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Sparse coding-that is, modelling data vectors as sparse linear combinations of basis elements-is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on learning the basis set, also called dictionary, to adapt it to specific data, an approach that has recently proven to be very effective for signal reconstruction and classification in the audio and image processing domains. This paper proposes a new online optimization algorithm for dictionary learning, based on stochastic approximations, which scales up gracefully to large datasets with millions of training samples. A proof of convergence is presented, along with experiments with natural images demonstrating that it leads to faster performance and better dictionaries than classical batch algorithms for both small and large datasets.

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Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted dictionaries for images has been a major challenge. The K-SVD has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks. In this paper, we address the problem of learning dictionaries for color images and extend the K-SVD-based grayscale image denoising algorithm that appears in. This work puts forward ways for handling nonhomogeneous noise and missing information, paving the way to state-of-the-art results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper.

The envelope glycoproteins (Env) of human and simian immunodeficiency viruses (HIV and SIV, respectively) mediate virus binding to the cell surface receptor CD4 on target cells to initiate infection 1 . Env is a heterodimer of a transmembrane glycoprotein (gp41) and a surface glycoprotein (gp120), and forms trimers on the surface of the viral membrane. Using cryo-electron tomography combined with three-dimensional image classification and averaging, we report the threedimensional structures of trimeric Env displayed on native HIV-1 in the unliganded state, in complex with the broadly neutralizing antibody b12 and in a ternary complex with CD4 and the 17b antibody. By fitting the known crystal structures 2,3 of the monomeric gp120 core in the b12-and CD4/17b-bound conformations into the density maps derived by electron tomography, we derive molecular models for the native HIV-1 gp120 trimer in unliganded and CD4-bound states. We demonstrate that CD4 binding results in a major reorganization of the Env trimer, causing an outward rotation and displacement of each gp120 monomer. This appears to be coupled with a rearrangement of the gp41 region along the central axis of the trimer, leading to closer contact between the viral and target cell membranes. Our findings elucidate the structure and conformational changes of trimeric HIV-1 gp120 relevant to antibody neutralization and attachment to target cells. It is estimated that over 33 million individuals are at present infected with HIV (http://www.unaids.org). The development of an effective vaccine is therefore a challenge of fundamental medical interest. It has been widely recognized that a better understanding of the structure of trimeric Env in its various conformational states is likely to be an important element in the overall strategy for vaccine development 4 . Although X-ray crystallographic methods have led to atomic models for HIV-1 gp120 monomers complexed to antibodies in the presence and absence of CD4 (refs 2 , 3, 5 ), determination of the structures of intact trimers on native viruses has nevertheless remained elusive. Theoretical models for the structure of the trimer that take into account constraints determined from biochemical and mutagenesis studies of monomeric gp120 (refs 6 , 7 ) have been advanced, but the advent of electron tomographic methods 8 provides a unique opportunity for direct experimental determination of the structure of the intact trimer on the virus in its native state. Here we report structural analysis of native HIV-1 Env using alignment and classification procedures that take into account the missing wedge that arises from the limited angular range used for data collection in electron tomography. Our approach takes advantage of complexes containing monomeric gp120 for

The Human Connectome Project (HCP) is a collaborative 5-year effort to map human brain connections and their variability in healthy adults. A consortium of HCP investigators will study a population of 1200 healthy adults using multiple imaging modalities, along with extensive behavioral and genetic data. In this overview, we focus on diffusion MRI (dMRI) and the structural connectivity aspect of the project. We present recent advances in acquisition and processing that allow us to obtain very high-quality in-vivo MRI data, while enabling scanning of a very large number of subjects. These advances result from 2 years of intensive efforts in optimising many aspects of data acquisition and processing during the piloting phase of the project. The data quality and methods described here are representative of the datasets and processing pipelines that will be made freely available to the community at quarterly intervals, beginning in 2013.

Relations between anisotropic diffusion and robust statistics are described in this paper. Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The "edge-stopping" function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework. This connection leads to a new "edge-stopping" function based on Tukey's biweight robust estimator that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in an image that has been smoothed with anisotropic diffusion. Additionally, we derive a relationship between anisotropic diffusion and regularization with line processes. Adding constraints on the spatial organization of the line processes allows us to develop new anisotropic diffusion equations that result in a qualitative improvement in the continuity of edges.