Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Bin Han，University of Alberta
Inviter:	许志强研究员
Title:	Quasi-tight Framelets and Generalized Matrix Spectral Factorization of Multivariate Polynomials
Time & Venue:	2019.6.6 15:00-16:00 N702
Abstract:	Wavelets and tight framelets have many applications. However, constructing compactly supported multivariate tight framelets is known to be a challenging problem because it is linked to sum of squares and factorization of multivariate Laurent polynomials inalgebraic geometry. To circumvent this difficulty, we introduce the notion of quasi-tight framelets, which behaves almost identical to a tight framelet. From an arbitrary compactly supported multivariate refinable function (such as refinable box splines) with a general dilation matrix, we constructively prove that we can always derive a directional compactly supported quasi-tight framelet with vanishing moments. The key ingredient in constructing multivariate quasi-tight framelets is the generalize matrix spectral factorization of multivariate polynomials. This generalizes the famous one-dimensional matrix spectral factorization theorem (also called the Fejer-Riesz lemma) which is known to fail in high dimensions. This talk is based on [C. Diao and B. Han, Quasi-tight framelets with high vanishing moments derived from arbitrary refinable functions, Appl. Comput. Harmon. Anal., (2018), published online].