2016
Pulido, Jesus; Livescu, Daniel; Woodring, Jonathan; Ahrens, James; Hamann, Bernd
Survey and analysis of multiresolution methods for turbulence data Journal Article
In: Computers & Fluids, vol. 125, pp. 39 - 58, 2016, ISSN: 0045-7930, (LA-UR-15-20966).
Links | BibTeX | Tags: B-spline wavelet, Curvelet, Surfacelet, turbulence, Wavelet
@article{PULIDO201639b,
title = {Survey and analysis of multiresolution methods for turbulence data},
author = {Jesus Pulido and Daniel Livescu and Jonathan Woodring and James Ahrens and Bernd Hamann},
url = {http://www.sciencedirect.com/science/article/pii/S004579301500362X},
doi = {https://doi.org/10.1016/j.compfluid.2015.11.001},
issn = {0045-7930},
year = {2016},
date = {2016-01-01},
journal = {Computers & Fluids},
volume = {125},
pages = {39 - 58},
note = {LA-UR-15-20966},
keywords = {B-spline wavelet, Curvelet, Surfacelet, turbulence, Wavelet},
pubstate = {published},
tppubtype = {article}
}
2013
Brislawn, Christopher M.
Group-theoretic structure of linear phase multirate filter banks Journal Article
In: IEEE Transactions on Information Theory, vol. 59, no. 9, 2013, (LA-UR-12-20858).
Abstract | Links | BibTeX | Tags: Filter bank, free product, group, group lifting structure, JPEG 2000., Lifting, Linear phase filter, Polyphase matrix, semidirect product, Unique factorization, Wavelet
@article{Bris:13b:Group-theoretic-structure,
title = {Group-theoretic structure of linear phase multirate filter banks},
author = {Christopher M. Brislawn},
url = {https://datascience.dsscale.org/wp-content/uploads/2016/06/Group-TheoreticStructureOfLinearPhaseMultirateFilterBanks.pdf},
year = {2013},
date = {2013-08-06},
journal = {IEEE Transactions on Information Theory},
volume = {59},
number = {9},
abstract = {Unique lifting factorization results for group lifting structures are used to characterize the group-theoretic structure of two-channel linear phase FIR perfect reconstruction filter bank groups. For Dinvariant, order-increasing group lifting structures, it is shown that the associated lifting cascade group C is isomorphic to the free product of the upper and lower triangular lifting matrix groups. Under the same hypotheses, the associated scaled lifting group S is the semidirect product of C by the diagonal gain scaling matrix group D. These results apply to the group lifting structures for the two principal classes of linear phase perfect reconstruction filter banks, the whole- and half-sample symmetric classes. Since the unimodular whole-sample symmetric class forms a group, W, that is in fact equal to its own scaled lifting group, W = SW, the results of this paper characterize the group-theoretic structure of W up to isomorphism. Although the half-sample symmetric class H does not form a group, it can be partitioned into cosets of its lifting cascade group, CH, or, alternatively, into cosets of its scaled lifting group, SH. Homomorphic comparisons reveal that scaled lifting groups covered by the results in this paper have a structure analogous to a 'noncommutative vector space.'},
note = {LA-UR-12-20858},
keywords = {Filter bank, free product, group, group lifting structure, JPEG 2000., Lifting, Linear phase filter, Polyphase matrix, semidirect product, Unique factorization, Wavelet},
pubstate = {published},
tppubtype = {article}
}
Unique lifting factorization results for group lifting structures are used to characterize the group-theoretic structure of two-channel linear phase FIR perfect reconstruction filter bank groups. For Dinvariant, order-increasing group lifting structures, it is shown that the associated lifting cascade group C is isomorphic to the free product of the upper and lower triangular lifting matrix groups. Under the same hypotheses, the associated scaled lifting group S is the semidirect product of C by the diagonal gain scaling matrix group D. These results apply to the group lifting structures for the two principal classes of linear phase perfect reconstruction filter banks, the whole- and half-sample symmetric classes. Since the unimodular whole-sample symmetric class forms a group, W, that is in fact equal to its own scaled lifting group, W = SW, the results of this paper characterize the group-theoretic structure of W up to isomorphism. Although the half-sample symmetric class H does not form a group, it can be partitioned into cosets of its lifting cascade group, CH, or, alternatively, into cosets of its scaled lifting group, SH. Homomorphic comparisons reveal that scaled lifting groups covered by the results in this paper have a structure analogous to a 'noncommutative vector space.'
