Omar DeGuchy

University of California, Merced

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Roummel F. Marcia

University of California, Merced

Jennifer B. Erway

Wake Forest University

Mukesh Singhal

University of California, Merced

Aditya Ranganath

Lawrence Livermore National Laboratory

Lasith Adhikari

Philips (United States)

Jacqueline Alvarez

University of California, Merced

Fabián Santiago

Université Paris 8

Arnold D. Kim

University of California, Merced

Mario Banuelos

California State University, Fresno

Michael Fernando Mendez Jimenez

University of California, Merced

Cooperative Institutions

University of California, Merced

Applied Mathematics (United States)

University of California System

Wake Forest University

Universidad Nacional Autónoma de México

California State University, Fresno

University of California, San Diego

Moffitt Cancer Center

University of Florence

Universitat Autònoma de Barcelona

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Trust-Region Minimization Algorithm for Training Responses (TRMinATR): The Rise of Machine Learning Techniques

2021 29th European Signal Processing Conference (EUSIPCO) (2018)

Jacob Rafati Omar DeGuchy Roummel F. Marcia

Deep learning is a highly effective machine learning technique for large-scale problems. The optimization of nonconvex functions in deep learning literature is typically restricted to the class of first-order algorithms. These methods rely on gradient information because of the computational complexity associated with the second derivative Hessian matrix inversion and the memory storage required in large scale data problems. The reward for using second derivative information is that the methods can result in improved convergence properties for problems typically found in a non-convex setting such as saddle points and local minima. In this paper we introduce TRMinATR - an algorithm based on the limited memory BFGS quasi-Newton method using trust region - as an alternative to gradient descent methods. TRMinATR bridges the disparity between first order methods and second order methods by continuing to use gradient information to calculate Hessian approximations. We provide empirical results on the classification task of the MNIST dataset and show robust convergence with preferred generalization characteristics.

Hessian matrix

MNIST database

Maxima and minima

Saddle point

Trust region

Empirical risk minimization

10.23919/eusipco.2018.8553243

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Citations (7)

Compact representation of the full Broyden class of quasi-Newton updates

arXiv (Cornell University) (2017)

Omar DeGuchy Jennifer B. Erway Roummel F. Marcia

In this paper, we present the compact representation for matrices belonging to the the Broyden class of quasi-Newton updates, where each update may be either rank-one or rank-two. This work extends previous results solely for the restricted Broyden class of rank-two updates. In this article, it is not assumed the same Broyden update is used each iteration; rather, different members of the Broyden class may be used each iteration. Numerical experiments suggest that a practical implementation of the compact representation is able to accurately represent matrices belonging to the Broyden class of updates. Furthermore, we demonstrate how to compute the compact representation for the inverse of these matrices, as well as a practical algorithm for solving linear systems with members of the Broyden class of updates. We demonstrate through numerical experiments that the proposed linear solver is able to efficiently solve linear systems with members of the Broyden class of matrices to high accuracy. As an immediate consequence of this work, it is now possible to efficiently compute the eigenvalues of any limited-memory member of the Broyden class of matrices, allowing for the computation of condition numbers and the ability perform sensitivity analysis.

Representation

Solver

Rank (graph theory)

10.48550/arxiv.1705.08306

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Image Classification in Synthetic Aperture Radar Using Reconstruction from Learned Inverse Scattering

IGARSS 2022 - 2022 IEEE International Geoscience and Remote Sensing Symposium (2020)

Jacqueline Alvarez Omar DeGuchy Roummel F. Marcia

Synthetic aperture radar (SAR) is a remote sensing technique used to obtain high-resolution images, where image classification is a primary application. However, reconstructing SAR data is difficult which makes the classification of these images even more challenging. We present a study that investigates techniques for classifying SAR images using machine learning. In particular, we compare the classification accuracy using three different training data: raw SAR observation data, reconstructions using Kirchoff migration, and reconstructions by learning an approximation to the inverse of the SAR sensing operator. We consider two different architectures, namely a multi-layer perceptron and a convolutional neural network. The training set is composed of 50,000 images from the CIFAR-10 dataset. We find that the images reconstructed using the learned approximate inverse have a higher classification accuracy than that from the SAR measurement and the Kirchoff migration approach.

