Polar Polytopes and Recovery of Sparse Representations

Suppose we have a signal y which we wish to represent using a linear combination of a number of basis atoms a_i, y=sum_i x_i a_i = Ax. The problem of finding the minimum L0 norm representation for y is a hard problem. The Basis Pursuit (BP) approach proposes to find the minimum L1 norm representation instead, which corresponds to a linear program (LP) that can be solved using modern LP techniques, and several recent authors have given conditions for the BP (minimum L1 norm) and sparse (minimum L0 solutions) representations to be identical. In this paper, we explore this sparse representation problem} using the geometry of convex polytopes, as recently introduced into the field by Donoho. By considering the dual LP we find that the so-called polar polytope P of the centrally-symmetric polytope P whose vertices are the atom pairs +-a_i is particularly helpful in providing us with geometrical insight into optimality conditions given by Fuchs and Tropp for non-unit-norm atom sets. In exploring this geometry we are able to tighten some of these earlier results, showing for example that the Fuchs condition is both necessary and sufficient for L1-unique-optimality, and that there are situations where Orthogonal Matching Pursuit (OMP) can eventually find all L1-unique-optimal solutions with m nonzeros even if ERC fails for m, if allowed to run for more than m steps

Traction for low back pain, the evidence is flawed : a thesis presented in partial fulfilment of the requirements for the Masters of Health Science (MHlthSci) in Environmental Health at Massey University Campus, Wellington, New Zealand

Research suggests the burden of low back pain is growing despite recent advances in investigative technology and the explosion in research. Evidence based practice is necessary within physiotherapy. However, the best evidence component must be clinically appropriate, accurate, and grounded within pertinent research. The selection of participants and the methodological designs of the studies must be appropriate to provide results valid to everyday clinical practice. Systematic reviews and meta-analyses consider primary research to critically analyse research questions, and formulate scientific conclusions on the efficacy of interventions. These research derived conclusions then inform clinical practice guidelines which are envisioned to improve clinical practice. These guidelines are also utilised by educational facilities to flavour their curriculum, and by insurance and governmental policy writers in accrediting specific interventions. Information from today will dictate the beliefs, attitudes, and practices of future graduates, and determine approved treatment options. The reported negative conclusions on the efficacy of traction as an intervention for low back pain have resulted in traction no longer being recommended within clinical practice guidelines, any remaining sporadic use questioned by professional colleagues and policy writers, and it no longer taught at undergraduate level. This is despite its long history, popularity amongst some practitioners, anecdotal evidence supporting its use in the clinical setting, and its demonstrable effects in scientific studies. This masters project argues that the cause of the disparity lies within incongruous study designs, which are not valid to clinical practice. Specifically, caused by the misappropriation of historical definitions and classifications vis-à-vis low back pain cohorts. This has resulted in substantial heterogeneity within study populations themselves, both between groups and between studies, which along with other methodological flaws and inappropriate reporting, has given rise to unwarranted conclusions. These fundamental errors have made the conclusions of scientific trials, systematic reviews, and clinical practice guidelines erroneous, and inapplicable to everyday clinical practice. The ‘evidence based’ recommendations of th

Segregating Event Streams and Noise with a Markov Renewal Process Model

DS and MP are supported by EPSRC Leadership Fellowship EP/G007144/1

Learning incoherent dictionaries for sparse approximation using iterative projections and rotations

This work was supported by the Queen Mary University of London School Studentship, the EU FET-Open project FP7- ICT-225913-SMALL. Sparse Models, Algorithms and Learning for Large-scale data and a Leadership Fellowship from the UK Engineering and Physical Sciences Research Council (EPSRC)

Automatic large-scale classification of bird sounds is strongly improved by unsupervised feature learning

This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited. See: http://creativecommons.org/ licenses/by/4.0

Efficient Bayesian inference for harmonic models via adaptive posterior factorization

NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in NEUROCOMPUTING, [VOL72, ISSUE 1-3, (2008)] DOI10.1016/j.neucom.2007.12.05

Multichannel high resolution NMF for modelling convolutive mixtures of non-stationary signals in the time-frequency domain

Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies

Creating Cultures of Innovation: The Digital Creative Industries

date-added: 2015-03-24 04:16:59 +0000 date-modified: 2015-03-24 04:16:59 +0000date-added: 2015-03-24 04:16:59 +0000 date-modified: 2015-03-24 04:16:59 +0000date-added: 2015-03-24 04:16:59 +0000 date-modified: 2015-03-24 04:16:59 +0000This work was supported by the Arts and Humanities Research Council, CreativeWorks London Hub, grant AH/J005142/1, and the European Regional Development Fund, London Creative and Digital Fusion

Performance Following: Real-Time Prediction of Musical Sequences Without a Score

(c)2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works

PERFORMANCE FOLLOWING: TRACKING A PERFORMANCE WITHOUT A SCORE

EPSRC Doctoral Training Award; EPSRC Leadership Fellowshi