We construct a new orthonormal basis for L(R), whose elements are angularly integrated ridge functions — orthonormal ridgelets. The new basis functions are in L(R) and so are to be distinguished from the ridge function approximation system called ridgelets by Candès (1997, 1998), as ridge functions are not in L(R). Orthonormal ridgelet expansions have an interesting application in nonlinear app...

In this paper we develop a sublinear-time compressive sensing algorithm for approximating functions of many variables which are compressible in given Bounded Orthonormal Product Basis (BOPB). The resulting is shown to both have an associated best s-term recovery guarantee the BOPB, and also work well numerically solving sparse approximation problems involving contained span fairly general sets ...

An explicit family of polynomials on the unit ball B of R is constructed, so that it is an orthonormal family with respect to the inner product 〈f, g〉 = ρ Z Bd ∇f(x) · ∇g(x)dx + L(fg), where ρ > 0, ∇ is the gradient, and L(fg) is either the inner product on the sphere S or f(0)g(0).

Let G be a bounded simply-connected domain in the complex plane C, whose boundary Γ := ∂G is a Jordan curve, and let {pn} ∞ n=0 denote the sequence of Bergman polynomials of G. This is defined as the sequence pn(z) = λnz n + · · · , λn > 0, n = 0, 1, 2, . . . , of polynomials that are orthonormal with respect to the inner product

Our proof of [1, Theorem 1.1] is partially incorrect. The reason that, contrary to what we claimed, the construction space $${\mathscr {H}}^s$$ depends on orthonormal basis $$(\rho _k)$$ . We give in present note a new that needs little bit stronger assumption.

in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

In this paper we discuss a new robust tracking technique applied to histograms of intensity normalized color. This technique supports a video codec based on orthonormal basis coding. Orthonormal basis coding can be very efficient when the images to be coded have been normalized in size and position. However, an imprecise tracking procedure can have a negative impact on the efficiency and the qu...

We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models such as the Jukes-Cantor and Shimura models. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. A corollary of theoretical impor...