# Imaging and Sensing

The Optimization/Waves seminar is now part of the Imaging and Sensing track course credit!

## Fall 2023

For the Fall 2023 semester, seminars will take place on Tuesdays from 12pm to 1pm, with alternate topics, in Conference room 362C (ACS building).

• November 28th: Hannah Love (University of California, Merced)

Title:  An Iterative Method for Method of Fundamental Solutions for Multiple Scattering of Objects

Abstract: The aim is to solve the physical problem where a time-harmonic wave occurs on a collection of objects distributed through three-dimensional space then to scatter off of those objects. We strive to compute the scattered wave field everywhere that is exterior to these collection of objects. Despite what numerical method is used, our problem develops into a block system of equations. The main challenge is to solve this block system efficiently, thinking of storage and complexity. Described will be one particular method called the Method of Fundamental Solutions (MFS) that we use to solve this problem and then identify the numerical linear algebra problem to study.

• November 28th: Elsie Cortes (University of California, Merced)

Title: Optimizing the Modified Grid for the Multilayer Transmission Problem

Abstract: To simulate the scattering of a source over a permeable, multilayer object in R2, we look for the solution to the Helmholtz equation for the transmission problem. We use a boundary integral equation (BIE) system to solve for quantities on N boundaries, which are used to define our solution in the layers defined by the boundaries.  As part of solving this system, we define our periodic boundaries from M points. The question we wish to examine as part of this problem is how to best determine the optimal M on each boundary.  In general, the largest wave number, k, in the system determines the discretization of the boundaries as a more oscillatory solution requires large M to capture.  However, by defining a contrast between the exterior and interior values of k on each boundary, we hope to find a relationship between M and this contrast.  From there, we can decide how to optimize the discretization of the grid defining the solution domain.

• November 7th: Irabiel Romero Ruiz (University of California, Merced)

Title: An inverse problem, governed by DC Power-grids

• October 31st: Jeremy Hoskins (University of Chicago)

Title: Edge Effects at Insulator Interfaces

Abstract:  In this talk we will discuss computational methods for forward and inverse problems involving interfaces and nonlocal operators. Such problems arise naturally in a number of contexts including, inter alia, quantum optics, topological insulators, acoustics, and optics. In particular, in the first part of the talk we will focus on the problem of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schrödinger equation and the singular waveguide by appropriate jump conditions along the one-dimensional interface separating the insulators. We will discuss two integral equation based methods for solving this problem, discuss guarantees on solvability, and fast, efficient algorithms for approximating the solution. In the second part of the talk, we will turn to discussing an inverse scattering problem related to models of photon propagation in quantum optics.

• October 24th: Alexei Novikov (Pennsylvania State University)

Title: Correlation-informed ordered dictionary learning for imaging in complex media

Abstract: We propose an approach for imaging in strongly scattering media that uses dictionary learning and connectivity information to estimate the sensing matrices in these media. It has two steps. The first step estimates, with high accuracy, the true Green’s function vectors using array data from multiple sparse sets of sources, whose locations and amplitudes are not known to us. This step yields a dictionary for wave propagation whose columns are those of the sensing matrix up to permutations. The second step orders these columns using Multi-Dimensional Scaling (MDS) with connectivity information derived from cross-correlations of the estimated Green’s function vectors. For these two steps to work together, we must combine data from large and small arrays. Through simulation experiments, we show that the proposed approach is robust and is able to provide high-resolution images.

• October 10th: Jocelyn Ornelas Muñoz (University of California, Merced)

Title: Decoding the Hidden: Direct Image Classification using Coded Aperture Imaging

Abstract: Coded aperture imaging has emerged as a solution to enhance light sensitivity and enable imaging in challenging conditions. However, the computational expense of image reconstruction poses limitations in processing efficiency. To address this, we propose a direct classification method using convolutional neural networks. By leveraging raw coded measurements, our approach eliminates the need for explicit image reconstruction, reducing computational overhead. We evaluate the effectiveness of this approach compared to traditional methods on the MNIST and CIFAR10 datasets. Our results demonstrate that direct image classification using raw coded measurements achieves comparable performance to traditional methods while reducing computational overhead and enabling real-time processing. These findings highlight the potential of deep learning in enhancing the decoding process and improving the overall performance of coded aperture imaging systems.

• October 3rd: Joseph Simpson (University of California, Merced)

Title: Scattering By A Slender Ellipsoid

Abstract: We attempt to solve the direct scattering problem of a time-harmonic plane wave incident upon a sound-soft slender ellipsoid. For the axially incident case, we will compare the known asymptotic solution with a numerical approximation using the method of fundamental solutions. We will discuss issues of well-posedness for the Fredholm integral equation of the first kind that arises in the asymptotic solution as well as concerns about the reliability of our method of fundamental solutions results.

• September 26th: Benjamin Latham (University of California, Merced)

Title: Trefftz DG Plane Wave Methods for Plasmonic Scattering by Spheres & Disks

Abstract: We investigate scattering in negative media using a novel DG method with an application to surface plasmonics. We will construe surface plasmons as complex, near-resonance phenomena occurring on the interface of negative media. In this talk, we will develop a Trefftz function space and associated DG method and weak form for a Helmholtz scattering problem involving one or more penetrable objects. A brief overview of Trefftz methods for the Helmholtz equation will be included, and we will discuss their application and utility in particular for solving this near-resonance problem.

• September 19th: Kyle Wright (University of California, Merced)

Title: IEP with application to Quantum Sensing

Abstract: A system of tunnel-coupled quantum dots is considered in the presence of an applied electric field. Given the measurements of differences between ground state and excited state energy levels as the electric field is varied, we seek to recover the quantum Hamiltonians that describe this system. We formulate this as a parameterized inverse eigenvalue problem and develop algebraic and computational methods for solving for parameters to represent these Hamiltonians. The results demonstrate that this approach is highly precise even when there is error present within the measurements. This theory could aid in the design of high resolution, tunable quantum sensors.

• September 12th: Patrick Sprenger (University of California, Merced)

Title: Instabilities of one- and two-phase solutions of a generalized nonlinear Schrödinger equation

Abstract: The nonlinear Schrödinger (NLS) equation is a universal model for describing the nonlinear envelope of a monochromatic carrier wave. Depending on the coefficients within the equation, the NLS can exhibit either focusing behavior, where one- and two-phase solutions are prone to instability from long wavelength perturbations, or defocusing behavior, where the solutions remain stable. In this presentation, we delve into a generalized category of NLS models and investigate their solutions through the lens of Whitham modulation theory. Within this framework, we derive an explicit criterion to assess the stability of two-phase solutions within this class of equations.

• September 5th: Jacqueline Alvarez (University of California, Merced)

Title: Deep Learning Approaches for Radiography in Non-Destructive Testing

Abstract: Radiography is an imaging technique used in a variety of applications, such as medical diagnosis, airport security, and non- destructive testing. We present a deep learning approach for extracting information from radiographic image data. We perform various prediction tasks using our approach, including material classification and regression on the geometry of a given object that is being radiographed. Our framework is designed to fine-tune a pre-trained convolutional neural network using different datasets simulated by HADES, which is a radiographic simulation code developed at LLNL. Moreover, we apply this framework to different types of radiographs including low energy x-rays, high energy x-rays, and neutron imaging.

## Previous Semesters

Here you can find the Optimization Seminar and Waves seminar talks from semesters prior to Fall 2023.