An exact tree projection algorithm for wavelets by Cartis, C, Thompson, A

“…In contrast to other recently proposed algorithms which only give approximate tree projections for a given sparsity, our algorithm is guaranteed to calculate the projection exactly. …”

Quantitative recovery conditions for tree-based compressed sensing by Cartis, C, Thompson, A

“…As shown by Blumensath and Davies (2009) and Baraniuk et al. (2010), signals whose wavelet coefficients exhibit a rooted tree structure can be recovered using specially adapted compressed sensing algorithms from just n = O(k) measurements, where k is the sparsity of the signal. Motivated by these results, we introduce a simplified proportional-dimensional asymptotic framework, which enables the quantitative evaluation of recovery guarantees for tree-based compressed sensing. …”

A new and improved quantitative recovery analysis for iterative hard thresholding algorithms in compressed sensing by Cartis, C, Thompson, A

“…For both stepsize schemes, we obtain asymptotic phase transitions in a proportional-dimensional framework, quantifying the sparsity/undersampling trade-off for which recovery is guaranteed. …”

Phase transitions for greedy sparse approximation algorithms by Tanner, J, Blanchard, J, Cartis, C, Thompson, A

“…Bounds on RIP constants can be inserted into the algorithms RIP-based conditions, translating the conditions into requirements on the signal's sparsity level, length, and number of measurements. …”

A new and improved quantitative recovery analysis for iterative hard thresholding algorithms in compressed sensing by Cartis, C, Thompson, A

“…For both stepsize schemes, we obtain lower bounds on asymptotic phase transitions in a proportional-dimensional framework, quantifying the sparsity/undersampling tradeoff for which recovery is guaranteed. …”

A derivative-free optimisation method for global ocean biogeochemical models by Oliver, S, Cartis, C, Kriest, I, Tett, SFB, Khatiwala, S

“…We also find that the performance of DFO-LS is not significantly affected by observational sparsity, however fewer parameters were successfully optimised in the presence of observational uncertainty. …”