A recent trend in MRI, is to see imaging as a general inverse problem instead of the more conventional inverse fourier transform. This approach permits a lot of improvements in MRI: better resolution, less artifacts, fast acquisition sequences, improved robustness to noise. All these points represent a great challenge in order to facilitate clinician diagnostic.

The inverse problem point of view allows a large panel of reconstruction techniques. Among them, the linear ones present the advantage to be rapidly performed. This point is critical for real-time applications.

There exist several techniques of linear reconstruction: Wiener, Maximum a posteriori, quadratic regularisation... They all require a prior knowledge and perform the optimal estimate with respect to a certain criterion.

Steps of the project:

1. Implement a simple forward model based on the FFT. It will be used after in data simulation and reconstruction.
2. Find out the links between classical linear estimators.
3. Implement the corresponding reconstruction techniques.
4. Compare them in cases where they are not equivalent. We will focus on reconstruction accuracy in presence of noise, which is the crucial point in clinical applications.