C. Poon

Publications
Influence

Breaking the coherence barrier: A new theory for compressed sensing

B. Adcock, A. Hansen, C. Poon, B. Roman
Mathematics, Computer Science
3 February 2013

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

On instabilities of deep learning in image reconstruction and the potential costs of AI

Vegard Antun, Francesco Renna, C. Poon, B. Adcock, A. Hansen
Computer Science, Medicine
Proceedings of the National Academy of Sciences
14 February 2019

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

Geometric properties of solutions to the total variation denoising problem

A. Chambolle, V. Duval, G. Peyré, C. Poon
Mathematics
30 January 2016

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

On the Role of Total Variation in Compressed Sensing

C. Poon
Computer Science, Mathematics
SIAM J. Imaging Sci.
20 July 2014

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

Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing

B. Adcock, A. Hansen, C. Poon, B. Roman
Computer Science
ArXiv
4 February 2013

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

Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem

B. Adcock, A. Hansen, C. Poon
Computer Science, Mathematics
SIAM J. Math. Anal.
13 January 2013

Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. Expand

Local Convergence Properties of SAGA/Prox-SVRG and Acceleration

C. Poon, Jingwei Liang, C. Schoenlieb
Computer Science, Mathematics
ICML
7 February 2018

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

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-grid… Expand

Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames

C. Poon
Computer Science, Mathematics
ArXiv
20 May 2015

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

A Practical Guide to the Recovery of Wavelet Coefficients from Fourier Measurements

M. Gataric, C. Poon
Mathematics, Computer Science
SIAM J. Sci. Comput.
20 May 2015

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

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