Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate Quasi-tight Framelets with High Balancing Orders Derived
  from Any Compactly Supported Refinable Vector Functions   Generalizing wavelets by adding desired redundancy and flexibility,framelets
are of interest and importance in many applications such as image processing
and numerical algorithms. Several key properties of framelets are high
vanishing moments for sparse multiscale representation, fast framelet
transforms for numerical efficiency, and redundancy for robustness. However, it
is a challenging problem to study and construct multivariate nonseparable
framelets, mainly due to their intrinsic connections to factorization and
syzygy modules of multivariate polynomial matrices. In this paper, we
circumvent the above difficulties through the approach of quasi-tight
framelets, which behave almost identically to tight framelets. Employing the
popular oblique extension principle (OEP), from an arbitrary compactly
supported $\dm$-refinable vector function $\phi$ with multiplicity greater than
one, we prove that we can always derive from $\phi$ a compactly supported
multivariate quasi-tight framelet such that (i) all the framelet generators
have the highest possible order of vanishing moments;(ii) its associated fast
framelet transform is compact with the highest balancing order.For a refinable
scalar function $\phi$, the above item (ii) often cannot be achieved
intrinsically but we show that we can always construct a compactly supported
OEP-based multivariate quasi-tight framelet derived from $\phi$ satisfying item
(i).This paper provides a comprehensive investigation on OEP-based multivariate
quasi-tight multiframelets and their associated framelet transforms with high
balancing orders. This deepens our theoretical understanding of multivariate
quasi-tight multiframelets and their associated fast multiframelet transforms.

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The categories of this paper are: econ
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int