Chorafas Foundation Award 2013 - Gilles Puy

" For developing novel mathematical models and algorithms aimed at solving complex inverse problems in imaging and computer vision, and demonstrating they can be used to accelerate MRI scanning".

Abstract: Compressive sampling is a recent theory which proves that sparse signals can be sampled at a much lower rate than the Nyquist rate. Only few and non-adaptive linear measurements are sufficient to guarantee the reconstruction of sparse signals via non-linear algorithms.

In my thesis, I first describe efficient and optimal compressive acquisition strategies based on spread spectrum techniques. I study these strategies theoretically but also use them to accelerate MRI. Using in vivo data acquired on a MR scanner, I show that these techniques can reduce the amount of acquired measurements by 75 percent, and consequently accelerate the MR acquisition by a factor of 4, without impairing image quality.

In the second part of my thesis, I describe a novel algorithm which advantageously combines multiple measurements of a moving object, acquired at different positions, to improve the accuracy of the reconstructed image of this object. This method can be used in multiple scenarios including compressive sampling, super-resolution, or robust image alignment. In addition, I also test this algorithm on real cardiac MR data and show that it can estimate high-resolution images of the heart by automatically correcting for the heart motion occurring during MR scans.