The Ridgelet Packets library provides a large family of orthonormal bases for functions f(x, y) in L(dxdy) which includes orthonormal ridgelets as well as bases deriving from tilings reminiscent from the theory of wavelets and the study of oscillatory Fourier integrals. An intuitively appealing feature: many of these bases have elements whose envelope is strongly aligned along specified ‘ridges...

Calculations based on high-resolution quantizations prove that the distortion rate D( R) of an image transform coding is proportional to 2 2 R when R is large enough. In wavelet and block cosine bases, we show that if R < 1 bit/pixel, then D( R) varies like R1 2 , where remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. ...

For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: i) the bases are orthonormal, ii) in each basis, all the states have the same values of entanglement, and iii) they continuously interpolate between the product basis and the maximally entangled basis. The states thus constructed may find applications in many ...

We consider ultrametric space with a measure, such that the measure of any ball is positive. A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable functions is introduced. Pseudodifferential operators (PDO) in the ultrametric space are investigated. We prove that these operators are diagonal in the introduced bases of ultrametric wavelets and compute the...

A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable with respect to arbitrary measure functions on general (up to some topological restrictions) ultrametric space is introduced. Pseudodifferential operators (PDO) on the ultrametric space are investigated. We prove that these operators are diagonal in the introduced bases of ultrametric wavelets and com...

We introduce the notion of compatibility dimension for a set quantum measurements: it is largest Hilbert space on which given measurements are compatible. In Schrödinger picture, this corresponds to testing with ensembles states supported subspace, using incompatibility witnesses Carmeli, Heinosaari, and Toigo [Phys. Rev. A 98,012126 (2018) Phys. Lett. 122, 130402 (2019).]. provide several boun...

A new way of construction of ultrametric spaces of quite general form by completion of directed trees with respect to the metric, defined in the special way, is proposed. We introduce a measure on the constructed ultrametric space, such that the measure of any ball is positive. A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable with respect to the def...