We introduce a mathematical framework that generalizes the three standard pillars of compressed sensing - namely, sparsity, incoherence and uniform random subsampling - to three new concepts: asymptotic sparsity and multilevel random sampling.Expand

In this paper, we demonstrate a crucial phenomenon: Deep learning typically yields unstable methods for image reconstruction with potential to change the field.Expand

This article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher-Fatemi total… Expand

We prove that in order to obtain a reconstruction which is robust to noise and stable to inexact gradient sparsity of order $s$ with high probability, it suffices to draw ${\cal O}$ of the available Fourier coefficients uniformly at random.Expand

We introduce a mathematical framework that bridges a substantial gap between compressed sensing theory and its current use in real-world applications.Expand

We present a unified framework for the local convergence analysis of the SAGA/Prox-SVRG algorithms for proximal variance reduced stochastic optimisation methods, and mainly focus on the SAEA and Prox- SVRG methods.Expand

This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid… Expand

This paper extends the result of Adcock, Hansen, Poon and Roman (arXiv:1302.0561, 2013) [2] to the case where the sparsifying system forms a tight frame.Expand

We show that generalized sampling has a computational complexity of $\mathcal{O}\left(M(N)\log N\right)$ when recovering the first $N$ boundary-corrected wavelet coefficients of an unknown compactly supported function from pointwise evaluations of its Fourier transform.Expand