Brislawn, Christopher M.
On the group-theoretic structure of lifted filter banks Book Chapter
In: Andrews, Travis; Balan, Radu; Benedetto, John; Czaja, Wojciech; Okoudjou, Kasso (Ed.): Excursions in Harmonic Analysis, vol.~2, pp. 113-135, Birkh, Basel, 2013, (LA-UR-12-21217).
Abstract | Links | BibTeX | Tags: Filter bank, Group lift- ing structure, Group theory, group-theoretic structure, JPEG 2000, lifted filter banks, Lifting, Linear phase filter, Matrix polynomial, Polyphase matrix, Unique factorization, Wavelet
@inbook{Brislawn2013,
title = {On the group-theoretic structure of lifted filter banks},
author = {Christopher M. Brislawn},
editor = {Travis Andrews and Radu Balan and John Benedetto and Wojciech Czaja and Kasso Okoudjou},
url = {http://datascience.dsscale.org/wp-content/uploads/2016/06/OnTheGroup-TheoreticStructureOfLiftedFilterBanks.pdf},
doi = {10.1007/978-0-8176-8379-5_6},
year = {2013},
date = {2013-01-01},
booktitle = {Excursions in Harmonic Analysis, vol.~2},
pages = {113-135},
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series = {Applied and Numerical Harmonic Analysis},
abstract = {The polyphase-with-advance matrix representations of whole-sample symmetric (WS) unimodular filter banks form a multiplicative matrix Laurent poly- nomial group. Elements of this group can always be factored into lifting matrices with half-sample symmetric (HS) off-diagonal lifting filters; such linear phase lift- ing factorizations are specified in the ISO/IEC JPEG 2000 image coding standard. Half-sample symmetric unimodular filter banks do not form a group, but such filter banks can be partially factored into a cascade of whole-sample antisymmetric (WA) lifting matrices starting from a concentric, equal-length HS base filter bank. An al- gebraic framework called a group lifting structure has been introduced to formalize the group-theoretic aspects of matrix lifting factorizations. Despite their pronounced differences, it has been shown that the group lifting structures for both the WS and HS classes satisfy a polyphase order-increasing property that implies uniqueness (“modulo rescaling”) of irreducible group lifting factorizations in both group lifting structures. These unique factorization results can in turn be used to characterize the group-theoretic structure of the groups generated by the WS and HS group lifting structures.},
note = {LA-UR-12-21217},
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The polyphase-with-advance matrix representations of whole-sample symmetric (WS) unimodular filter banks form a multiplicative matrix Laurent poly- nomial group. Elements of this group can always be factored into lifting matrices with half-sample symmetric (HS) off-diagonal lifting filters; such linear phase lift- ing factorizations are specified in the ISO/IEC JPEG 2000 image coding standard. Half-sample symmetric unimodular filter banks do not form a group, but such filter banks can be partially factored into a cascade of whole-sample antisymmetric (WA) lifting matrices starting from a concentric, equal-length HS base filter bank. An al- gebraic framework called a group lifting structure has been introduced to formalize the group-theoretic aspects of matrix lifting factorizations. Despite their pronounced differences, it has been shown that the group lifting structures for both the WS and HS classes satisfy a polyphase order-increasing property that implies uniqueness (“modulo rescaling”) of irreducible group lifting factorizations in both group lifting structures. These unique factorization results can in turn be used to characterize the group-theoretic structure of the groups generated by the WS and HS group lifting structures.
2011
Woodring, Jonathan; Mniszewski, Susan; Brislawn, Christopher M.; DeMarle, David; Ahrens, James
Revisiting wavelet compression for large-scale climate data using JPEG 2000 and ensuring data precision Proceedings Article
In: Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on, pp. 31–38, IEEE 2011, (LA-UR-pending).
