Two simple constructive methods are presented to compute compactly supported tight
wavelet frames for any given refinable function whose mask satisfies the QMF or sub-QMF …

Using results on syzygy modules over a multivariate polynomial ring, we are able to
construct compactly supported wavelet bi-frames with few generators from almost any pair of …

Compared to scalar framelets, multiframelets have certain advantages, such as relatively
smaller supports on generators, high vanishing moments, etc. The balancing property of …

In this article, we construct compactly supported multivariate pairs of dual wavelet frames,
shortly called bi-frames, for an arbitrary dilation matrix. Our construction is based on the …

Dual Gramian analysis is one of the fundamental tools developed in a series of papers by
Amos Ron and Zouwei Shen for studying frames. Using dual Gramian analysis, the frame …

Construction of multivariate tight framelets is known to be a challenging problem because it
is linked to the difficult problem on sum of squares of multivariate polynomials in real …

Recent advances in real algebraic geometry and in the theory of polynomial optimization are
applied to answer some open questions in the theory of multivariate tight wavelet frames …

An important tool for the construction of tight wavelet frames is the Unitary Extension
Principle first formulated in the Fourier-domain by Ron and Shen. We show that the time …

Continuing our recent work in [5] we study polynomial masks of multivariate tight wavelet
frames from two additional and complementary points of view: convexity and system theory …

We present a new box spline wavelet frame and apply it for image edge analysis. The
wavelet frame is constructed using a box spline of eight directions. It is tight and has seldom …