between RF pulses at intervals of TR
  with time constant T1. Precession is
• transverse magnetization induce electrical
  signal in coil of wire , decaying at time
• constant T2. Imaging volume is restricted to a
  slice by specific frequencies in the
• RF pulse and magnetic field gradient

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A slice is excited . This is achieved with an
additional field az component. Thus varying
the Larmor frequency(?) ?Gz The sample is
irradiated with RF pulse and this excites spins
whose Resonace Frequencies are in the same RF
resonance. And tipped into transverse plane.
This excites signal in a thin slab of material
Perpendicular to the direction of the gradient
field.
Subject is placed in a strong and homogenous B0
, which produces Mz along the direction of B0
Later spins process around B0 at ? ?B0. spins
are further resolved in other 2 directions by
linear gradient fields to change the resonant
frequencies of spins at different spatial
locations.
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• If we acquire the signal produced by the subject
  and compute its spectrum, each
• frequency bin will be proportional to how much
  magnetization was at that
• position.
• Mathematically the signal received at time t can
  be shown as
• s(t) ?X M xy (x) e- I 2?k(t)x
  dx
• Simply at time t , the signal s(t) received is
  the value of the Fourier transform of
• 2d transverse magnetization Mxy sampled at the
  spatial frequency k(t).

Acquiring an MRI image is performed by sampling
the spatial frequency content of the image
directly , and then performing an inverse Fourier
transform to reconstruct the image
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MRI Acquisition Methods

• Previous equation reveals couple of ways
• To acquire MRI Data. The requirement is
• simply that enough of spatial frequency or k-
• space Be sampled to allow image reconstruction.
• 2DFT ( Spin Warp )
• Most common to sample k-space data
• Two element in any acquisition method and this is
  explained in a pulse-sequence diagram
• First is slice selection for excitation and the
  second element is 2DFT acquisition gradient which
  is the data encoding and acquisition
• Other alternatives EPI
• a common one, echo-planar imaging.

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K-space

• Raw data in time series. Where we store generated
  MR signals.
• K-space is simple a array of complex numbers,
  where when we
• convert into grey scale it gives us image as
  shown . It has
• mathematical relation to the image ( FT ). We
  need to fill a lot of
• k-space , line by line before generating the
  image

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Spatial Information Encoding

• After signal is activated , spatial information
  can be encoded into the signal . Since MR
• signal is in the form of a complex exponential ,
  2 ways of encoding the signal ,
• frequency encoding and phase encoding.

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Image Reconstruction
images
Raw data / k-space data
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• Spatial information is encoded into the k-space
  data. Depending on how the spatial information is
  encoded, the image reconstruction technique can
  vary
• Two fundamental image reconstruction are Fourier
  transform and Radon transofrm
• If K-space is sampled rectilinearly ( as a square
  ) then FT is used
• If K-space is sampled radially ( circularly )
  then RT is used
• Practical Reeconstruction techniques leads to one
  of this techniques as basic

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General issues in IR

• Understand the problem as finding an Image
  function, I which is consistent with the measured
  signal S, ( S Ti )
• Data consistency is very important. A violation
  will lead to loss of data violation or gain
  unwanted observation in image
• Stability , that is applicable to all signal
  collected, not applying to certain signals
• Understands the integration of scanning
  parameters ( FOV, slice selection, k-space
  density, image resolutions ) with information
  encoding before plotting k-space data
• Knows types of noises be produced such as
• Statistic Noise produced at low magnetic field
  strength
• Systematic noise at high magnetic field strength
• Noise produced by patient movement
• Understand the importance of Image Contrast to
  differentiate normal tissues, fluids, to identify
  the pathology condition
• Sginal to Noise ratio must be maximized
• Contrast to Noise ration must be maximized
• Artifacts minimization

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• Artifacts is signal produced by human
  workmanship. Produced during scanning period.
  Artifacts is produced by
• Patient movement including cardiac movement,
  blood flow or respiratory
• Any implants in patients body
• MR Hardware such as mechanical vibration,
  inhomogeneous RF coil etc
• MR software
• Lighting effects

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Image Reconstruction Techniques

• 1. General techniques such as directly applying
  Discrete Fourier Transform
• 2. Commercially available such as construction
  unrevealed techniques by MRI Scanner
  Manufacturers
• 3. Non-parametric techniques
• 4. Constrained parametric techniques

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Non parametric techniques

• Partial k-space reconstruction technique
• Based on Fourier transform , added functions to
  reduce noises and artifacts
• The data acquisition technique employed is
• 2DFT
• Limitation is time consuming, longer scanning
  time and Gibss ring is not removed
• Other techniques such as Direct FFT, Zero Filled
  FFT Reconstruction , The inverse Radon transform,
  Back projection reconstruction technique

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Advanced Reconstruction Techniques

• Different reconstruction algorithm suits
  different method of scanning. With a high speed
  imaging, reduced scanned approaches directly
  effects the information encoding. Also gives an
  additional problems such as spatial resolution
  new artifacts , etc. This creates an need for
  new and more stable techniques . Constrained
  reconstruction is a new area.
• Techniques such as Half Fourier reconstruction,
  Extrapolation Based Reconstruction and Parametric
  Construction are being introduced

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Parametric Reconstruction

• Introductin of a parametric model leaving behind
  the Fourier Series based reconstruction
• Parametric selection and estimation becoming the
  key step.
• Parametric model has a built in filtering
  capability to remove noise
• Example of Parametric technique is the use of
  ARMA model proposed by M.R. Smith in 1984

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ARMA

• Autoregressive Moving Average , an IIR Filter
• Motivated by high speed imaging, reduced scan
  time, and limitation by Fourier Series such as
  image artifacts and resolution loss
• Studies shows an 30 4 reduce in truncated
  energy, meaning reduced increase in resolution
  and reduction in image artifacts
• Limitation is practical complex algorithm due to
  parametric estimation.
• The solution is to use constrained the ARMA model
  to include a prior information and improve the
  algorithms.
• This leads to introduction of TERA , The
  Transient Error Reconstruction Algorithm an ARMA
  algorithm which attempts to model the MR signal
  as the output of an excited digital filter.( MR
  Smith )
• Same effort were done on DFT ( by ZP Liang) but
  not as successful as TERA model
• In TERA Algorithm, AR coefficients are modeled by
  a forwarding predicting linear prediction
  algorithm which is non stationary characteristics
  of MR signals components. And priori information
  is introduced by assuming that the ARMA filter is
  excited by a single pilse and setting the MA
  coefficient to prediction error.
• This method has been proved to be successful.
• Future developments are to extend to 2D with
  neural network based truncated data