Abstract | Links | BibTeX | Tags: climate modeling, coding and information theory, data compaction and compression, JPEG 2000, Wavelet
@inproceedings{woodring2011revisiting,
title = {Revisiting wavelet compression for large-scale climate data using JPEG 2000 and ensuring data precision},
author = {Jonathan Woodring and Susan Mniszewski and Christopher M. Brislawn and David DeMarle and James Ahrens},
url = {http://datascience.dsscale.org/wp-content/uploads/2016/06/RevisitingWaveletComp.pdf},
year = {2011},
date = {2011-01-01},
booktitle = {Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on},
pages = {31--38},
organization = {IEEE},
abstract = {We revisit wavelet compression by using a standards-based method to reduce large-scale data sizes for production scientific computing. Many of the bottlenecks in visualization and analysis come from limited bandwidth in data movement, from storage to networks. The majority of the processing time for visualization and analysis is spent reading or writing large-scale data or moving data from a remote site in a distance scenario. Using wavelet compression in JPEG 2000, we provide a mechanism to vary data transfer time versus data quality, so that a domain expert can improve data transfer time while quantifying compression effects on their data. By using a standards-based method, we are able to provide scientists with the state-of-the-art wavelet compression from the signal processing and data compression community, suitable for use in a production computing environment. To quantify compression effects, we focus on measuring bit rate versus maximum error as a quality metric to provide precision guarantees for scientific analysis on remotely compressed POP (Parallel Ocean Program) data.},
note = {LA-UR-pending},
keywords = {climate modeling, coding and information theory, data compaction and compression, JPEG 2000, Wavelet},
pubstate = {published},
tppubtype = {inproceedings}
}
We revisit wavelet compression by using a standards-based method to reduce large-scale data sizes for production scientific computing. Many of the bottlenecks in visualization and analysis come from limited bandwidth in data movement, from storage to networks. The majority of the processing time for visualization and analysis is spent reading or writing large-scale data or moving data from a remote site in a distance scenario. Using wavelet compression in JPEG 2000, we provide a mechanism to vary data transfer time versus data quality, so that a domain expert can improve data transfer time while quantifying compression effects on their data. By using a standards-based method, we are able to provide scientists with the state-of-the-art wavelet compression from the signal processing and data compression community, suitable for use in a production computing environment. To quantify compression effects, we focus on measuring bit rate versus maximum error as a quality metric to provide precision guarantees for scientific analysis on remotely compressed POP (Parallel Ocean Program) data.
2009
Woodring, Jonathan; Shen, Han-Wei
Multiscale time activity data exploration via temporal clustering visualization spreadsheet Journal Article
In: Visualization and Computer Graphics, IEEE Transactions on, vol. 15, no. 1, pp. 123–137, 2009.
Abstract | Links | BibTeX | Tags: animation, clustering, filter banks, K-means, time histogram, time-varying, transfer function, visualization spreadsheet, Wavelet
@article{woodring2009multiscale,
title = {Multiscale time activity data exploration via temporal clustering visualization spreadsheet},
author = {Jonathan Woodring and Han-Wei Shen},
url = {http://datascience.dsscale.org/wp-content/uploads/2016/06/MultiscaleTimeActivityDataExplorationViaTemporalClusteringVisualizationSpreadsheet.pdf},
year = {2009},
date = {2009-01-01},
journal = {Visualization and Computer Graphics, IEEE Transactions on},
volume = {15},
number = {1},
pages = {123--137},
publisher = {IEEE},
abstract = {Time-varying data is usually explored by animation or arrays of static images. Neither is particularly effective for classifying data by different temporal activities. Important temporal trends can be missed due to the lack of ability to find them with current visualization methods. In this paper, we propose a method to explore data at different temporal resolutions to discover and highlight data based upon time-varying trends. Using the wavelet transform along the time axis, we transform data points into multiscale time series curve sets. The time curves are clustered so that data of similar activity are grouped together at different temporal resolutions. The data are displayed to the user in a global time view spreadsheet, where she is able to select temporal clusters of data points and filter and brush data across temporal scales. With our method, a user can interact with data based on time activities and create expressive visualizations.},
keywords = {animation, clustering, filter banks, K-means, time histogram, time-varying, transfer function, visualization spreadsheet, Wavelet},
pubstate = {published},
tppubtype = {article}
}
Time-varying data is usually explored by animation or arrays of static images. Neither is particularly effective for classifying data by different temporal activities. Important temporal trends can be missed due to the lack of ability to find them with current visualization methods. In this paper, we propose a method to explore data at different temporal resolutions to discover and highlight data based upon time-varying trends. Using the wavelet transform along the time axis, we transform data points into multiscale time series curve sets. The time curves are clustered so that data of similar activity are grouped together at different temporal resolutions. The data are displayed to the user in a global time view spreadsheet, where she is able to select temporal clusters of data points and filter and brush data across temporal scales. With our method, a user can interact with data based on time activities and create expressive visualizations.
