A Hierarchical Bayesian Model for Frame Representation

In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the frame synthesis operator is not bijective. Consequently, the frame coefficients are not directly observable. This paper introduces a hierarchical Bayesian model for frame representation. The posterior distribution of the frame coefficients and model hyper-parameters is derived. Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample from this posterior distribution. The generated samples are then exploited to estimate the hyper-parameters and the frame coefficients of the target signal. Validation experiments show that the proposed algorithms provide an accurate estimation of the frame coefficients and hyper-parameters. Application to practical problems of image denoising show the impact of the resulting Bayesian estimation on the recovered signal quality

Sparse signal recovery using a Bernoulli generalized Gaussian prior

International audienceBayesian sparse signal recovery has been widely investigated during the last decade due to its ability to automatically estimate regularization parameters. Prior based on mixtures of Bernoulli and continuous distributions have recently been used in a number of recent works to model the target signals , often leading to complicated posteriors. Inference is therefore usually performed using Markov chain Monte Carlo algorithms. In this paper, a Bernoulli-generalized Gaussian distribution is used in a sparse Bayesian regularization framework to promote a two-level flexible sparsity. Since the resulting conditional posterior has a non-differentiable energy function , the inference is conducted using the recently proposed non-smooth Hamiltonian Monte Carlo algorithm. Promising results obtained with synthetic data show the efficiency of the proposed regularization scheme

Hybrid Sparse Regularization for Magnetic Resonance Spectroscopy

International audienceMagnetic resonance spectroscopy imaging (MRSI) is a powerful non-invasive tool for characterising markers of biological processes. This technique extends conventional MRI by providing an additional dimension of spectral information describing the abnormal presence or concentration of metabolites of interest. Unfortunately, in vivo MRSI suffers from poor signal-to-noise ratio limiting its clinical use for treatment purposes. This is due to the combination of a weak MR signal and low metabolite concentrations, in addition to the acquisition noise. We propose a new method that handles this challenge by efficiently denoising MRSI signals without constraining the spectral or spatial profiles. The proposed denoising approach is based on wavelet transforms and exploits the sparsity of the MRSI signals both in the spatial and frequency domains. A fast proximal optimization algorithm is then used to recover the optimal solution. Experiments on synthetic and real MRSI data showed that the proposed scheme achieves superior noise suppression (SNR increase up to 60%). In addition, this method is computationally efficient and preserves data features better than existing methods

Spatio-temporal wavelet regularization for parallel MRI reconstruction: application to functional MRI

Parallel MRI is a fast imaging technique that enables the acquisition of highly resolved images in space or/and in time. The performance of parallel imaging strongly depends on the reconstruction algorithm, which can proceed either in the original k-space (GRAPPA, SMASH) or in the image domain (SENSE-like methods). To improve the performance of the widely used SENSE algorithm, 2D- or slice-specific regularization in the wavelet domain has been deeply investigated. In this paper, we extend this approach using 3D-wavelet representations in order to handle all slices together and address reconstruction artifacts which propagate across adjacent slices. The gain induced by such extension (3D-Unconstrained Wavelet Regularized -SENSE: 3D-UWR-SENSE) is validated on anatomical image reconstruction where no temporal acquisition is considered. Another important extension accounts for temporal correlations that exist between successive scans in functional MRI (fMRI). In addition to the case of 2D+t acquisition schemes addressed by some other methods like kt-FOCUSS, our approach allows us to deal with 3D+t acquisition schemes which are widely used in neuroimaging. The resulting 3D-UWR-SENSE and 4D-UWR-SENSE reconstruction schemes are fully unsupervised in the sense that all regularization parameters are estimated in the maximum likelihood sense on a reference scan. The gain induced by such extensions is illustrated on both anatomical and functional image reconstruction, and also measured in terms of statistical sensitivity for the 4D-UWR-SENSE approach during a fast event-related fMRI protocol. Our 4D-UWR-SENSE algorithm outperforms the SENSE reconstruction at the subject and group levels (15 subjects) for different contrasts of interest (eg, motor or computation tasks) and using different parallel acceleration factors (R=2 and R=4) on 2x2x3mm3 EPI images.Comment: arXiv admin note: substantial text overlap with arXiv:1103.353

Translation-Invariant Shrinkage/Thresholding of Group Sparse Signals

This paper addresses signal denoising when large-amplitude coefficients form clusters (groups). The L1-norm and other separable sparsity models do not capture the tendency of coefficients to cluster (group sparsity). This work develops an algorithm, called 'overlapping group shrinkage' (OGS), based on the minimization of a convex cost function involving a group-sparsity promoting penalty function. The groups are fully overlapping so the denoising method is translation-invariant and blocking artifacts are avoided. Based on the principle of majorization-minimization (MM), we derive a simple iterative minimization algorithm that reduces the cost function monotonically. A procedure for setting the regularization parameter, based on attenuating the noise to a specified level, is also described. The proposed approach is illustrated on speech enhancement, wherein the OGS approach is applied in the short-time Fourier transform (STFT) domain. The denoised speech produced by OGS does not suffer from musical noise.Comment: 33 pages, 7 figures, 5 table

