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30
Bayesian orthogonal component analysis for sparse representation. Extension to nonhomogeneous sparsity level over times,” Univ
 Rep., Nov. 2009 [Online]. Available: http://dobigeon.perso.enseeiht.fr/publis.html
"... Abstract—This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This undercomplete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. T ..."
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Abstract—This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This undercomplete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli–Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A noninformative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on undercomplete dictionary is finally investigated. Index Terms—Bayesian inference, dictionary learning, Markov chain Monte Carlo (MCMC) methods, sparse representation.
Variational semiblind sparse image reconstruction with application to MRFM
 in Proc. Computational Imaging Conference in IS&T SPIE Symposium on Electronic Imaging Science and Technology
, 2012
"... Abstract — We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a ..."
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Cited by 6 (2 self)
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Abstract — We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a highdimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian MetropoliswithinGibbs sampling framework. The performance of our Bayesian semiblind algorithm for sparse images is superior to previously proposed semiblind algorithms such as the alternating minimization algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data. Index Terms — Bayesian inference, magnetic resonance force microscopy (MRFM) experiment, Markov chain Monte Carlo (MCMC) methods, semiblind (myopic) sparse deconvolution. I.
Segmentation of skin lesions in 2D and 3D ultrasound images using a spatially coherent generalized Rayleigh mixture model
, 2011
"... This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multipletissue highfrequency skin ultrasound images. The distribution of multipletissue images is modeled as a spatially coherent finite mixture of heavytailed Rayleigh distributions. Sp ..."
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Cited by 5 (5 self)
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This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multipletissue highfrequency skin ultrasound images. The distribution of multipletissue images is modeled as a spatially coherent finite mixture of heavytailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a labelvector associating each voxel to a tissue. More precisely, a hybrid MetropoliswithinGibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of invivo skin tumors in high frequency 2D and 3D ultrasound images.
BAYESIAN COMPRESSED SENSING IN ULTRASOUND IMAGING
"... Following our previous study on compressed sensing for ultrasound imaging, this paper proposes to exploit the image sparsity in the frequency domain within a Bayesian approach. A BernoulliGaussian prior is assigned to the Fourier transform of the ultrasound image in order to enforce sparsity and to ..."
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Cited by 5 (3 self)
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Following our previous study on compressed sensing for ultrasound imaging, this paper proposes to exploit the image sparsity in the frequency domain within a Bayesian approach. A BernoulliGaussian prior is assigned to the Fourier transform of the ultrasound image in order to enforce sparsity and to reconstruct the image via Bayesian compressed sensing. In addition, the Bayesian approach allows the image sparsity level in the spectral domain to be estimated, a significant parameter in the ℓ1 constrained minimization problem related to compressed sensing. Results obtained with a simulated ultrasound image and an in vivo image of a human thyroid gland show a reconstruction performance similar to a classical compressed sensing algorithm from half of spatial samples while estimating the sparsity level during reconstruction. Index Terms — Compressed sensing, ultrasound imaging, Bayesian reconstruction, sparsity.
1 Sensing, Compression and Recovery for WSNs: Sparse Signal Modeling and Monitoring Framework
"... Abstract—We address the problem of compressing large and distributed signals monitored by a Wireless Sensor Network (WSN) and recovering them through the collection of a small number of samples. We propose a sparsity model that allows the use of Compressive Sensing (CS) for the online recovery of la ..."
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Cited by 1 (0 self)
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Abstract—We address the problem of compressing large and distributed signals monitored by a Wireless Sensor Network (WSN) and recovering them through the collection of a small number of samples. We propose a sparsity model that allows the use of Compressive Sensing (CS) for the online recovery of large data sets in real WSN scenarios, exploiting Principal Component Analysis (PCA) to capture the spatial and temporal characteristics of real signals. Bayesian analysis is utilized to approximate the statistical distribution of the principal components and to show that the Laplacian distribution provides an accurate representation of the statistics of real data. This combined CS and PCA technique is subsequently integrated into
USING REEDMULLER SEQUENCES AS DETERMINISTIC COMPRESSED SENSING MATRICES FOR IMAGE RECONSTRUCTION
"... An image reconstruction algorithm using compressed sensing (CS) with deterministic matrices of secondorder ReedMuller (RM) sequences is introduced. The 1D algorithm of Howard et al. using CS with RM sequences suffers significant loss in speed and accuracy when the degree of sparsity is not high, m ..."
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An image reconstruction algorithm using compressed sensing (CS) with deterministic matrices of secondorder ReedMuller (RM) sequences is introduced. The 1D algorithm of Howard et al. using CS with RM sequences suffers significant loss in speed and accuracy when the degree of sparsity is not high, making it inviable for 2D signals. This paper describes an efficient 2D CS algorithm using RM sequences, provides medical image reconstruction examples, and compares it with the original 2D CS using noiselets. This algorithm entails several innovations that enhance its suitability for images: initial best approximation, a greedy algorithm for the nonzero locations, and a new approach in the leastsquares step. These enhancements improve fidelity, execution time, and stability in the context of image reconstruction.
7. PERFORMING ORGANIZATION NAMES AND ADDRESSES
, 2013
"... The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comm ..."
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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington
Variational Semiblind Sparse Image Reconstruction with Application to MRFM
"... This paper addresses the problem of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semiblind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruc ..."
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This paper addresses the problem of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semiblind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Simulation results demonstrate that the semiblind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It also outperforms nonmyopic algorithms that rely on perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM).
Myopic sparse image reconstruction with application to MRFM
"... We propose a solution to the image deconvolution problem where the convolution operator or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the uncertainty in a high dimensio ..."
Abstract
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We propose a solution to the image deconvolution problem where the convolution operator or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the uncertainty in a high dimensional space. Specifically, we assume the image is sparse corresponding to the natural sparsity of magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian MetropoliswithinGibbs sampling framework. The performance of our Bayesian myopic algorithm is superior to previously proposed algorithms such as the alternating minimization (AM) algorithm for sparse images. We illustrate our myopic algorithm on real MRFM tobacco virus data.
Myopic sparse image reconstruction with application to
"... We propose a solution to the image deconvolution problem where the convolution operator or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the uncertainty in a high dimensio ..."
Abstract
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We propose a solution to the image deconvolution problem where the convolution operator or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the uncertainty in a high dimensional space. Specifically, we assume the image is sparse corresponding to the natural sparsity of magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian MetropoliswithinGibbs sampling framework. The performance of our Bayesian myopic algorithm is superior to previously proposed algorithms such as the alternating minimization (AM) algorithm for sparse images. We illustrate our myopic algorithm on real MRFM tobacco virus data.