: . .
1.
Pulido, Jesus; Livescu, Daniel; Woodring, Jonathan; Ahrens, James; Hamann, Bernd
Survey and analysis of multiresolution methods for turbulence data Journal Article
In: Computers & Fluids, vol. 125, pp. 39 - 58, 2016, ISSN: 0045-7930, (LA-UR-15-20966).
@article{PULIDO201639b,
title = {Survey and analysis of multiresolution methods for turbulence data},
author = {Jesus Pulido and Daniel Livescu and Jonathan Woodring and James Ahrens and Bernd Hamann},
url = {http://www.sciencedirect.com/science/article/pii/S004579301500362X},
doi = {https://doi.org/10.1016/j.compfluid.2015.11.001},
issn = {0045-7930},
year = {2016},
date = {2016-01-01},
journal = {Computers & Fluids},
volume = {125},
pages = {39 - 58},
note = {LA-UR-15-20966},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2.
Brislawn, Christopher M.
Group-theoretic structure of linear phase multirate filter banks Journal Article
In: IEEE Transactions on Information Theory, vol. 59, no. 9, 2013, (LA-UR-12-20858).
@article{Bris:13b:Group-theoretic-structure,
title = {Group-theoretic structure of linear phase multirate filter banks},
author = {Christopher M. Brislawn},
url = {https://datascience.dsscale.org/wp-content/uploads/2016/06/Group-TheoreticStructureOfLinearPhaseMultirateFilterBanks.pdf},
year = {2013},
date = {2013-08-06},
journal = {IEEE Transactions on Information Theory},
volume = {59},
number = {9},
abstract = {Unique lifting factorization results for group lifting structures are used to characterize the group-theoretic structure of two-channel linear phase FIR perfect reconstruction filter bank groups. For Dinvariant, order-increasing group lifting structures, it is shown that the associated lifting cascade group C is isomorphic to the free product of the upper and lower triangular lifting matrix groups. Under the same hypotheses, the associated scaled lifting group S is the semidirect product of C by the diagonal gain scaling matrix group D. These results apply to the group lifting structures for the two principal classes of linear phase perfect reconstruction filter banks, the whole- and half-sample symmetric classes. Since the unimodular whole-sample symmetric class forms a group, W, that is in fact equal to its own scaled lifting group, W = SW, the results of this paper characterize the group-theoretic structure of W up to isomorphism. Although the half-sample symmetric class H does not form a group, it can be partitioned into cosets of its lifting cascade group, CH, or, alternatively, into cosets of its scaled lifting group, SH. Homomorphic comparisons reveal that scaled lifting groups covered by the results in this paper have a structure analogous to a 'noncommutative vector space.'},
note = {LA-UR-12-20858},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Unique lifting factorization results for group lifting structures are used to characterize the group-theoretic structure of two-channel linear phase FIR perfect reconstruction filter bank groups. For Dinvariant, order-increasing group lifting structures, it is shown that the associated lifting cascade group C is isomorphic to the free product of the upper and lower triangular lifting matrix groups. Under the same hypotheses, the associated scaled lifting group S is the semidirect product of C by the diagonal gain scaling matrix group D. These results apply to the group lifting structures for the two principal classes of linear phase perfect reconstruction filter banks, the whole- and half-sample symmetric classes. Since the unimodular whole-sample symmetric class forms a group, W, that is in fact equal to its own scaled lifting group, W = SW, the results of this paper characterize the group-theoretic structure of W up to isomorphism. Although the half-sample symmetric class H does not form a group, it can be partitioned into cosets of its lifting cascade group, CH, or, alternatively, into cosets of its scaled lifting group, SH. Homomorphic comparisons reveal that scaled lifting groups covered by the results in this paper have a structure analogous to a 'noncommutative vector space.'
