Some Comments on Variational Bayes Block Sparse Modeling with Correlated Entries
20 Aug 2018-pp 110-117
TL;DR: The effect of the threshold to prune out variance parameters of algorithms corresponding to several choices of marginals, viz. multivariate Jeffery prior, multivariate Laplace distribution and multivariate Student’s t distribution is discussed.
Abstract: We present some details of Bayesian block sparse modeling using hierarchical prior having deterministic and random parameters when entries within the blocks are correlated. In particular, the effect of the threshold to prune out variance parameters of algorithms corresponding to several choices of marginals, viz. multivariate Jeffery prior, multivariate Laplace distribution and multivariate Student’s t distribution, is discussed. We also provide details of experiments with Electroencephalograph (EEG) data which shed some light on the possible applicability of the proposed Sparse Variational Bayes framework.
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08 Aug 2013
TL;DR: A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build and serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject.
Abstract: At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians.A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
2,270 citations
TL;DR: The significance of the results presented in this paper lies in the fact that making explicit use of block-sparsity can provably yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem.
Abstract: We consider efficient methods for the recovery of block-sparse signals-ie, sparse signals that have nonzero entries occurring in clusters-from an underdetermined system of linear equations An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we introduce We then show that a block-version of the orthogonal matching pursuit algorithm recovers block -sparse signals in no more than steps if the block-coherence is sufficiently small The same condition on block-coherence is shown to guarantee successful recovery through a mixed -optimization approach This complements previous recovery results for the block-sparse case which relied on small block-restricted isometry constants The significance of the results presented in this paper lies in the fact that making explicit use of block-sparsity can provably yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem
1,289 citations
TL;DR: A recognition approach is proposed based on the extracted frequency features for an SSVEP-based brain computer interface (BCI) that were higher than those using a widely used fast Fourier transform (FFT)-based spectrum estimation method.
Abstract: Canonical correlation analysis (CCA) is applied to analyze the frequency components of steady-state visual evoked potentials (SSVEP) in electroencephalogram (EEG). The essence of this method is to extract a narrowband frequency component of SSVEP in EEG. A recognition approach is proposed based on the extracted frequency features for an SSVEP-based brain computer interface (BCI). Recognition Results of the approach were higher than those using a widely used fast Fourier transform (FFT)-based spectrum estimation method
826 citations
TL;DR: It is shown that exploiting intra-block correlation is very helpful in improving recovery performance, and two families of algorithms based on the framework of block sparse Bayesian learning (BSBL) are proposed to exploit such correlation and improve performance.
Abstract: We examine the recovery of block sparse signals and extend the recovery framework in two important directions; one by exploiting the signals' intra-block correlation and the other by generalizing the signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One family, directly derived from the BSBL framework, require knowledge of the block structure. Another family, derived from an expanded BSBL framework, are based on a weaker assumption on the block structure, and can be used when the block structure is completely unknown. Using these algorithms, we show that exploiting intra-block correlation is very helpful in improving recovery performance. These algorithms also shed light on how to modify existing algorithms or design new ones to exploit such correlation and improve performance.
491 citations
TL;DR: Experimental results show that block sparse Bayesian learning is better than state-of-the-art CS algorithms, and sufficient for practical use, and suggest that BSBL is very promising for telemonitoring of EEG and other nonsparse physiological signals.
Abstract: Telemonitoring of electroencephalogram (EEG) through wireless body-area networks is an evolving direction in personalized medicine. Among various constraints in designing such a system, three important constraints are energy consumption, data compression, and device cost. Conventional data compression methodologies, although effective in data compression, consumes significant energy and cannot reduce device cost. Compressed sensing (CS), as an emerging data compression methodology, is promising in catering to these constraints. However, EEG is nonsparse in the time domain and also nonsparse in transformed domains (such as the wavelet domain). Therefore, it is extremely difficult for current CS algorithms to recover EEG with the quality that satisfies the requirements of clinical diagnosis and engineering applications. Recently, block sparse Bayesian learning (BSBL) was proposed as a new method to the CS problem. This study introduces the technique to the telemonitoring of EEG. Experimental results show that its recovery quality is better than state-of-the-art CS algorithms, and sufficient for practical use. These results suggest that BSBL is very promising for telemonitoring of EEG and other nonsparse physiological signals.
244 citations