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MRI Reconstruction using Partial k-Space Scans

Farzi, Mohsen | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45985 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Fatemizadeh, Emadeddin
  7. Abstract:
  8. Based on Shannon theory, continuous-time band-limited signals are guaranteed to be recovered per-fectly subject to sampling with Nyquist rate. Due to inherently slow MRI sensors, sampling with Nyquist rate excruciatingly increases the scan time. This leads to patient inconvenience along with degradation in image quality caused by geometrical distortions.In recent years, Compressed Sensing (CS) has been introduced as an alternative to the Nyquist theory for the acquisition of sparse or compressible signals that can be well approximated by K ≪ N coeffi-cients from a N-dimensional basis. In CS theory, measurements are actually inner products of signal x with a base vector ϕi. In Fourier encoded MRI, images are first acquired in the Fourier space and then reconstructed via inverse Fourier transform. In other words, MRI imaging is equivalent to calculating the inner product of the image with Fourier bases. Hence, it is no surprise to reformulate MRI via CS theory. This thesis aims to enhance the reconstructed images based on partial k-sapce measurements. More specifically, online dynamic MRI reconstruction and brain multi-contrast MRI reconstruction is in-terested in this project. For this goal, each image is modeled as a random process with a specific probability distribution function. Then, a new regularizing function based on Mutual Information is presented based on non-parametric approximation of the distribution functions. Promising simulation results suggest that this function can be a good alternative to the standard ℓ1-norm or Total Variation regularizing functions. From a different point of view, probability distribution functions are approxi- mated via parametric methods by introduction of a well-posed hierarchical prior distribution function. Next, a Bayesian approach is utilized to solve the inverse problem.Reduction of reconstruction error from 1.19 % to half of this figure, i.e. 0.63 %, in multi-contrast appli- cation along with a reduction from 1.16 % to 0.61 % in online dynamic reconstruction using cartesian mask with random phase encoding are some of the singular results in this thesis. Reconstruction time of 0.4 second for images of size 256 × 256 and 0.2 second for images of size 128 × 128 makes our method a practical choice for online reconstruction applications
  9. Keywords:
  10. Magnetic Resonance Imagin (MRI) ; Compressive Sensing ; Bayesian Compressed Sensing ; Partial Fourier Sampling ; Dynamic Reconstruction

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