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16
Large scale Bayesian inference and experimental design for sparse linear models
- Journal of Physics: Conference Series
"... Abstract. Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or superresolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making prob ..."
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Cited by 22 (2 self)
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Abstract. Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or superresolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density’s mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex if and only if posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images. Parts of this work have been presented at
Motion Estimated and Compensated Compressed Sensing Dynamic Magnetic Resonance Imaging: What We Can Learn From Video Compression Techniques
, 2009
"... ABSTRACT: Compressed sensing has become an extensive research area in MR community because of the opportunity for unprecedented high spatio-temporal resolution reconstruction. Because dynamic magnetic resonance imaging (MRI) usually has huge redundancy along temporal direction, compressed sensing th ..."
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Cited by 17 (0 self)
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ABSTRACT: Compressed sensing has become an extensive research area in MR community because of the opportunity for unprecedented high spatio-temporal resolution reconstruction. Because dynamic magnetic resonance imaging (MRI) usually has huge redundancy along temporal direction, compressed sensing theory can be effectively used for this application. Historically, exploiting the temporal redundancy has been the main research topics in video compression technique. This article compares the similarity and differences of compressed sensing dynamic MRI and video compression and discusses what MR can learn from the history of video compression research. In particular, we demonstrate that the motion estimation and compensation in video compression technique can be also a powerful tool to reduce the sampling requirement in dynamic MRI. Theoretical derivation and experimental results are presented
Spread spectrum magnetic resonance imaging
- IEEE Trans. Med. Imag
"... Abstract—We propose a novel compressed sensing technique to accelerate the magnetic resonance imaging (MRI) acquisition process. The method, coined spread spectrum MRI or simply s MRI, consists of premodulating the signal of interest by a linear chirp before random-space under-sampling, and then rec ..."
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Cited by 16 (1 self)
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Abstract—We propose a novel compressed sensing technique to accelerate the magnetic resonance imaging (MRI) acquisition process. The method, coined spread spectrum MRI or simply s MRI, consists of premodulating the signal of interest by a linear chirp before random-space under-sampling, and then reconstructing the signal with nonlinear algorithms that promote sparsity. The effectiveness of the procedure is theoretically under-pinned by the optimization of the coherence between the sparsity and sensing bases. The proposed technique is thoroughly studied by means of numerical simulations, as well as phantom and in vivo experiments on a 7T scanner. Our results suggest that s MRI performs better than state-of-the-art variable density-space under-sampling approaches. Index Terms—Compressed sensing,magnetic resonance imaging (MRI), spread spectrum. I.
Expectation Propagation for Bayesian Multi-task Feature Selection
"... Abstract. In this paper we propose a Bayesian model for multi-task feature selection. This model is based on a generalized spike and slab sparse prior distribution that enforces the selection of a common subset of features across several tasks. Since exact Bayesian inference in this model is intract ..."
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Cited by 10 (4 self)
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Abstract. In this paper we propose a Bayesian model for multi-task feature selection. This model is based on a generalized spike and slab sparse prior distribution that enforces the selection of a common subset of features across several tasks. Since exact Bayesian inference in this model is intractable, approximate inference is performed through expectation propagation (EP). EP approximates the posterior distribution of the model using a parametric probability distribution. This posterior approximation is particularly useful to identify relevant features for prediction. We focus on problems for which the number of features d is significantly larger than the number of instances for each task. We propose an efficient parametrization of the EP algorithm that offers a computational complexity linear in d. Experiments on several multi-task datasets show that the proposed model outperforms baseline approaches for single-task learning or data pooling across all tasks, as well as two state-of-the-art multi-task learning approaches. Additional experiments confirm the stability of the proposed feature selection with respect to various sub-samplings of the training data. Keywords: Multi-task learning, feature selection, expectation propagation, approximate Bayesian inference. 1
Generalized Spike and Slab Priors for Bayesian Group Feature Selection Using Expectation Propagation
"... We describe a Bayesian method for group feature selection in linear regression problems. The method is based on a generalized version of the standard spike and slab prior distribution which is often used for individual feature selection. Exact Bayesian inference under the prior considered is infeasi ..."
