Inverse Problems Seminar, Fall 2012 - Department of Mathematics at Colorado State University

[ Schedule ]   [ Abstracts ]

Seminar in Inverse Problems   [Fall 2018]

Inverse problems is a field of mathematics comprised of many areas including analysis, modeling, PDE's and scientific computation. Inverse problems arise in abundance in engineering, biology, physics, geophysics and more. This seminar addresses fundamental topics in inverse problems in a variety of applications.

Regular meeting times & location: Thursdays at 2 pm in Weber 223



Speaker: Randy Bartels, Colorado State University



Time and location: Thursday, 2 pm, Weber 223





Title: Coherent imaging with incoherent light and super-resolution imaging with spatio-temporally modulated illumination light

Abstract: Optical imaging is a powerful tool that has found widespread use in vast areas of science and industry. Fluorescent imaging is an indispensable component of many biological investigations, owing to the ability to track specific molecules. Coherent nonlinear optical imaging, based on inelastic nonlinear light scattering driven by intense laser fields, provides contrast mechanisms that provide information not accessible by other optical imaging methods. For all optical imaging methods, the diffraction of light limits how fine of a spatial feature can be resolved with conventional optical microscopes to the order of the wavelength of light. Recent years have seen this "optical diffraction" limit shattered, and a number of far field super resolution optical microscopes are now routinely used that are able to capture spatial information well below the scale of the wavelength. These microscopes have all exploited nonlinear manipulation of the population of electronic states in molecules. Recently, we demonstrated that superresolution imaging can be performed with coherent nonlinear scattering by illuminating an object with spatially-temporally modulated illumination light, then detecting coherent nonlinear scattering with a single pixel detector. From these data, super-resolved images are formed, and like confocal imaging and laser scanning nonlinear microscopy, this new imaging method can record data in specimens that exhibit optical scattering. Single pixel detection also enables the recording of fluorescent light emission, quantitative phase imaging, absorption imaging, and enabling background free optical absorption imaging by recording modulated florescent light emission. In addition, the use of spatio-temporally modulated illumination allows fluorescent microscopes to make use of coherent optical imaging modalities, such as holography and tomography, which opens new approaches to imaging with spatially incoherent light spectroscopic information - enabling background free optical absorption imaging by recording modulated florescent light emission. In addition, the use of spatio-temporally modulated illumination allows fluorescent microscopes to make use of coherent optical imaging modalities, such as holography and tomography, which opens new approaches to imaging with spatially incoherent light (e.g,, fluorescent emission) that have been previously accessible only to spatially coherent light. I will discuss coherent holographic image reconstruction by phase transfer (CHIRPT), an imaging method that utilizes de-localized illumination intensity patterns, to collect optical diffraction tomography (ODT) images of fluorescent emission with a single-pixel detector. CHIRPT permits numerical reconstruction of 2D and 3D data sets by transferring the phase difference between two spatially-coherent illumination beams into temporal modulations of fluorescent emission. Since each fluorescent molecule in the illuminated region of the sample experiences a distinct temporal modulation pattern, the temporal signal collected from the single-pixel detector encodes the location of each fluorophore simultaneously. A single CHIRPT image provides highly non-isotropic image resolution - diffraction limited in the lateral dimension, yet unsectioned in the axial dimension. By acquiring multiple views of the specimen at varied illumination angles, we show that it is possible to synthesize 3D super-resolved images with isotropic spatial resolution in the lateral and axial dimensions. The reconstruction of the image from the set of measured data constitutes a computational imaging inverse problem. I will highlight our successes and challenges for extracting images from these methods.




Fall 2018 Schedule

Oct. 4 Attend Applied Math Seminar at 3 pm, Weber 223: The Role of the Push-Forward Measure in Solving Inverse Problems: An Interactive Talk Using Jupyter Notebooks Troy Butler, Univ. CO Denver
Oct. 11 Chemical-specific contrast in laser microscopy: inverse problems and nonlinear mappings Jesse Wilson, Dept. of ECE and SBME, CSU
Oct. 25 Hyperspectral Synthetic-Aperture Radar Andrew Horman, Matrix Research
Nov. 1 no seminar - Math Day
Nov. 15 Coherent imaging with incoherent light and super-resolution imaging with spatio-temporally modulated illumination light Randy Bartels, Dept. of ECE and SBME, CSU




Abstracts

Jesse Wilson, Dept. of ECE and SBME, CSU   Oct. 11
Title: Chemical-specific contrast in laser microscopy: inverse problems and nonlinear mappings

Abstract: The combination of nonlinear and time-resolved optical spectroscopy with laser-scanning microscopy presents new opportunities for molecular imaging. Our lab is investigating new approaches to estimating chemical composition and redox from the optical response of cells and tissues. I will present three projects: mapping oxygen distributions with an adaptive filter systems identification approach, estimating mitochondrial respiratory chain redox with optical transient absorption, and synthesizing advanced imaging modalities from simpler instruments already deployed in the clinics.

