Clarice Poon

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

Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with respect to an arbitrary basis or frame. Unlike more common approaches for this problem, such as the consistent reconstruction technique of Eldar and others, it leads to numerical methods possessing both guaranteed stability and accuracy. The purpose of this paper is twofold. First, we give a complete and formal analysis of generalized sampling, the main result of which being the derivation of new, sharp bounds for the accuracy and stability of this approach. Such bounds improve upon those given previously and result in a necessary and sufficient condition, the stable sampling rate, which guarantees a priori a good reconstruction. Second, we address the topic of optimality. Under some assumptions, we show that generalized sampling is an optimal, stable method. Correspondingly...

On the role of total variation in compressed sensing

This paper considers the problem of recovering a one- or two-dimensional discrete signal which is approximately sparse in its gradient from an incomplete subset of its Fourier coefficients which have been corrupted with noise. We prove that in order to obtain a reconstruction which is robust to noise and stable to inexact gradient sparsity of order

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

s

Sampling the Fourier Transform Along Radial Lines

with high probability, it suffices to draw

Recovery guarantees for TV regularized compressed sensing

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

\!{(s {\rm log} N)}

On optimal wavelet reconstructions from Fourier samples: Linearity and universality of the stable sampling rate

of the available Fourier coefficients uniformly at random. However, we also show that if one draws

Geometric properties of solutions to the total variation denoising problem

{\cal O}