RIT on Applied Harmonic Analysis Archives for Fall 2024 to Spring 2025
Organization Meeting
When: Mon, September 11, 2023 - 1:00pmWhere: Kirwan Hall (MTH) 1310
Speaker: Radu Balan (UMD) -
Coorbit Invariant Embeddings (1)
When: Mon, September 18, 2023 - 1:00pmWhere: Kirwan Hall (MTH) 1310
Speaker: Efstratios Tsoukanis (UMD) -
Abstract: Consider a real vector space V and a finite group G acting unitary on V. We study the general problem of constructing a stable embedding, whose domain is the quotient of the vector space modulo the group action, and whose target space is an Euclidean space. The embedding scheme we propose is based on taking a fixed subset out of sorted coorbit ()_g , where w_i are appropriate vectors. Finally, we show that injectivity on quotient space implies stability.
Coorbit Invariant Embeddings (2)
When: Mon, September 25, 2023 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Efstratios Tsoukanis (UMD) -
Coorbit Invariant Embeddings (3)
When: Mon, October 2, 2023 - 1:00pmWhere: Kirwan Hall (MTH) 1310
Speaker: Efstratios Tsoukanis (UMD) -
The HRT conjecture from the point of view of the Fock space (1)
When: Mon, October 9, 2023 - 1:00pmWhere: Kirwan Hall (MATH) 1310
Speaker: Matthias Wellershoff (UMD) -
Abstract: In this talk, we will introduce the HRT conjecture and prove it for two simple cases. Then, we will introduce the Fock space of entire functions and use it to show that the HRT conjecture holds for point configurations where all but one point lie on a line.
This talk is based on a book chapter by Daniel W. Stroock.
The HRT conjecture from the point of view of the Fock space (2)
When: Mon, October 16, 2023 - 1:00pmWhere: Kirwan Hall (Math) 1310
Speaker: Matthias Wellershoff (UMD) -
Abstract: This talk is a continuation of a presentation with the same name last week. By viewing the HRT conjecture from the point of view of the Fock space, we show that it holds for a dense subset of the square-integrable signals. Thereafter, we present a characterisation of this dense subset. This talk is based on a book chapter by Daniel W.~Stroock.
The HRT conjecture from the point of view of the Fock space (3)
When: Mon, October 23, 2023 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Matthias Wellershoff (UMD) -
Abstract: This talk is a continuation of a presentation with the same name last week. By viewing the HRT conjecture from the point of view of the Fock space, we show that it holds for a dense subset of the square-integrable signals. Thereafter, we present a characterization of this dense subset. This talk is based on a book chapter by Daniel W. Stroock.
Linear independence of time frequency translates of functions with greater than exponential decay
When: Mon, October 30, 2023 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Revati Jadhav (UMD) -
Abstract: This talk is based on the paper by Bownick and Speegle (2012) with the same title. We establish the linear independence of time-frequency translates of functions with faster than exponential decay, under some additional restrictions
Linear independence of time frequency translates of functions with greater than exponential decay (2)
When: Mon, November 6, 2023 - 1:00pmWhere: Kirwan Hall (MATH) 1310
Speaker: Revati Jadhav (UMD) -
Abstract: This talk is based on the paper by Bownick and Speegle (2012) with the same title. We establish the linear independence of time-frequency translates of functions with faster than exponential decay, under some additional restrictions.
Linear independence of time frequency translates of functions with greater than exponential decay (3)
When: Mon, November 13, 2023 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Revati Jadhav (UMD) -
Abstract: This talk is based on the paper by Bownick and Speegle (2012) with the same title. We establish the linear independence of time-frequency translates of functions with faster than exponential decay, under some additional restrictions.
Bilevel optimization for hyperparameter tuning
When: Mon, November 27, 2023 - 1:00pmWhere: Math (Kirwan Hall) 1310
Speaker: Shashank Sule (UMD) -
Abstract: Many inverse problems in science and engineering boil down to the solution of variationally regularized optimization problems containing a fidelity term measuring the fit to the data weighted against a regularization term penalizing the complexity of the solution. In this context, it is important to choose a good hyperparameter for weighting of the fidelity against the regularization to obtain stable and accurate solutions. In this talk, I will study this hyperparameter choice problem through the lens of bilevel optimization, an optimization framework where the constraint is also an optimization problem. In particular, I will present the results of Holler et. al (2018) and Ehrhardt et. al (2023) on: (1) existence of solutions to the bilevel problem and (2) positivity of solutions in the single weighting term case. Time-permitting, I will present some results on the fast computation of solutions using first-order methods.
Turan-Nazarov's inequality
When: Mon, December 4, 2023 - 1:00pmWhere: MATH 1310
Speaker: Revati Jadhav (UMD) -
Abstract: Turan Nazarov's inequality gives us a bound on how much non-harmonic exponential polynomials can shrink on subsets of the real line.
