Biomedical Imaging Group

Seminars

CONTENTS |

Seminars |

Cell detection by functional inverse diffusion and non-negative group sparsity07 May 2019

Internal seminar: abstract not available.

Measure Digital, Reconstruct Analog16 Apr 2019

Deep Learning for Non-Linear Inverse Problems02 Apr 2019

Numerical Investigation of Continuous-Domain Lp-norm Regularization in Generalized Interpolation19 Feb 2019

Inner-Loop-Free ADMM for Cryo-EM15 Jan 2019

Fast PET reconstruction: the home stretch11 Dec 2018

Self-Supervised Deep Active Accelerated MRI27 Nov 2018

Minimum Support Multi-Splines20 Nov 2018

Sparse Coding with Projected Gradient Descent for Inverse Problems 23 Oct 2018

Adversarially-Sandwiched VAEs for Inverse Problems02 Oct 2018

PSF-Extractor: from fluorescent beads measurements to continuous PSF model11 Sep 2018

Analysis of Planar Shapes through Shape Dictionary Learning with an Extension to Splines28 Aug 2018

Complex-order scale-invariant operators and self-similar processes21 Aug 2018

Variational Framework for Continuous Angular Refinement and Reconstruction in Cryo-EM14 Aug 2018

Looking beyond Pixels: Theory, Algorithms and Applications of Continuous Sparse Recovery07 Aug 2018

A L1 representer theorem of vector-valued learning17 Jul 2018

Computational Super-Sectioning for Single-Slice Structured-Illumination Microscopy 19 Jun 2018

Theoretical and Numerical Analysis of Super-Resolution without Grid19 Jun 2018

Fast rotational dictionary learning using steerability 08 May 2018

Hybrid spline dictionaries for continuous-domain inverse problems24 Apr 2018

Fast Multiresolution Reconstruction for Cryo-EM17 Apr 2018

Direct Reconstruction of Clipped Peaks in Bandlimited OFDM Signals13 Mar 2018

Sparsity-based techniques for diffraction tomography27 Feb 2018

Structured Illumination and the Analysis of Single Molecules in Cells09 Feb 2018

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems30 Jan 2018

Fast Piecewise-Affine Motion Estimation Without Segmentation19 Dec 2017

Continuous Representations in Bioimage Analysis: a Bridge from Pixels to the Real World12 Dec 2017

Steer&Detect on Images 14 Nov 2017

Fundamental computational barriers in inverse problems and the mathematics of information27 Oct 2017

Variational use of B-splines and Kernel Based Functions27 Oct 2017

Kernel Based Functions are generalizations of spline functions and radial basis functions. These R^d to R functions are in the form f = \sum_{i=1}^n λi φ(x−xi) or \sum_{i=1}^n λi φ(x−xi)+pk(x) where φ is called the kernel, (xi)_{i=1:n} ∈ (R^d)^n are the so called centers of f, (λi)_{i=1:n} are real coefficients, and pk is some degree k polynomial. When φ is a bell shaped function meeting some property (such as, in particular \sum_{i=1}^n φ(x) = 1 for any x ∈ R^d), we write it B and call it, for short, B-spline. In this talk we present two particular uses of these Kernel Based Functions, and a property of a specific polynomial interpolation. First, hierarchical B-splines: using B-splines of different scales, and a mean square optimization, we show how to approximate scattered data with possibility of zoom on some regions, adaptively from the data. We so obtain locally tensor product functions, where the grid of the centers is finer in some regions and coarser in other regions. Second, in a CAGD aim and using modified (variational) Bézier curves or surfaces, we show that it is possible to derive B-spline curves or surfaces being closer to (or further from) the control polygon, while being in the same vectorial space. This gives more flexibility to easily derive new forms. Third we present variational polynomial interpolation, which is true polynomial interpolation of any given data, and so obtain a polynomial interpolation without the famous Runge oscillations. These interpolating polynomials converge towards the interpolating polynomial spline of the data.

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