Related papers: Construction of Parseval wavelets from redundant f…
As constructing multi-D wavelets remains a challenging problem, we propose a new method called prime coset sum to construct multi-D wavelets. Our method provides a systematic way to construct multi-D non-separable wavelet filter banks from…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
Using the notions and tools from realization in the sense of systems theory, we establish an explicit and new realization formula for families of infinite products of rational matrix-functions of a single complex variable. Our realizations…
We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…
L$^\natural$ (natural)-convex functions encompass a large class of nonlinear functions over general integer domains and arise in a wide range of real-world applications. We explore the minimization of L$^\natural$-convex functions, of…
In this paper we show how wavelets originating from multiresolution analysis of scale N give rise to certain representations of the Cuntz algebras O_N, and conversely how the wavelets can be recovered from these representations. The…
We analyze representations of solvable Baumslag Solitar group that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive…
Matrix Schubert varieties (Fulton '92) carry natural actions of Levi groups. Their coordinate rings are thereby Levi-representations; what is a combinatorial counting rule for the multiplicities of their irreducibles? When the Levi group is…
In this paper we provide a complete and unifying characterization of compactly supported univariate scalar orthogonal wavelets and vector-valued or matrix-valued orthogonal multi-wavelets. This characterization is based on classical results…
Construction of multivariate tight framelets is known to be a challenging problem. Multivariate dual framelets with vanishing moments generalize tight framelets and are not easy to be constructed either. Compactly supported multivariate…
Like the continous shearlet transform and their relatives, discrete transformations based on the interplay between several filterbanks with anisotropic dilations provide a high potential to recover directed features in two and more…
We suggested an algorithm for searching the recursion operators for nonlinear integrable equations. It was observed that the recursion operator $R$ can be represented as a ratio of the form $R=L_1^{-1}L_2$ where the linear differential…
Wavelet families arise by scaling and translations of a prototype function, called the {\em {mother wavelet}}. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis…
Interpolatory filters are of great interest in subdivision schemes and wavelet analysis. Due to the high-order linear-phase moment property, interpolatory refinement filters are often used to construct wavelets and framelets with high-order…
We introduce a collection of convex polytopes associated to a torus-equivariant vector bundle on a smooth complete toric variety. We show that the lattice points in these polytopes correspond to generators for the space of global sections…
We implement numerically formulas of [Isaev, Novikov, arXiv:2107.07882] for finding a compactly supported function $v$ on $\mathbb{R}^d$, $d\geq 1$, from its Fourier transform $\mathcal{F} [v]$ given within the ball $B_r$. For the…
We introduce a class of generalized tube algebras which describe how finite, non-invertible global symmetries of bosonic 1+1d QFTs act on operators which sit at the intersection point of a collection of boundaries and interfaces. We develop…
We establish a reproducing formula for the ridgelet transform on $\mathbb{R}^n$ in the framework of Banach lattices introduced in a recent paper by Nieraeth. Our approach is based on the $k$-plane Radon transform and a wavelet-type…