3.
Brislawn, Christopher M.
On the group-theoretic structure of lifted filter banks Book Chapter
In: Andrews, Travis; Balan, Radu; Benedetto, John; Czaja, Wojciech; Okoudjou, Kasso (Ed.): Excursions in Harmonic Analysis, vol.~2, pp. 113-135, Birkh, Basel, 2013, (LA-UR-12-21217).
@inbook{Brislawn2013,
title = {On the group-theoretic structure of lifted filter banks},
author = {Christopher M. Brislawn},
editor = {Travis Andrews and Radu Balan and John Benedetto and Wojciech Czaja and Kasso Okoudjou},
url = {http://datascience.dsscale.org/wp-content/uploads/2016/06/OnTheGroup-TheoreticStructureOfLiftedFilterBanks.pdf},
doi = {10.1007/978-0-8176-8379-5_6},
year = {2013},
date = {2013-01-01},
booktitle = {Excursions in Harmonic Analysis, vol.~2},
pages = {113-135},
publisher = {Birkh},
address = {Basel},
series = {Applied and Numerical Harmonic Analysis},
abstract = {The polyphase-with-advance matrix representations of whole-sample symmetric (WS) unimodular filter banks form a multiplicative matrix Laurent poly- nomial group. Elements of this group can always be factored into lifting matrices with half-sample symmetric (HS) off-diagonal lifting filters; such linear phase lift- ing factorizations are specified in the ISO/IEC JPEG 2000 image coding standard. Half-sample symmetric unimodular filter banks do not form a group, but such filter banks can be partially factored into a cascade of whole-sample antisymmetric (WA) lifting matrices starting from a concentric, equal-length HS base filter bank. An al- gebraic framework called a group lifting structure has been introduced to formalize the group-theoretic aspects of matrix lifting factorizations. Despite their pronounced differences, it has been shown that the group lifting structures for both the WS and HS classes satisfy a polyphase order-increasing property that implies uniqueness (“modulo rescaling”) of irreducible group lifting factorizations in both group lifting structures. These unique factorization results can in turn be used to characterize the group-theoretic structure of the groups generated by the WS and HS group lifting structures.},
note = {LA-UR-12-21217},
keywords = {},
pubstate = {published},
tppubtype = {inbook}
}
The polyphase-with-advance matrix representations of whole-sample symmetric (WS) unimodular filter banks form a multiplicative matrix Laurent poly- nomial group. Elements of this group can always be factored into lifting matrices with half-sample symmetric (HS) off-diagonal lifting filters; such linear phase lift- ing factorizations are specified in the ISO/IEC JPEG 2000 image coding standard. Half-sample symmetric unimodular filter banks do not form a group, but such filter banks can be partially factored into a cascade of whole-sample antisymmetric (WA) lifting matrices starting from a concentric, equal-length HS base filter bank. An al- gebraic framework called a group lifting structure has been introduced to formalize the group-theoretic aspects of matrix lifting factorizations. Despite their pronounced differences, it has been shown that the group lifting structures for both the WS and HS classes satisfy a polyphase order-increasing property that implies uniqueness (“modulo rescaling”) of irreducible group lifting factorizations in both group lifting structures. These unique factorization results can in turn be used to characterize the group-theoretic structure of the groups generated by the WS and HS group lifting structures.
4.
Woodring, Jonathan; Mniszewski, Susan; Brislawn, Christopher M.; DeMarle, David; Ahrens, James
Revisiting wavelet compression for large-scale climate data using JPEG 2000 and ensuring data precision Proceedings Article
In: Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on, pp. 31–38, IEEE 2011, (LA-UR-pending).