Bilevel optimization for hyperparameter tuning (2)
When: Mon, December 11, 2023 - 1:00pmWhere: Kirwan 1310
Speaker: Shashank Sule (UMD) -
Abstract: We will prove a stability estimate for the hyperparameter tuning bilevel problem stated in the first talk. As a corollary, the existence of solutions to the upper level problem will follow. Time permitting we will also discuss the positivity of solutions to the bilevel problem, with a focus on the denoising case.
Organizational Meeting
When: Mon, February 5, 2024 - 1:00pmWhere: MTH 1310
Speaker: Radu Balan (UMD) -
Square-summable rank-one decomposition of nuclear operators
When: Mon, February 12, 2024 - 1:00pmWhere: MATH 1310
Speaker: Fushuai (Black) Jiang (UMD) -
Abstract: A problem posed by H. Feichtinger (and subsequently modified by C. Heil and D. Larson) asks whether a type of positive-definite integral operators with $M_1$ kernel admits a rank-one decomposition series that is also strongly square-summable in $M_1$. In this first talk, we will approach this problem by considering its matrix (and finite-dimensional) variant and analyzing several functionals that measure the optimality of such decomposition. Some of the results are based on the joint work with Radu Balan.
Square-summable rank-one decomposition of nuclear operators (2)
When: Mon, February 26, 2024 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Fushuai Jiang (UMD) -
Square-summable rank-one decomposition of nuclear operators (3)
When: Mon, March 4, 2024 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Fushuai Jiang (UMD) -
CUR Matrix Approximation Using Convex Optimization
When: Mon, March 25, 2024 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Kathryn Linehan (UMD) -
Abstract: In this talk we present a CUR matrix approximation that uses a novel convex optimization formulation to select the columns and rows of the data matrix for inclusion in C and R, respectively. We discuss implementation of the algorithm using the surrogate functional of Daubechies et al. [Communications on Pure and Applied Mathematics, 57.11 (2004)] and extend the theoretical guarantees of this approach to our formulation. Applications using CUR as a feature selection method for classification will be shown, if time. In addition, the proximal operator of the L-infinity norm is used in our CUR algorithm. We present a neural network approximation to this proximal operator that uses a novel feature selection process based on moments of the input data in order to allow vectors of varying lengths to be input into the network.
: A short survey on Lipschitz extension problems
When: Mon, April 15, 2024 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Fushuai Jiang (UMD) -
Abstract: Let X and Y be metric spaces, S be a closed subset of X, and f be a Lipschitz map from S to Y. How can we know if f can be extended to globally defined Lipschitz map preserving (or almost preserving) the Lipschitz constant of f? How do we construct such an extension? For what kind of metric spaces can this always be done?
In this series, we survey some of the key results in the study of the Lipschitz extension problem. We will start by introducing classical construction by McShane and Whitney and an existence result by Kirszbraun. Tentatively, we will explore some of the more advanced flavors, including the ball intersection property (existence), Nagata dimension and connectedness (constructive), and a recent explicit Kirszbraun formula by D. Azagra et. al.
A short survey on Lipschitz extension problems (2)
When: Mon, April 29, 2024 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Fushuai Jiang (UMD) -
Abstract: Let X and Y be metric spaces, S be a closed subset of X, and f be a Lipschitz map from S to Y. How can we know if f can be extended to globally defined Lipschitz map preserving (or almost preserving) the Lipschitz constant of f? How do we construct such an extension? For what kind of metric spaces can this always be done?
In this series, we survey some of the key results in the study of the Lipschitz extension problem. We will start by introducing classical construction by McShane and Whitney and an existence result by Kirszbraun. Tentatively, we will explore some of the more advanced flavors, including the ball intersection property (existence), Nagata dimension and connectedness (constructive), and a recent explicit Kirszbraun formula by D. Azagra et. al
Hyperspectral Reconstruction of Skin Through Fusion of Scattering Transform Features
When: Mon, May 6, 2024 - 1:00pmWhere: Kirwan Hall 1310
Speaker: Brandon Kolstoe (UMD) -
Abstract: Hyperspectral Imaging (HSI) is an established technique with an array of applications, but its use is limited due to both practical and technical issues associated with spectral devices. In this talk, I will discuss work my collaborators and I have done as part of the ICASSP 2024 Grand Challenge on Hyperspectral Skin Vision on reconstructing HSI of human skin from matching RGB images and an infrared band. To address this problem, we proposed a model based on the matching of features from the scattering transform - a type of convolutional neural network with predefined wavelet filters. I will introduce this model, show our results, and discuss possible improvements to the model