Publications (38)
A duality principle for groups II: Multi-frames meet super-frames
Radu Balan, Dorin Ervin Dutkay, Deguang Han +2
The duality principle for group representations developed in \cite{DHL-JFA, HL_BLM} exhibits a fact that the well-known duality principle in Gabor analysis is not an isolated incid…
Redundancy for localized and Gabor frames
Radu Balan, Pete Casazza, Zeph Landau
Redundancy is the qualitative property which makes Hilbert space frames so useful in practice. However, developing a meaningful quantitative notion of redundancy for infinite frame…
Multi-window Gabor frames in amalgam spaces
Radu Balan, Jens G. Christensen, Ilya A. Krishtal +2
We show that multi-window Gabor frames with windows in the Wiener algebra are Banach frames for all Wiener amalgam spaces. As a byproduct of our results w…
Relationships between the Phase Retrieval Problem and Permutation Invariant Embeddings
Radu Balan, Efstratios Tsoukanis
This paper discusses the connection between the phase retrieval problem and permutation invariant embeddings. We show that the real phase retrieval problem for …
Approximation of the Proximal Operator of the Norm Using a Neural Network
Kathryn Linehan, Radu Balan
Computing the proximal operator of the norm, , generally requires a sort of the input data, or at least a partial sort…
Optimal l-one Rank One Matrix Decompositions
Radu Balan, Kasso A. Okoudjou, Michael Rawson +2
In this paper we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of opti…
On signal reconstruction without noisy phase
Radu Balan, Pete Casazza, Dan Edidin
We construct new classes of Parseval frames for a Hilbert space which allow signal reconstruction from the absolute value of the frame coefficients. As a consequence, signal recons…
Measure Functions for Frames
Radu Balan, Zeph Landau
This paper addresses the natural question: ``How should frames be compared?'' We answer this question by quantifying the overcompleteness of all frames with the same index set. We…
Robust Uniform Recovery of Structured Signals from Nonlinear Observations
Pedro Abdalla, Radu Balan, Junren Chen
While it is well known that the restricted isometry property (RIP) guarantees uniform sparse recovery from noisy linear measurements, uniform recovery of structured signals from no…
Learning flexible representations of stochastic processes on graphs
Addison Bohannon, Brian Sadler, Radu Balan
Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolutio…
Reconstruction of Signals from Magnitudes of Redundant Representations
Radu Balan
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real or complex Hilbert space when only the magnitudes of the coefficients of the vecto…
Convergence Guarantees for Deep Epsilon Greedy Policy Learning
Michael Rawson, Radu Balan
Policy learning is a quickly growing area. As robotics and computers control day-to-day life, their error rate needs to be minimized and controlled. There are many policy learning…
Lipschitz Analysis of Generalized Phase Retrievable Matrix Frames
Radu Balan, Chris B. Dock
The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames…
Lipschitz Properties for Deep Convolutional Networks
Radu Balan, Maneesh Singh, Dongmian Zou
In this paper we discuss the stability properties of convolutional neural networks. Convolutional neural networks are widely used in machine learning. In classification they are ma…
Reconstruction of Signals from Magnitudes of Redundant Representations: The Complex Case
Radu Balan
This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under…
Invertibility and Robustness of Phaseless Reconstruction
Radu Balan, Yang Wang
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a r…
Permutation Invariant Representations with Applications to Graph Deep Learning
Radu Balan, Naveed Haghani, Maneesh Singh
This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application i…
G-Invariant Representations using Coorbits: Bi-Lipschitz Properties
Radu Balan, Efstratios Tsoukanis
Consider a finite dimensional real vector space and a finite group acting unitarily on it. We study the general problem of constructing Euclidean stable embeddings of the quotient…
Frames and Phaseless Reconstruction
Radu Balan
Frame design for phaseless reconstruction is now part of the broader problem of nonlinear reconstruction and is an emerging topic in harmonic analysis. The problem of phaseless rec…
Phase Retrieval using Lipschitz Continuous Maps
Radu Balan, Dongmian Zou
In this note we prove that reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem") can be performed using Lipschitz continuous maps. Specific…