Contextual image classification

Data set

Multilayer perceptron

10.1109/igarss39084.2020.9323529

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Citations (1)

Non-convex Shannon entropy for photon-limited imaging

Omar DeGuchy Lasith Adhikari Marcia F. Roummel Reheman Baikejiang

Reconstructing high-dimensional sparse signals from low-dimensional low-count photon observations is a challenging nonlinear optimization problem. In this paper, we build upon previous work on minimizing the Poisson log-likelihood and incorporate recent work on the generalized nonconvex Shannon entropy function for promoting sparsity in solutions. We explore the effectiveness of the proposed approach using numerical experiments.

10.1117/12.2274466

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Recurrent Nerual Imaging: An Evolutionary Approach for Mixed Possion-Gaussian Image Denoising

Aditya Ranganath Omar DeGuchy Fabián Santiago Mukesh Singhal Roummel F. Marcia

Recurrent neural networks (RNNs) are traditionally used for machine learning applications for temporal sequences such as natural language processing. Its application to image processing is relatively new. In this paper, we apply RNNs to denoise images corrupted by mixed Poisson and Gaussian noise. The motivation for using an RNN comes from viewing the denoising of the Poisson-Gaussian realization as a temporal process. The network then attempts to trace back the steps that create the noisy realization in order to arrive at the noiseless reconstruction. Numerical experiments demonstrate that our proposed RNN approach outperforms convolutional autoen-coder methods for denoising and upsampling low-resolution images from the CIFAR-10 dataset.

Upsampling

Realization (probability)

Gaussian Noise

TRACE (psycholinguistics)

10.1109/icmla55696.2022.00078

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Citations (1)

Large-Scale Optimization and Deep Learning Techniques for Data-Driven Signal Processing

Omar DeGuchy

Author(s): DeGuchy, Omar | Advisor(s): Marcia, Roummel F | Abstract: The collection of data has become an integral part of our everyday lives. The algorithms necessary to process this information become paramount to our ability to interpret this resource. This type of data is typically recorded in a variety of signals including images, sounds, time series, and bio-informatics. In this work, we develop a number of algorithms to recover these types of signals in a variety of modalities. This work is mainly presented in two parts.Initially, we apply and develop large-scale optimization techniques used for signal processing. This includes the use of quasi-Newton methods to approximate second derivative information in a trust-region setting to solve regularized sparse signal recovery problems. We also formulate the compact representation of a large family of quasi-Newton methods known as the Broyden class. This extension of the classic quasi-Newton compact representation allows different updates to be used at every iteration. We also develop the algorithm to perform efficient solves with these representations. Within the realm of sparse signal recovery, but particular to photon-limited imaging applications, we also propose three novel algorithms for signal recovery in a low-light regime. First, we recover the support and lifetime decay of a flourophore from time dependent measurements. This type of modality is useful in identifying different types of molecular structures in tissue samples. The second algorithm identifies and implements the Shannon entropy function as a regularization technique for the promotion of sparsity in reconstructed signals from noisy downsampled observations. Finally, we also present an algorithm which addresses the difficulty of choosing the optimal parameters when solving the sparse signal recovery problem. There are two parameters which effect the quality of the reconstruction, the norm being used, as well as the intensity of the penalization imposed by that norm. We present an algorithm which uses a parallel asynchronous search along with a metric in order to find the optimal pair.The second portion of the dissertation draws on our experience with large-scale optimization and looks towards deep learning as an alternative to solving signal recovery problems. We first look to improve the standard gradient based techniques used during the training of these deep neural networks by presenting two novel optimization algorithms for deep learning. The first algorithm takes advantage of the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm in a trust-region setting in order to address the large scale minimization problem associated with deep learning. The second algorithm uses second derivative information in a trust region setting where the Hessian is not explicitly stored. We then use a conjugate based method in order to solve the trust-region subproblem.Finally, we apply deep learning techniques to a variety of applications in signal recovery. These applications include revisiting the photon-limited regime where we recover signals from noisy downsampled observations, image disambiguation which involves the recovery of two signals which have been superimposed, deep learning for synthetic aperture radar (SAR) where we recover information describing the imaging system as well as evaluate the impact of reconstruction on the ability to perform target detection, and signal variation detection in the human genome where we leverage the relationships between subjects to provide better detection.

