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Construction of k -Angle Tight Frames.

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Title: Construction of k -Angle Tight Frames.
Authors: Datta, Somantika1 (AUTHOR) sdatta@uidaho.edu, Oldroyd, Jesse1 (AUTHOR)
Source: Numerical Functional Analysis & Optimization. 2016, Vol. 37 Issue 8, p975-989. 15p.
Subjects: Frames (Combinatorial analysis), Signal processing, Robust control, Error analysis in mathematics, Vector analysis
Abstract: Frames have become standard tools in signal processing due to their robustness against transmission errors and their resilience to noise. Equiangular tight frames (ETFs) are particularly useful and have been shown to be optimal for transmission under a certain number of erasures. Unfortunately, ETFs do not exist in many cases and are hard to construct when they do exist. However, it is known that an ETF ofd + 1 vectors in addimensional space always exists. This article gives an explicit construction of ETFs ofd + 1 vectors in addimensional space. This construction works for both real and complex cases and is simpler than existing methods. The absence of ETFs of arbitrary sizes in a given space leads to generalizations of ETFs. One way to do this to consider tight frames where the set of (acute) angles between pairs of vectors haskdistinct values. This article presents a construction of tight frames such that for a given value ofk, the angles between pairs of vectors take at mostkdistinct values. These tight frames can be related to regular graphs and association schemes. [ABSTRACT FROM AUTHOR]
Copyright of Numerical Functional Analysis & Optimization is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Construction of k -Angle Tight Frames.
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  Data: <searchLink fieldCode="DE" term="%22Frames+%28Combinatorial+analysis%29%22">Frames (Combinatorial analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Signal+processing%22">Signal processing</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+control%22">Robust control</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+analysis%22">Vector analysis</searchLink>
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  Data: Frames have become standard tools in signal processing due to their robustness against transmission errors and their resilience to noise. Equiangular tight frames (ETFs) are particularly useful and have been shown to be optimal for transmission under a certain number of erasures. Unfortunately, ETFs do not exist in many cases and are hard to construct when they do exist. However, it is known that an ETF ofd + 1 vectors in addimensional space always exists. This article gives an explicit construction of ETFs ofd + 1 vectors in addimensional space. This construction works for both real and complex cases and is simpler than existing methods. The absence of ETFs of arbitrary sizes in a given space leads to generalizations of ETFs. One way to do this to consider tight frames where the set of (acute) angles between pairs of vectors haskdistinct values. This article presents a construction of tight frames such that for a given value ofk, the angles between pairs of vectors take at mostkdistinct values. These tight frames can be related to regular graphs and association schemes. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Numerical Functional Analysis & Optimization is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1080/01630563.2016.1176580
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      – Code: eng
        Text: English
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        PageCount: 15
        StartPage: 975
    Subjects:
      – SubjectFull: Frames (Combinatorial analysis)
        Type: general
      – SubjectFull: Signal processing
        Type: general
      – SubjectFull: Robust control
        Type: general
      – SubjectFull: Error analysis in mathematics
        Type: general
      – SubjectFull: Vector analysis
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              Text: 2016
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