Andrew Horman, Matrix Research   Oct. 25
Title: Hyperspectral Synthetic-Aperture Radar

Abstract: Typical synthetic aperture radar (SAR) imaging techniques neglect frequency-dependent dispersive effects. We propose an imaging algorithm, hyperspectral synthetic aperture radar (HSAR) which forms an image of the complex-valued scene reflectivity function as it depends on (x, y, frequency), or equivalently, (x, y, time delay). The algorithm permits arbitrary flight paths and arbitrary waveforms. We provide some numerical examples illustrating the approach. This work was done jointly with Margaret Cheney and Matthew Ferrara.

Randy Bartels, Dept. of ECE and SBME, CSU   Nov. 15
Title: Coherent imaging with incoherent light and super-resolution imaging with spatio-temporally modulated illumination light

Abstract: Abstract: Optical imaging is a powerful tool that has found widespread use in vast areas of science and industry. Fluorescent imaging is an indispensable component of many biological investigations, owing to the ability to track specific molecules. Coherent nonlinear optical imaging, based on inelastic nonlinear light scattering driven by intense laser fields, provides contrast mechanisms that provide information not accessible by other optical imaging methods. For all optical imaging methods, the diffraction of light limits how fine of a spatial feature can be resolved with conventional optical microscopes to the order of the wavelength of light. Recent years have seen this "optical diffraction" limit shattered, and a number of far field super resolution optical microscopes are now routinely used that are able to capture spatial information well below the scale of the wavelength. These microscopes have all exploited nonlinear manipulation of the population of electronic states in molecules. Recently, we demonstrated that superresolution imaging can be performed with coherent nonlinear scattering by illuminating an object with spatially-temporally modulated illumination light, then detecting coherent nonlinear scattering with a single pixel detector. From these data, super-resolved images are formed, and like confocal imaging and laser scanning nonlinear microscopy, this new imaging method can record data in specimens that exhibit optical scattering. Single pixel detection also enables the recording of fluorescent light emission, quantitative phase imaging, absorption imaging, and enabling background free optical absorption imaging by recording modulated florescent light emission. In addition, the use of spatio-temporally modulated illumination allows fluorescent microscopes to make use of coherent optical imaging modalities, such as holography and tomography, which opens new approaches to imaging with spatially incoherent light spectroscopic information - enabling background free optical absorption imaging by recording modulated florescent light emission. In addition, the use of spatio-temporally modulated illumination allows fluorescent microscopes to make use of coherent optical imaging modalities, such as holography and tomography, which opens new approaches to imaging with spatially incoherent light (e.g,, fluorescent emission) that have been previously accessible only to spatially coherent light. I will discuss coherent holographic image reconstruction by phase transfer (CHIRPT), an imaging method that utilizes de-localized illumination intensity patterns, to collect optical diffraction tomography (ODT) images of fluorescent emission with a single-pixel detector. CHIRPT permits numerical reconstruction of 2D and 3D data sets by transferring the phase difference between two spatially-coherent illumination beams into temporal modulations of fluorescent emission. Since each fluorescent molecule in the illuminated region of the sample experiences a distinct temporal modulation pattern, the temporal signal collected from the single-pixel detector encodes the location of each fluorophore simultaneously. A single CHIRPT image provides highly non-isotropic image resolution - diffraction limited in the lateral dimension, yet unsectioned in the axial dimension. By acquiring multiple views of the specimen at varied illumination angles, we show that it is possible to synthesize 3D super-resolved images with isotropic spatial resolution in the lateral and axial dimensions. The reconstruction of the image from the set of measured data constitutes a computational imaging inverse problem. I will highlight our successes and challenges for extracting images from these methods.





Past Seminars

[Spring 2015] [Fall 2014]