Expectation-maximization Bernoulli-Gaussian approximate message passing

Vila, Jeremy; Schniter, Philip

doi:10.1109/acssc.2011.6190117

Cited by 121 publications

(135 citation statements)

References 14 publications

(21 reference statements)

Supporting

Mentioning

133

Contrasting

Order By: Relevance

“…We modify adaptive GAMP to calibrate the measurement system by learning S directly from L measurement vectors. Our work thus extends the scenario considered in [7][8][9] where S is assumed to be known.…”

Section: Relation To Prior Workmentioning

confidence: 82%

“…The algorithm relies on the Central Limit Theorem to simplify loopy belief propagation by replacing continuous-domain convolutions with matrix-vector multiplications followed by pointwise nonlinearities [6,13]. Although the basic GAMP algorithm requires perfect knowledge of S, λ, and v w for reconstruction, it was recently extended to incorporate parameter learning [7][8][9]. In particular, a recently introduced adaptive GAMP method combines maximum-likelihood (ML) estimation with the standard GAMP updates [7].…”

Section: Calibration With Adaptive Gampmentioning

confidence: 99%

“…Recently, a generalized version of GAMP called adaptive GAMP was proposed for solving inverse problems where the signal and noise distributions have parametric uncertainties [7]. Adaptive GAMP generalizes several prior works [8,9], and provably yields asymptotically consistent estimates of the unknown parameters. In the following, we demonstrate that the adaptive GAMP framework can be extended in order to solve (1).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Autocalibrated signal reconstruction from linear measurements using adaptive GAMP

Kamilov

Bourquard

Bostan

et al. 2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

View full text Add to dashboard Cite

In this paper, we reconstruct signals from underdetermined linear measurements where the componentwise gains of the measurement system are unknown a priori. The reconstruction is performed through an adaptation of the messagepassing algorithm called adaptive GAMP that enables joint gain calibration and signal estimation. To evaluate our approach, we apply it to the problem of sparse recovery and compare it against an 1 -based approach. We numerically show that adaptive GAMP yields excellent results even for a moderate amount of data. It approaches the performance of oracle GAMP where the gains are perfectly known asymptotically.

show abstract

Section: Relation To Prior Workmentioning

confidence: 82%

Section: Calibration With Adaptive Gampmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Autocalibrated signal reconstruction from linear measurements using adaptive GAMP

Kamilov

Bourquard

Bostan

et al. 2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

View full text Add to dashboard Cite

show abstract

“…2) BG model: As mentioned in the introduction, BG model (6)- (7) has already been considered in some contributions ( [28], [29], [32], [33]) and under the marginal formulation (3) in [35], [36]. However all these contributions differ from the proposed approach by the estimation problem and the practical procedure introduced to solve it.…”

Section: ) Boltzmann Machinementioning

confidence: 92%

“…While σ 2 0 can be tuned to any positive real value in the first BG model presented above, it is set to 0 in the second one. This marginal formulation is directly used in many contributions as in [35], [36].…”

Section: A Standard Sparse Representation Algorithmsmentioning

confidence: 99%

Boltzmann Machine and Mean-Field Approximation for Structured Sparse Decompositions

Drémeau

Herzet

Daudet

2012

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

To cite this version:Angélique Drémeau, Cédric Herzet, Laurent Daudet. Boltzmann machine and mean-field approximation for structured sparse decompositions. Accepté à IEEE Trans. On Signal Processing. 2012. AbstractTaking advantage of the structures inherent in many sparse decompositions constitutes a promising research axis. In this paper, we address this problem from a Bayesian point of view. We exploit a Boltzmann machine, allowing to take a large variety of structures into account, and focus on the resolution of a marginalized maximum a posteriori problem. To solve this problem, we resort to a mean-field approximation and the "variational Bayes Expectation-Maximization" algorithm. This approach results in a soft procedure making no hard decision on the support or the values of the sparse representation. We show that this characteristic leads to an improvement of the performance over state-of-the-art algorithms. Index TermsStructured sparse representation, Bernoulli-Gaussian model, Boltzmann machine, mean-field approximation.

show abstract

A probabilistic Bayesian approach to recover R2*$$ {R}_{2\ast } $$ map and phase images for quantitative susceptibility mapping

Huang

Lah

Allen

et al. 2022

Magnetic Resonance in Med

View full text Add to dashboard Cite

Purpose Undersampling is used to reduce the scan time for high‐resolution three‐dimensional magnetic resonance imaging. In order to achieve better image quality and avoid manual parameter tuning, we propose a probabilistic Bayesian approach to recover R2∗$$ {R}_2^{\ast } $$ map and phase images for quantitative susceptibility mapping (QSM), while allowing automatic parameter estimation from undersampled data. Theory Sparse prior on the wavelet coefficients of images is interpreted from a Bayesian perspective as sparsity‐promoting distribution. A novel nonlinear approximate message passing (AMP) framework that incorporates a mono‐exponential decay model is proposed. The parameters are treated as unknown variables and jointly estimated with image wavelet coefficients. Methods Undersampling takes place in the y‐z plane of k‐space according to the Poisson‐disk pattern. Retrospective undersampling is performed to evaluate the performances of different reconstruction approaches, prospective undersampling is performed to demonstrate the feasibility of undersampling in practice. Results The proposed AMP with parameter estimation (AMP‐PE) approach successfully recovers R2∗$$ {R}_2^{\ast } $$ maps and phase images for QSM across various undersampling rates. It is more computationally efficient, and performs better than the state‐of‐the‐art l1$$ {l}_1 $$‐norm regularization (L1) approach in general, except a few cases where the L1 approach performs as well as AMP‐PE. Conclusion AMP‐PE achieves better performance by drawing information from both the sparse prior and the mono‐exponential decay model. It does not require parameter tuning, and works with a clinical, prospective undersampling scheme where parameter tuning is often impossible or difficult due to the lack of ground‐truth image.

show abstract

Expectation-maximization Bernoulli-Gaussian approximate message passing

Cited by 121 publications

References 14 publications

Autocalibrated signal reconstruction from linear measurements using adaptive GAMP

Autocalibrated signal reconstruction from linear measurements using adaptive GAMP

Boltzmann Machine and Mean-Field Approximation for Structured Sparse Decompositions

A probabilistic Bayesian approach to recover R2*$$ {R}_{2\ast } $$ map and phase images for quantitative susceptibility mapping

Contact Info

Product

Resources

About