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...

A certain class of Frobenius algebras has been used to characterize orthonormal bases and observables on finite-dimensional Hilbert spaces. The presence of units in these algebras means that they can only be realized finite-dimensionally. We seek a suitable generalization, which will allow arbitrary bases and observables to be described within categorical axiomatizations of quantum mechanics. W...

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. ...

In this paper we propose an eigenimage based superresolution reconstruction technique. Eigenimages of a database of several similar low resolution images are obtained and the given low resolution image is projected on to the eigenimages to compute the eigenimage coefficients. The eigenimages are then interpolated using any conventional interpolation method and approximated to the nearest orthon...

This paper presents an algebraic approach to construct M-band orthonormal wavelet bases with perfect reconstruction. We first derive the system of constraint equations of M-band filter banks, and then an algebraic solution based on matrix decomposition is developed. The structure of the solutions is presented, and practical construction procedures are given. By using this algebraic approach, so...

In a quantum system having a finite number N of orthogonal states, two orthonormal bases {a i } and {b j } are called mutually un-biased if all inner products a i |b j have the same modulus 1/ √ N. This concept appears in several quantum information problems. The number of pairwise mutually unbiased bases is at most N + 1 and various constructions of N + 1 such bases have been found when N is a...

Compressive sensing investigates the recovery of a signal that can be sparsely represented in an orthonormal basis or overcomplete dictionary given a small number of linear combinations of the signal. We present a novel matching pursuit algorithm that uses the measurements to probabilistically select a subset of bases that is likely to contain the true bases constituting the signal. The algorit...

Abstract G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that...

This paper will look at the connection of operators and frames respectively related sequences from different viewpoints. We will give a survey of the classification of frames and similar sequences by the properties of the associated operators. Furthermore an important part will be the investigation of how to find a matrix representation of operators with Bessel sequences, frames and Riesz bases...