Certain imaging applications can exploit features beyond the spatial resolution of a sensor through computational super-resolution techniques. One particular method, super-sampling, involves assimilating multiple frames of digital video into composite video frames of higher average sampling density than the original sensor. Under certain conditions of scene motion and sensor characteristics, th...

Frames are constructed on the unit ball Bd in Rd consisting of smooth functions with small shrinking supports. The new frames are designed so that they can be used for decomposition of weighted Triebel Lizorkin and Besov spaces on Bd with weight wμ(x) := (1 − |x|2)μ−1/2, μ half integer, μ ≥ 0.

We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct g(x) ∈ L2(R) in such a way the functions gn(x) = e 1g(x+an2), n ∈ Z2 and a some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice nat...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

We investigate frame theory over the binary field Z2, following work of Bodmann, Le, Reza, Tobi and Tomforde. We consider general finite dimensional vector spaces V over Z2 equipped with an (indefinite) inner product (·, ·)V which can be an arbitrary bilinear functional. We characterize precisely when two such spaces (V, (·, ·)V ) and (W, (·, ·)W ) are unitarily equivalent in the sense that the...

In the first part of this paper, we consider nonlinear extension of frame theory by introducing bi-Lipschitz maps F between Banach spaces. Our linear model of bi-Lipschitz maps is the analysis operator associated with Hilbert frames, p-frames, Banach frames, g-frames and fusion frames. In general Banach space setting, stable algorithm to reconstruct a signal x from its noisy measurement F (x) +...

We characterize the orthogonal frames and orthogonal multiwavelet frames in L2 R with matrix dilations of the form Df x √ |detA|f Ax , where A is an arbitrary expanding d × d matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present ...