CUR Matrix Approximation through Convex Optimization for Feature Selection
Kathryn Linehan, Radu Balan
The singular value decomposition (SVD) is commonly used in applications requiring a low rank matrix approximation. However, the singular vectors cannot be interpreted in terms of t…
A Noncommutative Wiener Lemma and A Faithful Tracial State on Banach Algebras of Time-Frequency Shift Operators
Radu Balan
In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also constru…
On Lipschitz Analysis and Lipschitz Synthesis for the Phase Retrieval Problem
Radu Balan, Dongmian Zou
In this paper we prove two results regarding reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem"). First we show that phase retrievability…
An Extension of Barbashin-Krasovski-LaSalle Theorem to a Class of Nonautonomous Systems
Radu Balan
In this paper we give an extension of the Barbashin-Krasovski-LaSalle Theorem to a class of time-varying dynamical systems, namely the class of systems for which the restricted vec…
Factorization of positive-semidefinite operators with absolutely summable entries
Radu Balan, Fushuai Jiang
A problem by Feichtinger, Heil, and Larson asks whether every infinite matrix with (an equivalent substitute for the Feichtinger algebra) that is…
Quantitative Bounds for Sorting-Based Permutation-Invariant Embeddings
Nadav Dym, Matthias Wellershoff, Efstratios Tsoukanis +2
We study permutation-invariant embeddings of -dimensional point sets, which are defined by sorting independent one-dimensional projections of the input. Such embeddings aris…
On a problem by Hans Feichtinger
Radu Balan, Kasso A. Okoudjou, Anirudha Poria
In this paper, we solve a spectral problem about positive semi-definite trace-class pseudodifferential operators on modulation spaces which was posed by H. Feichtinger. Later, C. H…
Stability of Phase Retrievable Frames
Radu Balan
In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set $\fc$ of vec…
Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equations
Xiongye Xiao, Defu Cao, Ruochen Yang +5
Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve…
Stability of sorting based embeddings
Radu Balan, Efstratios Tsoukanis, Matthias Wellershoff
Consider a group of order acting unitarily on a real inner product space . We show that the sorting based embedding obtained by applying a general linear map $α: \mathb…
ScoresActivation: A New Activation Function for Model Agnostic Global Explainability by Design
Emanuel Covaci, Fabian Galis, Radu Balan +2
Understanding the decision of large deep learning models is a critical challenge for building transparent and trustworthy systems. Although the current post hoc explanation methods…
Optimization methods for frame conditioning and application to graph Laplacian scaling
Radu Balan, Mathew Begué, Chae Clark +1
A frame is scalable if each of its vectors can be rescaled in such a way that the resulting set becomes a Parseval frame. In this paper, we consider four different optimization pro…
Motion correction in MRI using deep learning and a novel hybrid loss function
Lei Zhang, Xiaoke Wang, Michael Rawson +6
Purpose To develop and evaluate a deep learning-based method (MC-Net) to suppress motion artifacts in brain magnetic resonance imaging (MRI). Methods MC-Net was derived from a UNet…
On Lipschitz Bounds of General Convolutional Neural Networks
Dongmian Zou, Radu Balan, Maneesh Singh
Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs,…
G-Invariant Representations using Coorbits: Injectivity Properties
Radu Balan, Efstratios Tsoukanis
Consider a finite-dimensional real vector space equipped with a finite group acting unitarily on it. We address the general problem of constructing Euclidean stable embeddings of t…
PICore: Physics-Informed Unsupervised Coreset Selection for Data Efficient Neural Operator Training
Anirudh Satheesh, Anant Khandelwal, Mucong Ding +1
Neural operators offer a powerful paradigm for solving partial differential equations (PDEs) that cannot be solved analytically by learning mappings between function spaces. Howeve…
An Exact Hypergraph Matching Algorithm for Nuclear Identification in Embryonic Caenorhabditis elegans
Andrew Lauziere, Ryan Christensen, Hari Shroff +1
Finding an optimal correspondence between point sets is a common task in computer vision. Existing techniques assume relatively simple relationships among points and do not guarant…
VQ-Flows: Vector Quantized Local Normalizing Flows
Sahil Sidheekh, Chris B. Dock, Tushar Jain +2
Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current…