Generalized rotationally quasi-invariant cylindrical measures

Rotationally invariant similarity measures for nonlocal image denoising

Many natural or texture images contain structures that appear several times in the image. One of the denoising filters that successfully take advantage of such repetitive regions is the nonlocal means filter. It is simple and yields very good denoising results. Unfortunately, the block matching within the standard nonlocal means filter is not able to handle rotation or mirroring. Rotated or mir...

Admissible vector fields and quasi-invariant measures∗

Rotationally Invariant Wavelet Shrinkage

Most two-dimensional methods for wavelet shrinkage are efficient for edge-preserving image denoising, but they suffer from poor rotation invariance. We address this problem by designing novel shrinkage rules that are derived from rotationally invariant nonlinear diffusion filters. The resulting Haar wavelet shrinkage methods are computationally inexpensive and they offer substantially improved ...

Rotationally Invariant Multipartite States

We construct a class of multipartite states possessing rotational SO(3) symmetry – these are states of K spin-jA particles and K spin-jB particles. The construction of symmetric states follows our two recent papers devoted to unitary and orthogonal multipartite symmetry. We study basic properties of multipartite SO(3) symmetric states: separability criteria and multi-PPT conditions.

Invariant Measures for Generalized Gauss Transformations

We find the explicit expression of the absolutely continuous invariant measure for the p-numerated generalized Gauss transformation Tp(x) = { p x }. It allows us to generalize a series of results for the canonical continued fractions, such as Khinchin’s constant and Lévy’s constant. 1. The Invariant Measure The Gauss transformation T (x) = { 1 x } has been well studied. It has a strong relation...