A probabilistic compressive sensing framework with applications to ultrasound signal processing
Fuentes, Ramon and Mineo, Carmelo and Pierce, Stephen G. and Worden, Keith and Cross, Elizabeth J. (2019) A probabilistic compressive sensing framework with applications to ultrasound signal processing. Mechanical Systems and Signal Processing, 117. pp. 383-402. ISSN 0888-3270 (https://doi.org/10.1016/j.ymssp.2018.07.036)
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Abstract
The field of Compressive Sensing (CS) has provided algorithms to reconstruct signals from a much lower number of measurements than specified by the Nyquist-Shannon theorem. There are two fundamental concepts underpinning the field of CS. The first is the use of random transformations to project high-dimensional measurements onto a much lower-dimensional domain. The second is the use of sparse regression to reconstruct the original signal. This assumes that a sparse representation exists for this signal in some known domain, manifested by a dictionary. The original formulation for CS specifies the use of an l 1 penalised regression method, the Lasso. Whilst this has worked well in literature, it suffers from two main drawbacks. First, the level of sparsity must be specified by the user, or tuned using sub-optimal approaches. Secondly, and most importantly, the Lasso is not probabilistic; it cannot quantify uncertainty in the signal reconstruction. This paper aims to address these two issues; it presents a framework for performing compressive sensing based on sparse Bayesian learning. Specifically, the proposed framework introduces the use of the Relevance Vector Machine (RVM), an established sparse kernel regression method, as the signal reconstruction step within the standard CS methodology. This framework is developed within the context of ultrasound signal processing in mind, and so examples and results of compression and reconstruction of ultrasound pulses are presented. The dictionary learning strategy is key to the successful application of any CS framework and even more so in the probabilistic setting used here. Therefore, a detailed discussion of this step is also included in the paper. The key contributions of this paper are a framework for a Bayesian approach to compressive sensing which is computationally efficient, alongside a discussion of uncertainty quantification in CS and different strategies for dictionary learning. The methods are demonstrated on an example dataset from collected from an aerospace composite panel. Being able to quantify uncertainty on signal reconstruction reveals that this grows as the level of compression increases. This is key when deciding appropriate compression levels, or whether to trust a reconstructed signal in applications of engineering and scientific interest.
ORCID iDs
Fuentes, Ramon, Mineo, Carmelo ORCID: https://orcid.org/0000-0002-5086-366X, Pierce, Stephen G. ORCID: https://orcid.org/0000-0003-0312-8766, Worden, Keith and Cross, Elizabeth J.;-
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Item type: Article ID code: 65348 Dates: DateEvent15 February 2019Published16 August 2018Published Online21 July 2018Accepted31 January 2018SubmittedSubjects: Technology > Electrical engineering. Electronics Nuclear engineering Department: Faculty of Engineering > Electronic and Electrical Engineering Depositing user: Pure Administrator Date deposited: 03 Sep 2018 14:42 Last modified: 13 Sep 2024 00:33 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/65348