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- Thomas Blumensath, Mike E. Davies
- ArXiv
- 2008

Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when applied to the compressed sensing recovery problem. We show that the algorithm has the following properties… (More)

Sparse signal expansions represent or approximate a signal using a small number of elements from a large collection of elementary wave-forms. Finding the optimum sparse expansion is known to be NP hard in general and non-optimal strategies such as Matching Pursuit, Orthogonal Matching Pursuit, Basis Pursuit and Basis Pursuit De-noising are often called… (More)

- Juan Pablo Bello, Laurent Daudet, Samer A. Abdallah, Chris Duxbury, Mike E. Davies, Mark B. Sandler
- IEEE Transactions on Speech and Audio Processing
- 2005

Note onset detection and localization is useful in a number of analysis and indexing techniques for musical signals. The usual way to detect onsets is to look for "transient" regions in the signal, a notion that leads to many definitions: a sudden burst of energy, a change in the short-time spectrum of the signal or in the statistical properties, etc. The… (More)

- Sangnam Nam, Mike E. Davies, Michael Elad, Rémi Gribonval
- ArXiv
- 2011

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative , is markedly different.… (More)

- Thomas Blumensath, Mike E. Davies
- IEEE Journal of Selected Topics in Signal…
- 2010

Sparse signal models are used in many signal processing applications. The task of estimating the sparsest coefficient vector in these models is a combinatorial problem and efficient, often suboptimal strategies have to be used. Fortunately, under certain conditions on the model, several algorithms could be shown to efficiently calculate near-optimal… (More)

- Thomas Blumensath, Mike E. Davies
- IEEE Transactions on Signal Processing
- 2008

Sparse signal approximations have become a fundamental tool in signal processing with wide-ranging applications from source separation to signal acquisition. The ever-growing number of possible applications and, in particular, the ever-increasing problem sizes now addressed lead to new challenges in terms of computational strategies and the development of… (More)

- Mike E. Davies, Yonina C. Eldar
- IEEE Transactions on Information Theory
- 2012

This paper revisits the sparse multiple measurement vector (MMV) problem, where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem is an extension of single channel sparse recovery, which lies at the heart of compressed sensing. Inspired by the links to array signal processing, a new family of MMV… (More)

- Thomas Blumensath, Mike E. Davies
- IEEE Transactions on Information Theory
- 2009

Compressed sensing is an emerging signal acquisition technique that enables signals to be sampled well below the Nyquist rate, given that the signal has a sparse representation in an orthonormal basis. In fact, sparsity in an orthonormal basis is only one possible signal model that allows for sampling strategies below the Nyquist rate. In this paper, we… (More)

We explore the use of Mixture of Gaussians (MoGs) for noisy and overcomplete ICA when the source distributions are very sparse. The sparsity model can often be justified if an appropriate transform, such as the Modified Discrete Cosine Transform, is used. Given the sparsity assumption we are able to introduce a number of simplifying approximations to the… (More)

- Mike E. Davies, Christopher J. James
- Signal Processing
- 2007