Where: MATH 3206

Speaker: Organizational Meeting (-) - -

Abstract: We will plan this year's seminar, with special consideration for introductory talks aimed at first and second year students.

Where: MTH 3206

Speaker: Wojtek Czaja (UMCP) -

Where: MATH 3206

Speaker: Chae Clark (UMD) -

Abstract: Hyperspectral datasets have become pervasive in the field of signal processing.

To process this data we need efficient representations that require little space to store and transmit.

Two major methods for accomplishing this are low-rank methods that map the dataset to a lower-dimensional space, and sparsifying methods that lower the support of a dataset. The combination of these methods is the subject of this talk. Robust PCA attempts to decompose a dataset into sparse and low-rank components, resulting in efficient representations of the dataset.

Where: MATH 3206

Speaker: Michael Kreisel (UMCP) -

Abstract: Franz Luef's work demonstrates how projective modules over noncommutative tori provide structures which tie together many results on lattice Gabor frames. We shall show that a similar situation occurs in the case of Gabor frames coming from quasicrystals, where there are corresponding operator algebras and projective modules. In particular, there always exist multiwindow Gabor frames for a quasicrystal. The dimensions of the modules end up being equal to the frame measure as defined by Balan, Casazza, Heil, and Landau. The structure of the commutants also suggest that there are generalizations of Janssen's representation to quasicrystalline Gabor frames.

Where: MATH 3206

Speaker: Jacob Bedrossian (UMD) - http://www2.cscamm.umd.edu/~jacob/

Abstract: Landau damping is a fundamental stability mechanism in effectively collisionless plasmas caused by the mixing, and subsequent spatial homogenization, of charged particles. Despite being one of the simplest, physically relevant, examples of stability due to mixing, it largely resisted mathematically rigorous study on the nonlinear level due to subtle regularity issues intertwined with a special set of unusual nonlinear resonances known as plasma echoes. A major breakthrough was due to Mouhot and Villani in 2011, however, their work was far too unwieldy to be generalized to related mixing problems in fluid mechanics and elsewhere in kinetic theory. I will present a more recent proof due to Masmoudi, Mouhot and myself in 2013 which makes use of a few paradifferential calculus techniques (adapted from Masmoudi and I's work on mixing in fluid mechanics) to provide a more robust and significantly simplified proof of Landau damping in the natural regularity classes.

Where: MATH 3206

Speaker: Ed Bosch (NGA) -

Abstract:

During this talk we will demonstrate an elegant way of constructing 2D tight frames from a set of orthonormal vectors via upsampling and circular convolution. Furthermore, this framework allows us to analyze and visualize image data at multiple scales and directions, and exploit the representation redundancy in a computationally efficient manner. Finally, we employ this framework to perform image superresolution via edge detection and characterization.

Where: MATH 3206

Speaker: Ben Kedem (UMD) -

Abstract: In food safety and bio-surveillance in many cases it is often desired to estimate the probability that a contaminant such as some insecticide or pesticide exceeds unsafe very high thresholds. The probability or chance in question

is then very small. To estimate such a probability we need information about large values. However, in many cases the data do not contain information about exceedingly large contamination levels, which ostensibly makes the problem impossible to solve. A solution is provided whereby more information about small tail probabilities is obtained by FUSING the real data with computer generated random data. The method provides short but reliable interval estimates from moderately large samples. An illustration is provided using exposure data of methylmercury, dichlorophenol, and trichlorophenol obtained from the National Health and Nutrition Examination Survey (NHANES).

Where: MATH 3206

Speaker: James Murphy (UMD) -

Abstract: We shall discuss the problem of image registration, particularly in the context of remote sensing. An algorithm based on anisotropic features shall be detailed, with applications to data collected by NASA satellites.

Where: MATH 3206

Speaker: Chae Clark (UMD) -

Abstract: A (unit norm) frame is scalable if its vectors can be rescaled so as to result into a tight frame. Tight frames can be considered optimally conditioned because the condition number of their frame operators is unity.

In this paper we reformulate the scalability problem as a convex optimization question. In particular, we present examples of various formulations of the problem along with numerical results obtained by using our methods on randomly generated frames.

