Jakob Lemvig; Department of Applied Mathematics and Computer Science; DTU Compute; Technical University of Denmark

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[[#pub2018]]
! 2018 Publications

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* Click %height=16px%{$Filesdir}pdf.png to obtain '''preprint''' versions.

to:

* Click %height=16px%{$Filesdir}pdf.png to obtain '''preprint''' versions. If not availble, use [[http://arxiv.org| ArXiv.org]]

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>>comment<<

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>><<

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~~[[#pub2015]]~~
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Title: '''Wavelet Frames and Their Duals''' ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

to:

Title: '''Wavelet Frames and Their Duals''' ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

>>comment<<
!! Preprints & 2015 Publications

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>><<

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Title: '''Wavelet Frames and Their Duals''' ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

>>comment<<
!! 1998 – 2006
Use the links in the [[#sb|sidebar]].

bibtexquery:[bibfile.bib][strpos($this->get('AUTHOR'),'Lim')!==FALSE || strpos($this->get('AUTHOR'),'Lemvig')!==FALSE || strpos($this->get('AUTHOR'),'Kutyniok')!==FALSE][!$this->get('YEAR')][50]

!! Preprints
%rfloat%[[Attach:FFExistence.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]] [[index.php?n=Publications.Publications?action=bibentry&bibfile=bibfile.bib&bibref=MR2471937#MR2471937Bib |{$Filesdir}bibtex.gif"This link is NOT correct"]]%%
R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki. \\
%maroon%'''Fusion Frames: Existence and Construction.'''%%\\
Submitted (2009). (:toggle show="Show abstract" hide box1 button=0:)
>>id=box1 border='1px solid maroon' padding=5px bgcolor=#eee<<
%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval. %%
>><<

>>comment<<
%rfloat%[[Attach:FFExistence.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]]%%
P. Boufounos, G. Kutyniok, and H. Rauhut. \\
%maroon%'''Compressed Sensing for Fusion Frames'''.%%\\
Submitted (2009).\\

>>comment<<
!! 2009
%rfloat%[[Attach:Wavefront.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]] [[index.php?n=Publications.Publications?action=bibentry&bibfile=bibfile.bib&bibref=MR2471937#MR2471937Bib |{$Filesdir}bibtex.gif"View BibTeX entry"]]%%
bibtexsummary:[bibfile.bib,MR2471937].
(:toggle show="Show abstract" hide box3 button=0:)
>>id=box3 border='1px solid maroon' padding=5px bgcolor=#eee<<
%maroon%Abstract%%. It is known that the Continuous Wavelet Transform of a distribution {$f$} decays rapidly near the points where {$f$} is smooth, while it decays slowly near the irregular points. This property allows the identification of the singular support of {$f$}. However, the Continuous Wavelet Transform is unable to precisely identify the wavefront set of a distribution. In this paper, we employ the framework of affine systems to construct the so-called Continuous Shearlet Transform, which is defined by {$SH_f(a,s,t) = <f,\psi_{ast}>$}. The analyzing elements {$\psi_{ast}$} are dilated and translated copies of a single generating function {$\psi$}, where the dilation matrices form a two-parameter matrix group consisting of products of parabolic scaling and shear matrices. We show that the elements {$\psi_{ast}$} form a system of smooth functions at continuous scales {$a >0$}, locations {$t \in R^2$}, and oriented along lines of slope {$s \in R$} in the frequency domain. We then prove that the Continuous Shearlet Transform does exactly resolve the wavefront set of a distribution {$f$}. Finally, we point out several variations of this approach.
>><<
>><<

>>comment<<
#%item value=2% [[#article2]] Lemvig, J.: Constructing pairs of dual bandlimited framelets with desired time localization, Adv. Comput. Math. '''30''' (2009) 231-247, [[Attach:lemvig_pairs-dual-framelets_A4.pdf |a4]] or [[Attach:lemvig_pairs-dual-framelets_LETTER.pdf |letter]].
#%item value=1% [[{$mb} | Bownik,M.]]; Lemvig, J.: The canonical and alternate duals of a wavelet frame, Appl. Comput. Harmon. Anal. '''23''' (2007) 263–272. [[Attach:cadwf_A4.pdf |a4]] or [[Attach:cadwf_LETTER.pdf |letter]].
>><<

to:

