• Publications
  • Influence
Breaking the coherence barrier: A new theory for compressed sensing
TLDR
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
  • 202
  • 13
  • PDF
On instabilities of deep learning in image reconstruction and the potential costs of AI
TLDR
In this paper, we demonstrate a crucial phenomenon: Deep learning typically yields unstable methods for image reconstruction with potential to change the field. Expand
  • 69
  • 6
  • PDF
Geometric properties of solutions to the total variation denoising problem
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 totalExpand
  • 43
  • 6
  • PDF
On the Role of Total Variation in Compressed Sensing
  • C. Poon
  • Computer Science, Mathematics
  • SIAM J. Imaging Sci.
  • 20 July 2014
TLDR
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
  • 40
  • 5
  • PDF
Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing
TLDR
We introduce a mathematical framework that bridges a substantial gap between compressed sensing theory and its current use in real-world applications. Expand
  • 62
  • 4
  • PDF
Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem
TLDR
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. Expand
  • 56
  • 4
  • PDF
Local Convergence Properties of SAGA/Prox-SVRG and Acceleration
TLDR
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
  • 18
  • 4
  • PDF
MultiDimensional Sparse Super-Resolution
  • C. Poon, G. Peyré
  • Mathematics, Computer Science
  • SIAM J. Math. Anal.
  • 10 September 2017
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-gridExpand
  • 25
  • 3
  • PDF
Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames
  • C. Poon
  • Computer Science, Mathematics
  • ArXiv
  • 20 May 2015
TLDR
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
  • 16
  • 2
  • PDF
A Practical Guide to the Recovery of Wavelet Coefficients from Fourier Measurements
TLDR
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
  • 12
  • 2
  • PDF