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Cited by 1 (0 self)
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We describe a Bayesian method for group feature selection in linear regression problems. The method is based on a generalized version of the standard spike and slab prior distribution which is often used for individual feature selection. Exact Bayesian inference under the prior considered is infeasible for typical regression problems. However, approximate inference can be carried out efficiently using Expectation Propagation (EP). A detailed analysis of the generalized spike and slab prior shows that it is well suited for regression problems that are sparse at the group level. Furthermore, this prior can be used to introduce prior knowledge about specific groups of features that are a priori believed to be more relevant. An experimental evaluation compares the performance of the proposed method with those of group LASSO, Bayesian group LASSO, automatic relevance determination and additional variants used for group feature selection. The results of these experiments show that a model based on the generalized spike and slab prior and the EP algorithm has state-of-the-art prediction performance in the problems analyzed. Furthermore, this model is also very useful to carry out sequential experimental design (also known as active learning), where the data instances that are most informative are iteratively included in the training set, reducing the number of instances needed to obtain a particular level of prediction accuracy.
Info-greedy sequential adaptive compressed sensing
, 2015
"... We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted in-formation conditioned on the previous measurements. We show that the widely used bisection approach is Info-Greedy for a family o ..."
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Cited by 1 (0 self)
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We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted in-formation conditioned on the previous measurements. We show that the widely used bisection approach is Info-Greedy for a family of-sparse signals by connecting compressed sensing and blackbox complexity of sequential query algorithms, and present Info-Greedy algorithms for Gaussian and Gaussian mixture model (GMM) signals, as well as ways to design sparse Info-Greedy measurements. Numerical examples demonstrate the good performance of the proposed algorithms using simulated and real data: Info-Greedy Sensing shows significant improvement over random projection for signals with sparse and low-rank covariance matrices, and adaptivity brings robustness when there is a mismatch between the assumed and the true distributions.
www.worldsciencepublisher.org Compressed Sensing for brain MRIs
"... Abstract: Compressed sensing and magnetic resonance imaging are hot topics in the field of signal processing. In this study we introduced in Lustig’s variable density sampling method, integrated it to compressed sensing, and applied it to brain MRI acquisition. The realistic experiment shows the var ..."
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Abstract: Compressed sensing and magnetic resonance imaging are hot topics in the field of signal processing. In this study we introduced in Lustig’s variable density sampling method, integrated it to compressed sensing, and applied it to brain MRI acquisition. The realistic experiment shows the variable density sampling recovery better than traditional random sampling method on a 256x256 brain magnetic resonance image at acceleration factor as 3.
glm-ie: Generalised Linear Models Inference & Estimation Toolbox
"... Theglm-ie toolbox contains functionality for estimation and inference in generalised linear models over continuous-valued variables. Besides a variety of penalised least squares solvers for estimation, it offers inference based on (convex) variational bounds, on expectation propagation and on factor ..."
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Theglm-ie toolbox contains functionality for estimation and inference in generalised linear models over continuous-valued variables. Besides a variety of penalised least squares solvers for estimation, it offers inference based on (convex) variational bounds, on expectation propagation and on factorial mean field. Scalable and efficient inference in fully-connected undirected graphical models or Markov random fields with Gaussian and non-Gaussian potentials is achieved by casting all the computations as matrix vector multiplications. We provide a wide choice of penalty functions for estimation, potential functions for inference and matrix classes with lazy evaluation for convenient modelling. We designed the glm-ie package to be simple, generic and easily expansible. Most of the code is written in Matlab including some MEX files to be fully compatible to both Matlab 7.x and GNU Octave 3.3.x. Large scale probabilistic classification as well as sparse linear modelling can be performed in a common algorithmical framework by theglm-ie toolkit.
Machine Learning Group, ICTEAM
"... We describe a Bayesian method for group feature selection in linear regression problems. The method is based on a generalized version of the standard spike-and-slab prior distribution which is often used for individual feature selection. Exact Bayesian inference under the prior considered is infeasi ..."
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We describe a Bayesian method for group feature selection in linear regression problems. The method is based on a generalized version of the standard spike-and-slab prior distribution which is often used for individual feature selection. Exact Bayesian inference under the prior considered is infeasible for typical regression problems. However, approximate inference can be carried out efficiently using Expectation Propagation (EP). A detailed analysis of the generalized spike-and-slab prior shows that it is well suited for regression problems that are sparse at the group level. Furthermore, this prior can be used to introduce prior knowledge about specific groups of features that are a priori believed to be more relevant. An experimental evaluation compares the performance of the proposed method with those of group LASSO, Bayesian group LASSO, automatic relevance determination and additional variants used for group feature selection. The results of these experiments show that a model based on the generalized spike-and-slab prior and the EP algorithm has state-of-the-art prediction performance in the problems analyzed. Furthermore, this model is also very useful to carry out sequential experimental design (also known as active learning), where the data instances that are most informative are iteratively included in the training set, reducing the number of instances needed to obtain a particular level of prediction accuracy.