Bayesian Compressive Sensing for Cluster Structured Sparse Signals

International audienceIn traditional framework of compressive sensing (CS), only sparse prior on the property of signals in time or frequency domain is adopted to guarantee the exact inverse recovery. Other than sparse prior, structures on the sparse pattern of the signal have also been used as an additional prior, called model-based compressive sensing, such as clustered structure and tree structure on wavelet coefficients. In this paper, the cluster structured sparse signals are investigated. Under the framework of Bayesian compressive sensing, a hierarchical Bayesian model is employed to model both the sparse prior and cluster prior, then Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms which are also taking into account the cluster prior, the proposed algorithm solves the inverse problem automatically--prior information on the number of clusters and the size of each cluster is unknown. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms

Inverse problems in medical ultrasound images - applications to image deconvolution, segmentation and super-resolution

In the field of medical image analysis, ultrasound is a core imaging modality employed due to its real time and easy-to-use nature, its non-ionizing and low cost characteristics. Ultrasound imaging is used in numerous clinical applications, such as fetus monitoring, diagnosis of cardiac diseases, flow estimation, etc. Classical applications in ultrasound imaging involve tissue characterization, tissue motion estimation or image quality enhancement (contrast, resolution, signal to noise ratio). However, one of the major problems with ultrasound images, is the presence of noise, having the form of a granular pattern, called speckle. The speckle noise in ultrasound images leads to the relative poor image qualities compared with other medical image modalities, which limits the applications of medical ultrasound imaging. In order to better understand and analyze ultrasound images, several device-based techniques have been developed during last 20 years. The object of this PhD thesis is to propose new image processing methods allowing us to improve ultrasound image quality using postprocessing techniques. First, we propose a Bayesian method for joint deconvolution and segmentation of ultrasound images based on their tight relationship. The problem is formulated as an inverse problem that is solved within a Bayesian framework. Due to the intractability of the posterior distribution associated with the proposed Bayesian model, we investigate a Markov chain Monte Carlo (MCMC) technique which generates samples distributed according to the posterior and use these samples to build estimators of the ultrasound image. In a second step, we propose a fast single image super-resolution framework using a new analytical solution to the l2-l2 problems (i.e., $\ell_2$-norm regularized quadratic problems), which is applicable for both medical ultrasound images and piecewise/ natural images. In a third step, blind deconvolution of ultrasound images is studied by considering the following two strategies: i) A Gaussian prior for the PSF is proposed in a Bayesian framework. ii) An alternating optimization method is explored for blind deconvolution of ultrasound

Integration of magnetic resonance spectroscopic imaging into the radiotherapy treatment planning

L'objectif de cette thèse est de proposer de nouveaux algorithmes pour surmonter les limitations actuelles et de relever les défis ouverts dans le traitement de l'imagerie spectroscopique par résonance magnétique (ISRM). L'ISRM est une modalité non invasive capable de fournir la distribution spatiale des composés biochimiques (métabolites) utilisés comme biomarqueurs de la maladie. Les informations fournies par l'ISRM peuvent être utilisées pour le diagnostic, le traitement et le suivi de plusieurs maladies telles que le cancer ou des troubles neurologiques. Cette modalité se montre utile en routine clinique notamment lorsqu'il est possible d'en extraire des informations précises et fiables. Malgré les nombreuses publications sur le sujet, l'interprétation des données d'ISRM est toujours un problème difficile en raison de différents facteurs tels que le faible rapport signal sur bruit des signaux, le chevauchement des raies spectrales ou la présence de signaux de nuisance. Cette thèse aborde le problème de l'interprétation des données d'ISRM et la caractérisation de la rechute des patients souffrant de tumeurs cérébrales. Ces objectifs sont abordés à travers une approche méthodologique intégrant des connaissances a priori sur les données d'ISRM avec une régularisation spatio-spectrale. Concernant le cadre applicatif, cette thèse contribue à l'intégration de l'ISRM dans le workflow de traitement en radiothérapie dans le cadre du projet européen SUMMER (Software for the Use of Multi-Modality images in External Radiotherapy) financé par la Commission européenne (FP7-PEOPLE-ITN).The aim of this thesis is to propose new algorithms to overcome the current limitations and to address the open challenges in the processing of magnetic resonance spectroscopic imaging (MRSI) data. MRSI is a non-invasive modality able to provide the spatial distribution of relevant biochemical compounds (metabolites) commonly used as biomarkers of disease. Information provided by MRSI can be used as a valuable insight for the diagnosis, treatment and follow-up of several diseases such as cancer or neurological disorders. Obtaining accurate and reliable information from in vivo MRSI signals is a crucial requirement for the clinical utility of this technique. Despite the numerous publications on the topic, the interpretation of MRSI data is still a challenging problem due to different factors such as the low signal-to-noise ratio (SNR) of the signals, the overlap of spectral lines or the presence of nuisance components. This thesis addresses the problem of interpreting MRSI data and characterizing recurrence in tumor brain patients. These objectives are addressed through a methodological approach based on novel processing methods that incorporate prior knowledge on the MRSI data using a spatio-spectral regularization. As an application, the thesis addresses the integration of MRSI into the radiotherapy treatment workflow within the context of the European project SUMMER (Software for the Use of Multi-Modality images in External Radiotherapy) founded by the European Commission (FP7-PEOPLE-ITN framework)