P. Weiss : Concentration inequalities for the synthesis problem in compressive sampling
In this talk, I will present algorithms in order to solve the synthesis problem in compressive sampling: for fixed representation and measurement bases, how to design sampling patterns that guarantee accurate reconstruction of sparse signals?
This work is based on a recent contribution of Juditski et al. who proposed randomized algorithms that consist in selecting measurements independently at random. We propose a simple convergence proof based on concentration inequalities. This proof extends to more complex frameworks where the sampling schemes are generated using random walks on the space of measurements. Such sampling strategies are relevant for practical imaging systems such as MRI where successive samples should be close.