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Multi-Stage Gaussian Noise Reduction with Recurrent Neural Networks

2014 48th Asilomar Conference on Signals, Systems and Computers (2021)

Aditya Ranganath Omar DeGuchy Mukesh Singhal Roummel F. Marcia

In this paper, we implement multi-stage deep learning methods to recover signals from noisy observations. We seek an alternative to the traditional iterative optimization-based methods by exploiting the denoising properties of autoencoders. The novelty of our method is in the reformulation of the denoising problem as a multi-stage process and in the use of recurrent neural networks to gradually recover the intended signal. Numerical experiments on a modified version of the CIFAR-10 dataset show that signal recovery in multiple stages produces sharper images than a standard autoencoder approach. We present quantitative evidence of improvement using both the mean squared error and the structural similarity index.

Autoencoder

Gaussian Noise

SIGNAL (programming language)

Similarity (geometry)

10.1109/ieeeconf53345.2021.9723266

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Compact representation of the full Broyden class of quasi‐Newton updates

Numerical Linear Algebra with Applications (2018)

Omar DeGuchy Jennifer B. Erway Roummel F. Marcia

Summary In this paper, we present the compact representation for matrices belonging to the Broyden class of quasi‐Newton updates, where each update may be either rank one or rank two. This work extends previous results solely for the restricted Broyden class of rank‐two updates. In this article, it is not assumed that the same Broyden update is used in each iteration; rather, different members of the Broyden class may be used in each iteration. Numerical experiments suggest that a practical implementation of the compact representation is able to accurately represent matrices belonging to the Broyden class of updates. Furthermore, we demonstrate how to compute the compact representation for the inverse of these matrices and a practical algorithm for solving linear systems with members of the Broyden class of updates. We demonstrate through numerical experiments that the proposed linear solver is able to efficiently solve linear systems with members of the Broyden class of matrices with high accuracy. As an immediate consequence of this work, it is now possible to efficiently compute the eigenvalues of any limited‐memory member of the Broyden class of matrices, allowing for the computation of condition numbers and the ability to perform sensitivity analysis.

Solver

Representation

Rank (graph theory)

10.1002/nla.2186

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Citations (10)

Deep Convolutional Autoencoders for Deblurring and Denoising Low-Resolution Images

IEICE Proceeding Series (2020)

Michael Fernando Mendez Jimenez Omar DeGuchy Marcia Roummel

Deblurring

Source

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Realistic SAR data augmentation using machine learning techniques

Benjamin Lewis Omar DeGuchy Joseph Sebastian John Kaminski

While many aspects of the image recognition problem have been largely solved by presenting large datasets to convolutional neural networks, there is still much work to do when data is sparse. For synthetic aperture radar (SAR), there is a lack of data that stems both from the cost of collecting data as well as the small size of the community that collects and uses such data. In this case, electromagnetic simulation is an effective stopgap measure, but its effectiveness at mirroring reality is upper bounded both by the quality of the electromagnetic prediction code as well as the fidelity of the target's digital model. In practice, we find that classification models trained on synthetic data generalize poorly to measured data. In this work, we investigate three machine learning networks, with the goal of using the network to bridge the gap between measured and synthetic data. We experiment with two types of generative adversarial networks as well as a modification of a convolutional autoencoder. Each network tackles a different aspect in the problem of the disparity between measured and synthetic data, namely: generating new, realistic, labeled data; translating data between the measured and synthetic domain; and joining the manifold of the two domains into an intermediate representation. Classification results using widely-employed neural network classifiers are presented for each experiment; these results suggest that such data manipulation improves classification generalization for measured data.

Autoencoder

Synthetic data

Mirroring

Contextual image classification

10.1117/12.2518452

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Citations (21)