MRI Reconstructions

From the Theory to the Implementation

The Monalisa toolbox for MRI reconstruction has been originaly developed at CIBM-CHUV between 2018 and 2023 by Bastien Milani. It continued to evovled until now, notably by the contribution of Berk Can Açikgöz while working in QIS lab at Inselspital and university of Bern.

Originally, the development of the toolbox began by the implementation of non-cartesian reconstructions. The first reconstruction implemented was a gridded reconstruction which is part of the static non-iterative familly. After that, some static iterative reconstruction were added and later 3D-CINE iterative reconstructions with temporal regularisation were implemented (4D and 5D), all for non-cartesian data. Iterative 3D-CINE reconstruction for cartesian data were then implemented on the same model. The toolbox was further enriched with GRAPPA implementations.

This toolbox can be used freely for any resonable personal or academic application, including publications. But any redistribution or commercial usage must be done in collaboration with lincensors (see the LICENSE file).

• Installation
  • Install Git
    • On Windows
    • On Linux
  • Clone the repository
  • Take a first look at the Monalisa folder
  • Install a c++ compiler
    • On Windows
    • On Linux
  • Compilation in Matlab
• Theoretical Background
  • Some Notions of MRI Physics
    • The \(\vec{M}\)
    • The \(\vec{B}_0\)
    • Thermal Equilibrium
    • The \(\vec{B}_1\)
    • The Larmor Frequency
    • The selection of the resonating nuclei
    • Excitation of resonating nuclei
    • Free relaxation
    • Reciprocity principle
    • Steady State
    • Signal equation
  • The Discret Reconstruction Problems
    • Discretization of the Signal Equation
    • The Different Fourier Transforms
    • The Coil-Sensitivity map
    • The Linear Model of MRI Reconstruction
    • Image-space \(X\) and Data-space \(Y\)
  • Algorithms
    • The Conjugate Gradient Descent
    • ADMM Algorithme
• Tutorials
  • Tutorial 0 : testing of the installation and of the multi-threading
    • Introduction
    • Sparse matrix-vector multiplication
    • Further explanation
  • Tutorial 1 : A gridded-zero-padded reconstrcution for non-cartesian data
    • Introduction
    • Initialization
    • Reconstructions
    • Further Explanation
  • Tutorial 2 : Some static, iterative, non-cartesian reconstructions
    • Introduction
    • Initialisation, initial image and gridding matrices
    • The reconstructions
    • Further Explanation
  • Tutorial 3 : Iterative CINE reconstructions with 1 temporal dimension for non-cartesian data
    • Initial image
    • \(l_1\)-regularized least-square reconstruction with 1 temporal dimension for non-cartesian data
    • \(l_2\)-regularized least-square reconstruction with 1 temporal dimension for non-cartesian data
    • Further explanation
• Sketching a Classical Thermodynamic Theory of Information for MRI Reconstructions
  • Introduction
  • Iterative Reconstructions
  • The Phase Space
  • The Space of Memory States
  • The Heat Engine
  • The Computer as an Engine
  • A Postulate for the Thermodynamical Entropy of the Dynamic Memory
  • Information and Efficiency
  • Connection with the Theory of Information
  • Parallel Computing
  • Connection with the Landauer’s Principle
  • Connection with Statistical Mechanic
  • Artificial Intelligence as an Amplification of Efficiency
  • Conclusion