Title: '''Wavelet Frames and Their Duals''' ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

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[[early]]

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[[#early]]

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[[#preprints]]

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[[#phdthesis]]

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26.03.2012, at 13:58 UTC by Jakob -

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Title: Wavelet Frames and Their Duals ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

to:

Title: '''Wavelet Frames and Their Duals''' ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

26.03.2012, at 11:28 UTC by Jakob -

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!! ~~2008~~ - 2011 Publications

to:

!! 2007 - 2011 Publications

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bibtexquery:[bibfile.bib][$this->get('YEAR')=='2007'][$this->get('AUTHOR')][50]

26.03.2012, at 11:27 UTC by Jakob -

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bibtexquery:[bibfile.bib][$this->get('YEAR')=='~~2018~~'][$this->get('AUTHOR')][50]

to:

bibtexquery:[bibfile.bib][$this->get('YEAR')=='2008'][$this->get('AUTHOR')][50]

26.03.2012, at 11:27 UTC by Jakob -

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~~!! Quick~~ Guide:

to:

'''Quick Guide:'''

26.03.2012, at 11:27 UTC by Jakob -

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* Click {$Filesdir}bibtex.gif to retrieve '''BibTeX''' metadata.

to:

* Click %height=16px%{$Filesdir}bibtex.gif to retrieve '''BibTeX''' metadata.

26.03.2012, at 11:26 UTC by Jakob -

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* Click %height=16px%{$Filesdir}pdf.png or use external links [[http://www.home.uni-osnabrueck.de/kutyniok/publications.html| Publications:Kutyniok]], [[{$Anawww}jlemvig/index.php?n=Mathematics.Publications| Publications:Lemvig]], or [[http://arxiv.org/| arXiv.org]] to obtain '''preprint''' versions.

to:

* Click %height=16px%{$Filesdir}pdf.png to obtain '''preprint''' versions.

26.03.2012, at 11:26 UTC by Jakob -

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!! ~~Newest~~ preprint

to:

!! Quick Guide:
* Click %height=18px%{$Filesdir}world.png to go to the '''journal''' version of the paper ([[http://doi.org | DOI links]])
* Click %height=16px%{$Filesdir}pdf.png or use external links [[http://www.home.uni-osnabrueck.de/kutyniok/publications.html| Publications:Kutyniok]], [[{$Anawww}jlemvig/index.php?n=Mathematics.Publications| Publications:Lemvig]], or [[http://arxiv.org/| arXiv.org]] to obtain '''preprint''' versions.
* Click {$Filesdir}bibtex.gif to retrieve '''BibTeX''' metadata.

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!! ~~Quick Guide~~:
* Click %height=18px%{$Filesdir}world.png to go to the '''journal''' version of the paper ([[http://doi.org | DOI links]])
* Click %height=16px%{$Filesdir}pdf.png or use external links [[http://www.~~home~~.~~uni-osnabrueck.de/kutyniok/publications.html| Publications:Kutyniok]], [[{$Anawww}jlemvig/index~~.~~php?n=Mathematics~~.~~Publications| Publications~~:~~Lemvig]], or [[http://arxiv.org/| arXiv~~.org]] to obtain '''preprint''' versions.
* Click {$Filesdir}bibtex.gif to retrieve '''BibTeX''' metadata.

to:

!! Ph.D. Thesis

Title: Wavelet Frames and Their Duals ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

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!! Preprints
%rfloat%[[Attach:FFExistence.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]] [[index.php?n=Publications.Publications?action=bibentry&bibfile=bibfile.bib&bibref=MR2471937#MR2471937Bib |{$Filesdir}bibtex.gif"This link is NOT correct"]]%%
R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki. \\
%maroon%'''Fusion Frames: Existence and Construction.'''%%\\
Submitted (2009). (:toggle show="Show abstract" hide box1 button=0:)
>>id=box1 border='1px solid maroon' padding=5px bgcolor=#eee<<
%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval. %%

Deleted lines 39-50:

!! Ph.D. Thesis

Title: Wavelet Frames and Their Duals ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