@inproceedings{woodring2011revisiting,
title = {Revisiting wavelet compression for large-scale climate data using JPEG 2000 and ensuring data precision},
author = {Jonathan Woodring and Susan Mniszewski and Christopher M. Brislawn and David DeMarle and James Ahrens},
url = {http://datascience.dsscale.org/wp-content/uploads/2016/06/RevisitingWaveletComp.pdf},
year = {2011},
date = {2011-01-01},
booktitle = {Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on},
pages = {31--38},
organization = {IEEE},
abstract = {We revisit wavelet compression by using a standards-based method to reduce large-scale data sizes for production scientific computing. Many of the bottlenecks in visualization and analysis come from limited bandwidth in data movement, from storage to networks. The majority of the processing time for visualization and analysis is spent reading or writing large-scale data or moving data from a remote site in a distance scenario. Using wavelet compression in JPEG 2000, we provide a mechanism to vary data transfer time versus data quality, so that a domain expert can improve data transfer time while quantifying compression effects on their data. By using a standards-based method, we are able to provide scientists with the state-of-the-art wavelet compression from the signal processing and data compression community, suitable for use in a production computing environment. To quantify compression effects, we focus on measuring bit rate versus maximum error as a quality metric to provide precision guarantees for scientific analysis on remotely compressed POP (Parallel Ocean Program) data.},
note = {LA-UR-pending},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
We revisit wavelet compression by using a standards-based method to reduce large-scale data sizes for production scientific computing. Many of the bottlenecks in visualization and analysis come from limited bandwidth in data movement, from storage to networks. The majority of the processing time for visualization and analysis is spent reading or writing large-scale data or moving data from a remote site in a distance scenario. Using wavelet compression in JPEG 2000, we provide a mechanism to vary data transfer time versus data quality, so that a domain expert can improve data transfer time while quantifying compression effects on their data. By using a standards-based method, we are able to provide scientists with the state-of-the-art wavelet compression from the signal processing and data compression community, suitable for use in a production computing environment. To quantify compression effects, we focus on measuring bit rate versus maximum error as a quality metric to provide precision guarantees for scientific analysis on remotely compressed POP (Parallel Ocean Program) data.
5.
Woodring, Jonathan; Shen, Han-Wei
Multiscale time activity data exploration via temporal clustering visualization spreadsheet Journal Article
In: Visualization and Computer Graphics, IEEE Transactions on, vol. 15, no. 1, pp. 123–137, 2009.
@article{woodring2009multiscale,
title = {Multiscale time activity data exploration via temporal clustering visualization spreadsheet},
author = {Jonathan Woodring and Han-Wei Shen},
url = {http://datascience.dsscale.org/wp-content/uploads/2016/06/MultiscaleTimeActivityDataExplorationViaTemporalClusteringVisualizationSpreadsheet.pdf},
year = {2009},
date = {2009-01-01},
journal = {Visualization and Computer Graphics, IEEE Transactions on},
volume = {15},
number = {1},
pages = {123--137},
publisher = {IEEE},
abstract = {Time-varying data is usually explored by animation or arrays of static images. Neither is particularly effective for classifying data by different temporal activities. Important temporal trends can be missed due to the lack of ability to find them with current visualization methods. In this paper, we propose a method to explore data at different temporal resolutions to discover and highlight data based upon time-varying trends. Using the wavelet transform along the time axis, we transform data points into multiscale time series curve sets. The time curves are clustered so that data of similar activity are grouped together at different temporal resolutions. The data are displayed to the user in a global time view spreadsheet, where she is able to select temporal clusters of data points and filter and brush data across temporal scales. With our method, a user can interact with data based on time activities and create expressive visualizations.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Time-varying data is usually explored by animation or arrays of static images. Neither is particularly effective for classifying data by different temporal activities. Important temporal trends can be missed due to the lack of ability to find them with current visualization methods. In this paper, we propose a method to explore data at different temporal resolutions to discover and highlight data based upon time-varying trends. Using the wavelet transform along the time axis, we transform data points into multiscale time series curve sets. The time curves are clustered so that data of similar activity are grouped together at different temporal resolutions. The data are displayed to the user in a global time view spreadsheet, where she is able to select temporal clusters of data points and filter and brush data across temporal scales. With our method, a user can interact with data based on time activities and create expressive visualizations.