David Ketcheson
King Abdullah University of Science and Technology
United States
Aron Jamil Ahmadia
Columbia University
United States
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A Unified Software Framework for Empirical Gramians
Abstract
A common approach in model reduction is balanced truncation, which is based on gramian matrices classifiying certain attributes of states or parameters of a given dynamic system.
Initially restricted to linear systems, the empirical gramians not only extended this concept to nonlinear systems, but also provide a uniform computational method.
This work introduces a unified software framework supplying routines for six types of empirical gramians.
The gramian types will be discussed and applied in a model reduction framework for multipleinputmultipleoutput (MIMO) systems.
Himpe,
C.,
"A Unified Software Framework for Empirical Gramians",
Institute for Computational and Applied Mathematics at the University of Muenster.
Authors:
Himpe
Ohlberger
Coders:
Himpe
Last update
02/05/2013
Ranking
9999
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N.A.
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N.A.

LSD: A Fast Line Segment Detector with a False Detection Control
Abstract
We propose a lineartime line segment detector that gives accurate results, a controlled number of false detections, and requires no parameter tuning. This algorithm is tested and compared to stateoftheart algorithms on a wide set of natural images.
Grompone von Gioi,
R.,
"LSD: A Fast Line Segment Detector with a False Detection Control",
IEEE Transactions on Pattern Analysis and Machine Intelligence, 32, 722732.
Authors:
Grompone von Gioi
Jakubowicz Morel Randall
Coders:
Grompone von Gioi
Last update
10/08/2012
Ranking
13
Runs
61
Visits
280

CrossGramian Based Combined State and Parameter Reduction
Abstract
An accepted model reduction technique is balanced truncation, by which negligible states of a linear system of ODEs are determined by balancing the systems controllability and observability gramian matrices. To be applicable for nonlinear system this method was enhanced through the empirical gramians, while the cross gramian conjoined both gramians into one gramian matrix. This work introduces the empirical cross gramian for square MultipleInputMultipleOutput systems as well as the (empirical) joint gramian. Based on the cross gramian, the joint gramian determines, in addition to the Hankel singular values, the parameter identifiability allowing a combined model reduction, concurrently reducing state and parameter spaces. Furthermore, a controllability and an observability based combined reduction method are presented and the usage of empirical gramians is extended to parameter reduction in (Bayesian) inverse problems. All methods presented are evaluated by numerical experiments.
Himpe,
C.,
"CrossGramian Based Combined State and Parameter Reduction",
WWU Muenster.
Authors:
Himpe
Ohlberger
Coders:
Himpe
Last update
02/05/2013
Ranking
9999
Runs
N.A.
Visits
N.A.

A Unified Software Framework for Empirical Gramians
Abstract
A common approach in model reduction is balanced truncation, which is based on gramian matrices classifiying certain attributes of states or parameters of a given dynamic system.
Initially restricted to linear systems, the empirical gramians not only extended this concept to nonlinear systems, but also provide a uniform computational method.
This work introduces a unified software framework supplying routines for six types of empirical gramians.
The gramian types will be discussed and applied in a model reduction framework for multipleinputmultipleoutput (MIMO) systems.
Himpe,
C.,
"A Unified Software Framework for Empirical Gramians",
Institute for Computational and Applied Mathematics at the University of Muenster.
Authors:
Himpe
Ohlberger
Coders:
Himpe
Last update
02/20/2013
Ranking
9999
Runs
N.A.
Visits
N.A.

RudinOsherFatemi Total Variation Denoising using Split Bregman
Abstract
Denoising is the problem of removing noise from an image. The most commonly studied case is with additive white Gaussian noise (AWGN), where the observed noisy image f is related to the underlying true image u by
f = u + η,
and η is at each point in space independently and identically distributed as a zeromean Gaussian random variable.
Total variation (TV) regularization is a technique that was originally developed for AWGN image denoising by Rudin, Osher, and Fatemi. The TV regularization technique has since been applied to a multitude of other imaging problems, see for example Chan and Shen's book. We focus here on the split Bregman algorithm of Goldstein and Osher for TVregularized denoising.
Getreuer,
P.,
"RudinOsherFatemi Total Variation Denoising using Split Bregman",
Image Processing On Line, 2012.
Authors:
Getreuer
Coders:
Getreuer
Last update
10/08/2012
Ranking
12
Runs
9
Visits
99

Deterministic Matrices Matching the Compressed Sensing Phase Transitions of Gaussian Random Matrices
Abstract
In compressed sensing, one takes n < N samples of an N dimensional vector x0 using an n × N matrix A, obtaining undersampled measurements y = Ax0 . For random matrices with Gaussian i.i.d entries, it is known that, when x0 is ksparse, there is a precisely determined phase transition: for a certain region in the (k/n, n/N )phase diagram, convex optimization min x_1 subject to y = Ax, x ∈ X^N typically ﬁnds the sparsest solution, while outside that region, it typically fails. It has been shown empirically that the same property – with the same phase transition location – holds for a wide range of nonGaussian random matrix ensembles. We consider speciﬁc deterministic matrices including Spikes and Sines, Spikes and Noiselets, Paley Frames, DelsarteGoethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Extensive experiments show that for a typical ksparse object, convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian matrices. In our experiments, we considered coefﬁcients constrained to X^N for four different sets X ∈ {[0, 1], R_+ , R, C}. We establish this ﬁnding for each of the associated four phase transitions.
Monajemi,
H.,
D.
Donoho,
"Deterministic Matrices Matching the Compressed Sensing Phase Transitions of Gaussian Random Matrices",
Stanford University.
Authors:
Monajemi
Jafarpour Gavish Donoho
Coders:
Monajemi
Donoho Last update
01/04/2013
Ranking
9999
Runs
13
Visits
86

Sparks and Deterministic Constructions of Binary Measurement Matrices from Finite Geometry
Abstract
This codes and data generates the figures in the paper "Sparks and Deterministic Constructions of Binary Measurement Matrices from Finite Geometry" by ShuTao Xia, XinJi Liu, Yong Jiang, HaiTao Zheng.
Liu,
X.,
"Sparks and Deterministic Constructions of Binary Measurement Matrices from Finite Geometry",
Ideas.
Authors:
Liu
Coders:
Liu
Last update
09/21/2013
Ranking
9999
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N.A.
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N.A.

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