Sandrine Anthoine

Reconstructing Sunyaev¿Zel'dovich clusters in future cosmic microwave background experiments

We present a new method for component separation aimed to extract SunyaevZeldovich (SZ) galaxy clusters from multifrequency maps of Cosmic Microwave Background (CMB) experiments. This method is designed to recover non-Gaussian, spatially localized and sparse signals. We first characterize the cluster non-Gaussianity by studying it on simulated SZ maps. We the apply our estimator on simulated observations of the Planck and Atacama Cosmology Telescope (ACT) experiments. The method presented here outperforms multi-frequency Wiener filtering both in the reconstructed average intensity for given input and in the associated error. In the absence of point source contamination, this technique reconstructs the ACT (Planck) bright (big) clusters central y parameter with an intensity which is about 84 (43) per cent of the original input value. The associated error in the reconstruction is about 12 and 27 per cent for the 50 (12) ACT (Planck) clusters considered. For ACT, the error is dominated by beam smearing. In the Planck case the error in the reconstruction is largely determined by the noise level: a noise reduction by a factor 7 would imply almost perfect reconstruction and 10 per cent error for a large sample of clusters. We conclude that the selection function of Planck clusters will strongly depend on the noise properties in different sky regions, as well as from the specific cluster extraction method assumed.

Some proximal methods for CBCT and PET tomography

The reconstruction of the images obtained via the Cone Beam Computerized Tomography (CBCT) and Positron Emission Tomography (PET) Scanners are ill-posed inverse problems. One needs to adress carefully the problem of inversion of the mathematical operators involved. Recent advances in optimization have yielded efficient algorithms to solve very general classes of inverse problems via the minimization of non-differentiable convex functions. We show that such models are well suited to solve the CBCT and PET reconstruction problems. On the one hand, they can incorporate directly the physics of new acquisition devices, free of dark noise; on the other hand, they can take into account the specificity of the pure Poisson noise. We propose various fast numerical schemes to recover the original data and compare them to state-of-the-art algorithms on simulated data. We study more specifically how different contrasts and resolutions may be resolved as the level of noise and/or the number of projections of the acquired sinograms decrease. We conclude that the proposed algorithms compare favorably with respect to well-established methods in tomography.

Image retrieval via Kullback-Leibler divergence of patches of multiscale coefficients in the KNN framework

In this paper, we define a similarity measure between images in the context of (indexing and) retrieval. We use the Kullback-Leibler (KL) divergence to compare sparse multiscale image representations. The KL divergence between parameterized marginal distributions of wavelet coefficients has already been used as a similarity measure between images. Here we use the Laplacian pyramid and consider the dependencies between coefficients by means of nonparametric distributions of mixed intra/interscale and interchannel patches. To cope with the high-dimensionality of the resulting description space, we estimate the KL divergences in the k-th nearest neighbor (kNN) framework (instead of classical fixed size kernel methods). Query-by-example experiments show the accuracy and robustness of the method.

Sparse Multiscale Patches (SMP) for Image Categorization

In this paper we address the task of image categorization using a new similarity measure on the space of Sparse Multiscale Patches (SMP ). SMP s are based on a multiscale transform of the image and provide a global representation of its content. At each scale, the probability density function (pdf ) of the SMP s is used as a description of the relevant information. The closeness between two images is defined as a combination of Kullback-Leibler divergences between the pdfs of their SMP s. In the context of image categorization, we represent semantic categories by prototype images, which are defined as the centroids of the training clusters. Therefore any unlabeled image is classified by giving it the same label as the nearest prototype. Results obtained on ten categories from the Corel collection show the categorization accuracy of the SMP method.

On the efficiency of proximal methods in CBCT and PET

Cone Beam Computerized Tomography (CBCT) and Positron Emission Tomography (PET) Scans are medical imaging devices that require solving ill-posed inverse problems. The models considered come directly from the physics of the acquisition devices, and take into account the specificity of the (Poisson) noise. We propose various fast numerical schemes to compute the solution. In particular, we show that a new algorithm recently introduced by A. Chambolle and T. Pock is well suited in the PET case when considering non differentiable regularizations such as total variation or wavelet ℓ1-regularization. Numerical experiments indicate that the proposed algorithms compare favorably with respect to well-established methods in tomography.

