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Seminars |
Variational Framework for Continuous Angular Refinement and Reconstruction in Cryo-EM14 Aug 2018
In the field of single particle reconstruction (SPR) in Cryo-electron microscopy (Cryo-EM), the target is to recover a high resolution density map of the molecule from a set of particle images. In this imaging modality, each particle image corresponds to the X-ray transform of the molecule from an unknown 3D pose corrupted by contrast transfer function (CTF) of the microscope and noise. In this presentation, we describe a variational framework that performs a joint optimization of the density map and the underlying angular variables. We solve this joint optimization problem by taking alternating ADMM and gradient descent steps to update the density map and 3D pose variables iteratively. Note that, our method serves as a 3D refinement step in the whole Cryo-EM pipeline. Thus, we start from an initial map and some rough estimations of the 3D poses and then refine both gradually. In our framework, unlike the current state of the art reconstruction techniques, we resolve the 3D pose variables on the continuum. Meaning that rather than descretizing the space of 3D poses, we represent these variables in their continuous form. This enables us to perform gradient steps on the angular variables in order to minimize the cost function. Thus, rather than comparing each particle image with a set of template projections of the density map taken from discretized points on the sphere, which is the essence of projection matching methods, we perform gradient steps in order to update these variables. Our preliminary results indicate that starting from a coarse estimation of the map and the angles, refinement of both is achievable.
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
Deep learning based data manifold projection - a new regularization for inverse problems17 Oct 2017
GlobalBioIm Lib - v2: new tools, more flexibility, and improved composition rules.03 Oct 2017
Fractional Integral transforms and Time-Frequency Representations02 Jun 2017
First steps toward fast PET reconstruction30 May 2017
Lipid membranes and surface reconstruction - a biologically inspired method for 3D segmentation16 May 2017
Optical Diffraction Tomography: Principles and Algorithms09 May 2017
Compressed Sensing for Dose Reduction in STEM Tomography11 Apr 2017
Chasing Mycobacteria10 Apr 2017
Multifractal analysis for signal and image classification23 Mar 2017
Inverse problems and multimodality for biological imaging28 Feb 2017