!! Preprints
%rfloat%[[Attach:FFExistence.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]] [[index.php?n=Publications.Publications?action=bibentry&bibfile=bibfile.bib&bibref=MR2471937#MR2471937Bib |{$Filesdir}bibtex.gif"This link is NOT correct"]]%%
R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki. \\
%maroon%'''Fusion Frames: Existence and Construction.'''%%\\
Submitted (2009). (:toggle show="Show abstract" hide box1 button=0:)
>>id=box1 border='1px solid maroon' padding=5px bgcolor=#eee<<
%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval. %%

26.03.2012, at 11:25 UTC by Jakob -

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bibtexquery:[bibfile.bib][~~][!~~$this->get('YEAR')][50]

to:

bibtexquery:[bibfile.bib][$this->get('YEAR')=='2011'][$this->get('AUTHOR')][50]
bibtexquery:[bibfile.bib][$this->get('YEAR')=='2010'][$this->get('AUTHOR')][50]
bibtexquery:[bibfile.bib][$this->get('YEAR')=='2009'][$this->get('AUTHOR')][50]
bibtexquery:[bibfile.bib][$this->get('YEAR')=='2018'][$this->get('AUTHOR')][50]

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>>comment<<

Deleted line 25:

~~>>comment<<~~

26.03.2012, at 10:54 UTC by Jakob -

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%rfloat%[[Attach:FFExistence.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]] [[index.php?n=Publications.Publications?action=bibentry&bibfile=bibfile.bib&bibref=MR2471937#MR2471937Bib |{$Filesdir}bibtex.gif"This link is NOT correct"]]%%
R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki. \\

to:

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to:

%rfloat%[[Attach:FFExistence.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]] [[index.php?n=Publications.Publications?action=bibentry&bibfile=bibfile.bib&bibref=MR2471937#MR2471937Bib |{$Filesdir}bibtex.gif"This link is NOT correct"]]%%
R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki. \\
%maroon%'''Fusion Frames: Existence and Construction.'''%%\\
Submitted (2009). (:toggle show="Show abstract" hide box1 button=0:)
>>id=box1 border='1px solid maroon' padding=5px bgcolor=#eee<<
%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval. %%

26.03.2012, at 10:52 UTC by Jakob -

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%maroon%'''Fusion Frames: Existence and Construction.'''%%\\
Submitted (2009). (:toggle show="Show abstract" hide box1 button=0:)
>>id=box1 border='1px solid maroon' padding=5px bgcolor=#eee<<
%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval. %%

to:

26.03.2012, at 10:52 UTC by Jakob -

Changed lines 9-10 from:

%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval.
%%

to:

%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval. %%

26.03.2012, at 10:52 UTC by Jakob -

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%%

26.03.2012, at 10:51 UTC by Jakob -

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!! Newest preprint
%rfloat%[[Attach:FFExistence.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]] [[index.php?n=Publications.Publications?action=bibentry&bibfile=bibfile.bib&bibref=MR2471937#MR2471937Bib |{$Filesdir}bibtex.gif"This link is NOT correct"]]%%
R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki. \\
%maroon%'''Fusion Frames: Existence and Construction.'''%%\\
Submitted (2009). (:toggle show="Show abstract" hide box1 button=0:)
>>id=box1 border='1px solid maroon' padding=5px bgcolor=#eee<<
%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval.

Changed lines 37-42 from:

%rfloat%[[Attach:FFExistence.pdf | {$Filesdir}pdf2.png"Download article as PDF file"]] [[index.php?n=Publications.Publications?action=bibentry&bibfile=bibfile.bib&bibref=MR2471937#MR2471937Bib |{$Filesdir}bibtex.gif"This link is NOT correct"]]%%
R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki. \\
%maroon%'''Fusion Frames: Existence and Construction.'''%%\\
Submitted (2009). (:toggle show="Show abstract" hide box1 button=0:)
>>id=box1 border='1px solid maroon' padding=5px bgcolor=#eee<<
%maroon%Abstract%%. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}, does there exist a fusion frame in {$\mathbb{R}^M$} with {$N$} subspaces of dimension {$m$} for which {$\{\lambda_j\}_{j=1,...,M}$} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters {$M, N, m \in \mathbb{N}$} and {$\{\lambda_j\}_{j=1,...,M}$}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval.

