English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Generalizing wavelets by adding desired redundancy and flexibility,frameletsare of interest and importance in many applications such as image processingand numerical algorithms. Several key properties of framelets are highvanishing moments for sparse multiscale representation, fast framelettransforms for numerical efficiency, and redundancy for robustness. However, itis a challenging problem to study and construct multivariate nonseparableframelets, mainly due to their intrinsic connections to factorization andsyzygy modules of multivariate polynomial matrices. In this paper, wecircumvent the above difficulties through the approach of quasi-tightframelets, which behave almost identically to tight framelets. Employing thepopular oblique extension principle (OEP), from an arbitrary compactlysupported $\dm$-refinable vector function $\phi$ with multiplicity greater thanone, we prove that we can always derive from $\phi$ a compactly supportedmultivariate quasi-tight framelet such that (i) all the framelet generatorshave the highest possible order of vanishing moments;(ii) its associated fastframelet transform is compact with the highest balancing order.For a refinablescalar function $\phi$, the above item (ii) often cannot be achievedintrinsically but we show that we can always construct a compactly supportedOEP-based multivariate quasi-tight framelet derived from $\phi$ satisfying item(i).This paper provides a comprehensive investigation on OEP-based multivariatequasi-tight multiframelets and their associated framelet transforms with highbalancing orders. This deepens our theoretical understanding of multivariatequasi-tight multiframelets and their associated fast multiframelet transforms.

Multivariate Quasi-tight Framelets with High Balancing Orders Derived from Any Compactly Supported Refinable Vector Functions