We present a novel framework for the reconstruction of 1D composite signals assumed to be
a mixture of two additive components, one sparse and the other smooth, given a finite …

We study the growth properties of the family of iid random sequences, also known as
discrete white noises, and of their continuous-domain generalization, the family of L\'evy …

The paper presents two new families of stochastic processes called hyperkernel convolution
train and-counting processes. These models generalize respectively the spike train and …

In this paper, we precisely quantify the wavelet compressibility of compound Poisson
processes. To that end, we expand the given random process over the Haar wavelet basis …

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction
of sparse signals and to develop efficient algorithms to solve such problems …

In this thesis, we reveal that supervised learning and inverse problems share similar
mathematical foundations. Consequently, we are able to present a unified variational view of …