Type I and Type II Bayesian Methods for Sparse Signal Recovery Using Scale Mixtures

Giri, Ritwik; Rao, Bhaskar D.

doi:10.1109/tsp.2016.2546231

Cited by 120 publications

(100 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…17,20 The hierarchical formulation of SBL inference offers both a computationally convenient Gaussian posterior distribution for adaptive processing (type-I maximum likelihood) and automatic regularization towards robust sparse estimates determined by the hyperparameters which maximize the evidence (type-II maximum likelihood). 21 In array signal processing, SBL is shown to improve significantly the resolution in beamforming 22 and in general the accuracy of DOA estimation, [23][24][25][26][27][28] 26 and multifrequency 23,24,27,28 SBL inference exploits the common sparsity profile across snapshots for stationary signals and frequencies for broadband signals to provide robust estimates by alleviating the ambiguity in the spatial mapping between sources and sensors due to noise and frequency-dependent spatial aliasing, respectively. Accounting for the statistics of modelling errors in SBL estimation, e.g., due to sensor position, sound speed uncertainty or basis mismatch, further improves support recovery.…”

mentioning

confidence: 99%

Sound source localization and speech enhancement with sparse Bayesian learning beamforming

Xenaki

Boldt

Christensen

2018

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

Speech localization and enhancement involves sound source mapping and reconstruction from noisy recordings of speech mixtures with microphone arrays. Conventional beamforming methods suffer from low resolution, especially with a limited number of microphones. In practice, there are only a few sources compared to the possible directions-of-arrival (DOA). Hence, DOA estimation is formulated as a sparse signal reconstruction problem and solved with sparse Bayesian learning (SBL). SBL uses a hierarchical two-level Bayesian inference to reconstruct sparse estimates from a small set of observations. The first level derives the posterior probability of the complex source amplitudes from the data likelihood and the prior. The second level tunes the prior towards sparse solutions with hyperparameters which maximize the evidence, i.e., the data probability. The adaptive learning of the hyperparameters from the data auto-regularizes the inference problem towards sparse robust estimates. Simulations and experimental data demonstrate that SBL beamforming provides high-resolution DOA maps outperforming traditional methods especially for correlated or non-stationary signals. Specifically for speech signals, the high-resolution SBL reconstruction offers not only speech enhancement but effectively speech separation.

show abstract

mentioning

confidence: 99%

Sound source localization and speech enhancement with sparse Bayesian learning beamforming

Xenaki

Boldt

Christensen

2018

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

“…There has been increased interest in Bayesian probabilistic approaches to sparse signal recovery (SSR) problems, [4,20,21,29,32]. There are two categories of Bayesian probabilistic methods for SSR that encompass many well-known recovery algorithms in practice, [20]. The first is type-I, or maximum a posteriori (MAP) Bayesian estimation which uses a fixed prior.…”

Section: Probabilistic Approachmentioning

confidence: 99%

“…Capturing the sparsity of solutions more accurately in the SSR problem has been widely studied, [4,8,9,10,20,21,29,32]. More recently, there has been increased interest in Bayesian probabilistic approaches to SSR, [4,20,21,29,32]. Within the probabilistic approaches there are two categories.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we focus our efforts on a particular type-II method called sparse Bayesian learning (SBL), also called the relevance vector machine (RVM), [29]. In [20], SBL typically outperformed all other methods including 1 regularization, [8], iteratively reweighted 1 , [9], and iteratively reweighted 2 regularization methods, [10], as well as a variety of type-II methods for SSR. The strength of SBL is also supported by evidence from [21], which looked at SBL from the perspective of compressed sensing, [8,14], and showed that SBL could recover a sparse signal with better accuracy than 1 regularization using the same amount of data.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Detecting Edges from Non-uniform Fourier Data via Sparse Bayesian Learning

Churchill

Gelb

2019

J Sci Comput

View full text Add to dashboard Cite

In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an 1 -regularized least squares cost function. This result can also be derived by employing a Bayesian formulation. Specifically, reconstruction of an edge map using 1 regularization corresponds to a so-called type-I (maximum a posteriori ) Bayesian estimate. In this paper, we use the Bayesian framework to design an improved algorithm for detecting edges from non-uniform Fourier data. In particular, we employ what is known as type-II Bayesian estimation, specifically a method called sparse Bayesian learning. We also show that our new edge detection method can be used to improve downstream processes that rely on accurate edge information like image reconstruction, especially with regards to compressed sensing techniques. 2 regularization, [10]. The second category is type-II, or evidence maximization Bayesian estimation which employs a hierarchical, flexible parametrized prior that is learned from the given data. For SSR, [20] provides * Department of Mathematics, Dartmouth College, USA 1 Note that while here we only explicitly consider non-uniform Fourier samples, all methods described here apply to uniform Fourier samples as well.2 Although ideally the 0 semi-norm should be used to regularize this problem, the resulting optimization problem is NP-hard. Hence the 1 norm has become a popular convex surrogate that makes the problem computationally tractable and also offers theoretical guarantees for exact reconstruction, [8], as well as a variety of other benefits related to compressed sensing, [14].

show abstract

“…Cramer-Rao bounds for SBL solution are discussed in [20]. Various sparse signal recovery solutions including LASSO and SBL are unified within the Bayesian framework in [21].…”

Section: Introductionmentioning

confidence: 99%

Sparse Bayesian learning with multiple dictionaries

et al. 2019

View full text Add to dashboard Cite

Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, approximately solves a non-convex optimization problem using fixed point updates. It provides comparable performance and is significantly faster than convex optimization techniques used in sparse processing. We propose a signal model which accounts for dictionary mismatch and the presence of errors in the weight vector at low signal-to-noise ratios. A fixed point update equation is derived which incorporates the statistics of mismatch and weight errors. We also process observations from multiple dictionaries. Noise variances are estimated using stochastic maximum likelihood. The derived update equations are studied quantitatively using beamforming simulations applied to direction-of-arrival (DoA). Performance of SBL using single-and multi-frequency observations, and in the presence of aliasing, is evaluated. SwellEx-96 experimental data demonstrates qualitatively the advantages of SBL.

show abstract

Type I and Type II Bayesian Methods for Sparse Signal Recovery Using Scale Mixtures

Cited by 120 publications

References 37 publications

Sound source localization and speech enhancement with sparse Bayesian learning beamforming

Sound source localization and speech enhancement with sparse Bayesian learning beamforming

Detecting Edges from Non-uniform Fourier Data via Sparse Bayesian Learning

Sparse Bayesian learning with multiple dictionaries

Contact Info

Product

Resources

About