Videos by Mathematical Challenges in Biomolecular/Biomedical Imaging and Visualization
Dictionary Learning and Compressive Imaging
Larry Carin's lecture onDictionary Learning and Compressive Imaging....
Incorporation of Prior Fourier Domain Edge Information in the L1 Minimization Problem for Compressed Sensing
In applications such as functional Magnetic Resonance Imaging (fMRI), full, uniformly-sampled Cartesian Fourier (frequency space) measurements are acquired. In order to reduce scan time and increase temporal resolution for fMRI studies, one would like to accurately reconstruct these images from a highly reduced set of Fourier measurements. Compressed Sensing (CS) has gi...
Michael Knopp's lecture on Imaging Technologies....
An Orthogonal Solution and Kernel Correction Algorithm for Inverse Source Problems with Applications in Fluorescence Tomography
We present a new approach to solve the inverse source problem arising in Fluorescence Tomography (FT). In general, the solution is non-unique and the problem is severely ill-posed. It poses tremendous challenges in image reconstructions. In practice, the most widely used methods are based on Tikhonov-type regularizations, which minimize a cost function consisting of a r...
Convolutional Gridding and Fourier Frame Approximation
The technique of covolutional gridding (CG) has been widely used in applications with non-uniform (Fourier) data such as magnetic resonance imaging (MRI). On the other hand, its error analysis is not fully understood. We consider it as a Fourier frame approximation and present an error analysis accordingly. Moreover, we propose a generalized convolutional gridding (GCG)...
Incorporating Edge Information in Fourier Reconstruction Schemes with Application to Magnetic Resonance Imaging
Fourier reconstruction of piecewise-smooth functions suffers from the familiar Gibbs phenomenon. In Fourier imaging modalities such as magnetic resonance imaging (MRI), this manifests as a loss of detail in the neighborhood of tissue boundaries (due to the Gibbs ringing artifact) as well as long scan times necessitated by the collection of a large number of spectral coe...
Operator splitting ADI schemes for nonlinear biomolecular solvation models
Recently, we have introduced a pseudo-time coupled nonlinear partial differential equation (PDE) model for biomolecular solvation analysis. Based on a free energy optimization, a boundary value system is derived to couple a nonlinear Poisson-Boltzmann (NPB) equation for electrostatic potential with a generalized Laplace-Beltrami (GLB) equation defining the biomolecular ...
Extracting structural information from electron tomograms
Electron tomography is the most widely applicable method for obtaining 3D information by electron microscopy. It has been realized that electron tomography is capable of providing a complete, molecular resolution three-dimensional mapping of entire proteomes including their detailed interactions. However, to realize this goal, information needs to be extracted efficient...
The Phase Retrieval Problem
The classical phase retrieval problem concerns the reconstruction of a function from the magnitude of its Fourier transform. Phase retrieval is an important problem in many applications such as molecular imaging and signal processing. Today the phase retrieval problem has been extended to include more general reconstructions for magnitudes of samples. In this talk I wil...
Geometric Blind Source Separation Methods and Their Applications in NMR Spectroscopy
Eric Yuanchang Sun
Nuclear magnetic resonance spectroscopy (NMR) is heavily employed by chemists and biochemists to study the structures and properties of chemical compounds. The measured data however often contain mixtures of chemicals, subject to changing background and environmental noise. A mathematical problem is to unmix or decompose the measured data into a set of pure or source sp...
Tunnels, Handles and Bottlenecks
We present a method for computing "choking" loops - a set of surface loops that describe the narrowing of the volumes inside/outside of the surface and extend the notion of surface homology and homotopy loops. The intuition behind their definition is that a choking loop represents the region where an offset of the original surface would get pinched. Our generalized loop...
Challenges in Interacting with Protein Interactions
Biology has become accessible to an understanding of processes that span from atom to organism. As such we now have the opportunity to build a spatio-temporal picture of living systems at the molecular level. In our recent work we attempt to create, interact with, and communicate physical representations of complex molecular environments. I will discuss the challenges a...