Proceedings ArticleDOI
Compressive sensing for ultrasound RF echoes using a-Stable Distributions
Alin Achim,Benjamin Buxton,George Tzagkarakis,Panagiotis Tsakalides +3 more
- Vol. 2010, pp 4304-4307
TLDR
An approach to ℓp norm minimisation that employs the iteratively reweighted least squares (IRLS) algorithm but in which the parameter p is judiciously chosen by relating it to the characteristic exponent of the underlying alpha-stable distributed data.Abstract:
This paper introduces a novel framework for compressive sensing of biomedical ultrasonic signals based on modelling data with stable distributions. We propose an approach to l p norm minimisation that employs the iteratively reweighted least squares (IRLS) algorithm but in which the parameter p is judiciously chosen by relating it to the characteristic exponent of the underlying alpha-stable distributed data. Our results show that the proposed algorithm, which we prefer to call S±S-IRLS, outperforms previously proposed l 1 minimisation algorithms, such as basis pursuit or orthogonal matching pursuit, both visually and in terms of PSNR.read more
Citations
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Journal ArticleDOI
Fourier-domain beamforming: the path to compressed ultrasound imaging
TL;DR: In this paper, the authors extend the concept of beamforming in frequency to a general concept, which allows exploitation of the low bandwidth of the ultrasound signal and bypassing of the oversampling dictated by digital implementation of beamformers in time.
Journal ArticleDOI
Pre-beamformed RF signal reconstruction in medical ultrasound using compressive sensing
TL;DR: This paper proposes to perform and assess CS reconstruction of channel RF data using the recently introduced wave atoms [1] representation, which exhibit advantageous properties for sparsely representing such oscillatory patterns and shows the superiority of the wave atom representation.
Journal ArticleDOI
Frequency Domain Compressive Sampling for Ultrasound Imaging
TL;DR: In this article, compressive sampling is used to sample signals or images below the classic Shannon-Nyquist theorem limit in medical imaging modalities such as magnetic resonance imaging, computed tomography, or photoacoustics.
Journal ArticleDOI
Compressed Sensing Reconstruction of 3D Ultrasound Data Using Dictionary Learning and Line-Wise Subsampling
TL;DR: In this study, the dictionary was learned using the K-SVD algorithm on patches extracted from a training dataset constituted of simulated 3D non-log envelope US volumes, showing the potential of the overcomplete dictionaries.
Journal ArticleDOI
Compressive Deconvolution in Medical Ultrasound Imaging
TL;DR: In this paper, the authors proposed a compressive deconvolution-based image processing technique to enhance the ultrasound images by combining random projections and 2D convolution with a spatially invariant point spread function.
References
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Journal ArticleDOI
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: It is demonstrated theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal.
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.
Proceedings ArticleDOI
Iteratively reweighted algorithms for compressive sensing
Rick Chartrand,Wotao Yin +1 more
TL;DR: A particular regularization strategy is found to greatly improve the ability of a reweighted least-squares algorithm to recover sparse signals, with exact recovery being observed for signals that are much less sparse than required by an unregularized version.