Where: MATH 3206

Speaker: Matt Begue (UMD) -

Abstract: Many data sets can be represented in the form of graphs. Matrices, such as the Laplacian or the adjacency matrix, capture the structure of the data graph and we can exploit spectral properties of these matrices to learn more about the graph and enable us to do harmonic analysis on graphs. However, graphs with many edges will have very dense Laplacians and this can become computationally expensive to work with, especially with large graphs. This lead to Spielmann and collaborators to introduce graph sparsification, where edges of the graph are deleted while trying to preserve the spectral structure of the Laplacian. Deleting edges makes the Laplacian more sparse which speeds up computations. We will present Spielman's most recent sparsification technique and analyze its performance, strengths, and weaknesses.

Where: MATH 3206

Speaker: Matt Guay (UMD) -

Abstract: TBA

Where: MATH 3206

Speaker: Mads Jakobsen (DTU) -

Abstract: In 1995 three groups of authors, Daubechies, Landau and Landau; Ron and Shen; and Janssen simultaneously announced the, so-called, duality principle for Gabor frames: a Gabor system is a frame for L2(R) if, and only if, the Gabor system with the adjoint lattice is a Riesz sequence in L2(R). Interestingly, the techniques to prove the result are very different in these three papers. Moreover, the articles are quite technical and difficult to understand and in most literature one simply states the result and refers the reader to the original papers for a proof. In my talk I will provide a complete (and straight forward) proof of the duality principle. On the way we will make use of the Janssen representation for the Gabor frame operator, take account of the properties of tight Gabor frames, use the short-time Fourier transform and exploit properties of the Modulation space M^1. Most importantly, the proof I will present immediately carries over to the more general case of non-separable Gabor systems on locally compact abelian groups.

Where: MATH 3206

Speaker: Dongmian Zhou (UMD) -

Abstract: In signal processing it is often difficult to measure a signal directly. In some applications one can only measure the magnitudes of its inner product with a finite or countable set of vectors. It is a critical problem to reconstruct the original signal (up to a phase factor) from the measurements of those magnitudes. In the C^n case, it was conjectured that the signal is uniquely determined from 4n-4 generic measurements. I will present an injectivity result by Conca, Edidin, Hering and Vinzant which solves the "4n-4 conjecture".

Where: MATH 3206

Speaker: Vignon Oussa (Bridgewater State University) -

Where: MATH 3206

Speaker: Mads Sielemann Jakobsen (DTU) -

Abstract: In 1995 three groups of authors, Daubechies, Landau and Landau; Ron and Shen; and Janssen simultaneously announced the, so-called, duality principle for Gabor frames: a Gabor system is a frame for L2(R) if, and only if, the Gabor system with the adjoint lattice is a Riesz sequence in L2(R). Interestingly, the techniques to prove the result are very different in these three papers. Moreover, the articles are quite technical and difficult to understand and in most literature one simply states the result and refers the reader to the original papers for a proof. In my talk I will provide a complete proof of the duality principle. On the way we will make use of the Janssen representation for the Gabor frame operator, use the short-time Fourier transform and exploit properties of the modulation space M^1, also known as Feichtingers algebra. Most importantly, the proof I will present immediately carries over to the more general case of non-separable Gabor systems on locally compact abelian groups.

Where: MATH 3206

Speaker: Karamatou (Djima) -

Where: MATH 3206

Speaker: Sivaram Narayan (Central Michigan University) -

Abstract: In this talk we discuss the combinatorial structure of frames and

their decomposition into tight or scalable subsets using partially-ordered

sets (posets). We define factor poset of a frame {fi}i∈I to be a col-

lection of subsets of I ordered by inclusion so that nonempty J ⊆ I

is in the factor poset if and only if {fj}j∈J is a tight frame for Hn.

A similar definition is given for the scalability poset of a frame. We

discuss conditions which factor posets satisfy and present the inverse

factor poset problem, which inquires when there exists a frame whose

factor poset is some given poset P. We mention a necessary condi-

tion for solving the inverse factor poset problem in Hn which is also

sufficient for H2. We describe how factor poset structure of frames is

preserved under orthogonal projections. We present results regarding

when a frame can be scaled to have a given factor poset.