820 research outputs found

    Reconstruction of undersampled signals and alignment in the frequency domain

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    Kinetochore alignment within the metaphase plate is regulated by centromere stiffness and microtubule depolymerases

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    During mitosis in most eukaryotic cells, chromosomes align and form a metaphase plate halfway between the spindle poles, about which they exhibit oscillatory movement. These movements are accompanied by changes in the distance between sister kinetochores, commonly referred to as breathing. We developed a live cell imaging assay combined with computational image analysis to quantify the properties and dynamics of sister kinetochores in three dimensions. We show that baseline oscillation and breathing speeds in late prometaphase and metaphase are set by microtubule depolymerases, whereas oscillation and breathing periods depend on the stiffness of the mechanical linkage between sisters. Metaphase plates become thinner as cells progress toward anaphase as a result of reduced oscillation speed at a relatively constant oscillation period. The progressive slowdown of oscillation speed and its coupling to plate thickness depend nonlinearly on the stiffness of the mechanical linkage between sisters. We propose that metaphase plate formation and thinning require tight control of the state of the mechanical linkage between sisters mediated by centromeric chromatin and cohesion

    An Improved Observation Model for Super-Resolution under Affine Motion

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    Super-resolution (SR) techniques make use of subpixel shifts between frames in an image sequence to yield higher-resolution images. We propose an original observation model devoted to the case of non isometric inter-frame motion as required, for instance, in the context of airborne imaging sensors. First, we describe how the main observation models used in the SR literature deal with motion, and we explain why they are not suited for non isometric motion. Then, we propose an extension of the observation model by Elad and Feuer adapted to affine motion. This model is based on a decomposition of affine transforms into successive shear transforms, each one efficiently implemented by row-by-row or column-by-column 1-D affine transforms. We demonstrate on synthetic and real sequences that our observation model incorporated in a SR reconstruction technique leads to better results in the case of variable scale motions and it provides equivalent results in the case of isometric motions

    Sampling—50 Years After Shannon

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    This paper presents an account of the current state of sampling, 50 years after Shannon's formulation of the sampling theorem. The emphasis is on regular sampling where the grid is uniform. This topic has benefited from a strong research revival during the past few years, thanks in part to the mathematical connections that were made with wavelet theory. To introduce the reader to the modern, Hilbert-space formulation, we re-interpret Shannon's sampling procedure as an orthogonal projection onto the subspace of bandlimited functions. We then extend the standard sampling paradigm for a representation of functions in the more general class of "shift-invariant" functions spaces, including splines and wavelets. Practically, this allows for simpler—and possibly more realistic—interpolation models, which can be used in conjunction with a much wider class of (anti-aliasing) pre-filters that are not necessarily ideal lowpass. We summarize and discuss the results available for the determination of the approximation error and of the sampling rate when the input of the system is essentially arbitrary; e.g., non-bandlimited. We also review variations of sampling that can be understood from the same unifying perspective. These include wavelets, multi-wavelets, Papoulis generalized sampling, finite elements, and frames. Irregular sampling and radial basis functions are briefly mentioned
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