Sparse Multiscale Patches for Image Processing

This paper presents a framework to define an objective measure of the similarity (or dissimilarity) between two images for image processing. The problem is twofold: 1) define a set of features that capture the information contained in the image relevant for the given task and 2) define a similarity measure in this feature space. In this paper, we propose a feature space as well as a statistical measure on this space. Our feature space is based on a global descriptor of the image in a multiscale transformed domain. After decomposition into a Laplacian pyramid, the coefficients are arranged in intrascale/ interscale/interchannel patches which reflect the dependencies between neighboring coefficients in presence of specific structures or textures. At each scale, the probability density function (pdf) of these patches is used as a descriptor of the relevant information. Because of the sparsity of the multiscale transform, the most significant patches, called Sparse Multiscale Patches (SMP) , characterize efficiently these pdfs. We propose a statistical measure (the Kullback-Leibler divergence) based on the comparison of these probability density functions. Interestingly, this measure is estimated via the nonparametric, k-th nearest neighbor framework without explicitly building the pdfs. This framework is applied to a query-by-example image retrieval task. Experiments on two publicly available databases showed the potential of our SMP approach. In particular, it performed comparably to a SIFT -based retrieval method and two versions of a fuzzy segmentation-based method (the UFM and CLUE methods), and it exhibited some robustness to different geometric and radiometric deformations of the images.

Finding SZ clusters in the ACBAR maps

Abstract We present a new method for component separation from multi-frequency maps aimed to extract Sunyaev–Zeldovich (SZ) galaxy clusters from cosmic microwave background (CMB) experiments. This method is best suited to recover non-Gaussian, spatially localized and sparse signals. We apply our method on simulated maps of the ACBAR experiment. We find that this method improves the reconstruction of the integrated y parameter by a factor of three with respect to the Wiener filter case. Moreover, the scatter associated with the reconstruction is reduced by 30%.

A greedy approach to sparse poisson denoising

In this paper we propose a greedy method combined with the Moreau-Yosida regularization of the Poisson likelihood in order to restore images corrupted by Poisson noise. The regularization provides us with a data fidelity term with nice properties which we minimize under sparsity constraints. To do so, we use a greedy method based on a generalization of the well-known CoSaMP algorithm. We introduce a new convergence analysis of the algorithm which extends it use outside of the usual scope of convex functions. We provide numerical experiments which show the soundness of the method compared to the convex l1-norm relaxation of the problem.

Using Neighborhood Distributions of Wavelet Coefficients for On-the-Fly, Multiscale-Based Image Retrieval

In this paper, we define a similarity measure to compare images in the context of (indexing and) retrieval. We use the Kullback-Leibler (KL) divergence to compare sparse multiscale image descriptions in a wavelet domain. The KL divergence between wavelet coefficient distributions has already been used as a similarity measure between images. The novelty here is twofold. Firstly, we consider the dependencies between the coefficients by means of distributions of mixed intra/interscale neighborhoods. Secondly, to cope with the high-dimensionality of the resulting description space, we estimate the KL divergences in the k-th nearest neighbor framework, instead of using classical fixed size kernel methods. Query-by-example experiments are presented.

Combining spatial and temporal patches for scalable video indexing

This paper tackles the problem of scalable video indexing. We propose a new framework combining spatial and motion patch descriptors. The spatial descriptors are based on a multiscale description of the image and are called Sparse Multiscale Patches. We propose motion patch descriptors based on block motion that describe the motion in a Group of Pictures. The distributions of these sets of patches are compared combining weighted Kullback-Leibler divergences between spatial and motion patches. These divergences are estimated in a non-parametric framework using a k-th Nearest Neighbor estimator. We evaluate this weighted dissimilarity measure on selected videos from the ICOS-HD ANR project. Experiments show that the spatial part of the measure is relevant to detect different sequences, while its motion part allows to detect clips within a sequence. Experiments combining the spatial and temporal parts of the dissimilarity measure show its robustness to resampling and compression; thus exhibiting the spatial scalability of the method on heterogeneous networks.