to:

26.03.2012, at 10:50 UTC by Jakob -

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~~!! Preprints~~

26.03.2012, at 10:49 UTC by Jakob -

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! ~~Selected AAG~~ Publications

to:

! Publications

!! Preprints

!! Preprints & 2012 Publications

bibtexquery:[bibfile.bib][$this->get('YEAR')=='2012'][$this->get('AUTHOR')][50]

!! 2008 - 2011 Publications

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Quick Guide:

to:

!! Quick Guide:

Deleted lines 16-31:

!! Preprints & 2010 Publications

bibtexquery:[bibfile.bib][$this->get('YEAR')=='2010'][$this->get('AUTHOR')][50]

!! 2009 Publications

bibtexquery:[bibfile.bib][$this->get('YEAR')=='2009'][$this->get('AUTHOR')][50]

!! 2008 Publications

bibtexquery:[bibfile.bib][$this->get('YEAR')=='2008'][$this->get('AUTHOR')][50]

!! 2007 Publications

bibtexquery:[bibfile.bib][$this->get('YEAR')=='2007'][$this->get('AUTHOR')][50]

26.03.2012, at 10:19 UTC by Jakob -

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bibtexquery:[bibfile.bib][][$this->get('YEAR')][50]

to:

bibtexquery:[bibfile.bib][][!$this->get('YEAR')][50]

26.03.2012, at 10:18 UTC by Jakob -

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bibtexquery:[bibfile.bib][][$this->get('~~AUTHOR~~')][50]

to:

bibtexquery:[bibfile.bib][][$this->get('YEAR')][50]

26.03.2012, at 10:15 UTC by Jakob -

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bibtexquery:[bibfile.bib][50]

to:

bibtexquery:[bibfile.bib][][$this->get('AUTHOR')][50]

26.03.2012, at 10:15 UTC by Jakob -

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bibtexquery:[bibfile.bib]

to:

bibtexquery:[bibfile.bib][50]

26.03.2012, at 10:14 UTC by Jakob -

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bibtexquery:[bibfile.bib~~][$this->get('YEAR')=<'2013'][$this->get('AUTHOR')][50~~]

to:

bibtexquery:[bibfile.bib]

26.03.2012, at 10:14 UTC by Jakob -

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bibtexquery:[bibfile.bib][$this->get('YEAR')<'2013'][$this->get('AUTHOR')][50]

to:

bibtexquery:[bibfile.bib][$this->get('YEAR')=<'2013'][$this->get('AUTHOR')][50]

26.03.2012, at 10:14 UTC by Jakob -

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bibtexquery:[bibfile.bib][$this->get('YEAR')<'2013'][$this->get('AUTHOR')][50]

26.03.2012, at 09:59 UTC by Jakob -

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Title: Wavelet Frames and Their Duals ([[Attach:~~phd-thesis~~.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

to:

Title: Wavelet Frames and Their Duals ([[Attach:lemvig_phdthesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

26.03.2012, at 09:57 UTC by Jakob -

Changed line 34 from:

Title: Wavelet Frames and Their Duals (Attach:~~PDF)~~. Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

to:

Title: Wavelet Frames and Their Duals ([[Attach:phd-thesis.pdf|pdf]]). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

26.03.2012, at 09:56 UTC by Jakob -

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!! Talks

Firstname Lastname: ~~'''What is Web 2.0?'''~~
(:~~toggle show="(Show slideshow)" hide box2 button=0~~:)
>>id=box2<<
(:slideshare what-is-web-20-1194363300579044-4:)

~~>>comment<<~~

to:

!! Ph.D. Thesis

Title: Wavelet Frames and Their Duals (Attach:PDF). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

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~~>><<~~

to:

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>><<

to:

>><<

25.03.2010, at 17:30 UTC by 131.173.40.72 -

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!! Preprints & 2009 Publications

to:

!! Preprints & 2010 Publications

bibtexquery:[bibfile.bib][$this->get('YEAR')=='2010'][$this->get('AUTHOR')][50]

!! 2009 Publications

Publications.Publications History