The lifting step of a reversible color space transform employed during image compression may increase the total amount of noise that has to be encoded. Previously, to alleviate this problem in the case of a simple color space transform RDgDb, we replaced transform lifting steps with reversible denoising and lifting steps (RDLS), which are lifting steps integrated with denoising filters. In this...

It was recently demonstrated [J. Electron. Imaging, 25(2), 2016] that one can perform fast non-local means (NLM) denoising of one-dimensional signals using a method called lifting. The cost of lifting is independent of the patch length, which dramatically reduces the run-time for large patches. Unfortunately, it is difficult to directly extend lifting for non-local means denoising of images. To...

We have developed a new theory for correcting track irregularities by applying their restored waveforms and carried out experimental levelling and lining work. In this theory, the optimum shifting/lifting values are obtained as solutions for a typical quadratic programming problem. Restrictions on shifting rails are formulated as constraint conditions of the optimization problem. Furthermore, i...

0. Introduction. This note announces some new methods in algebraic topology, based on the results of [1], [2] and [3]. The relative lifting problem [5, p. 415] is fundamental to that subject. It includes the extension problem, the retraction problem, the lifting problem, the section problem, the relative section problem and the computation of [X, Y] problem, among its particular cases. These pr...

This paper is first in a series of papers studying a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. In this paper we present the paradigm and revise underlying technical...

Classical nondecimated wavelet transforms are attractive for many applications. When the data comes from complex or irregular designs, the use of second generation wavelets in nonparametric regression has proved superior to that of classical wavelets. However, the construction of a nondecimated second generation wavelet transform is not obvious. In this paper we propose a new ‘nondecimated’ lif...

Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem within Euclidean spaces of changing dimension. Recently, an alternative approach which first decomposes complex space using triangular decomposition before r...

Given two polynomials F and G in R[x1, . . . , xn], we are going to find the nontrivial approximate GCD C and polynomials F , G ∈ R[x1, . . . , xn] such that ||F − CF ′|| < and ||G − CG′|| < , for some and some well defined norm. Many papers 1,2,3,5,8,10,11,13,15 have already discussed the problem in the case n = 1. Few of them 2,10,11 mentioned the case n > 1. Approximate GCD computation of un...

The description of all solutions to the relaxed commutant lifting problem in terms of an underlying contraction, obtained earlier in joint work of the author with A.E. Frazho and M.A. Kaashoek, is transformed into a linear fractional Redheffer state space form. Under certain additional conditions the coefficient functions in this representation are described explicitly in terms of the original ...

A new discretization based solution to the sampled-data H 1 control problem is given. In contrast to previous solution procedures, the method is not based on the lifting technique. Instead, an equivalent nite-dimensional discrete problem representation is derived directly from a description of the sampled-data system. This is achieved via a closed-loop expression of the worst-case intersample d...