Model based analysis or explicit definition/listing of all models or assumptions used in the derivation of an image fusion method allows us to understand the rationale or properties of existing methods and shows a way for a proper usage or proposal/selection of new methods ‘better’ satisfying the needs of a particular application. Most existing pan-sharpening methods are based mainly on the two...

The partial least squares (PLS) method computes a sequence of approximate solutions xk ∈ Kk(AA,A b), k = 1, 2, . . . , to the least squares problem minx ‖Ax− b‖2. If carried out to completion, the method always terminates with the pseudoinverse solution x† = A†b. Two direct PLS algorithms are analyzed. The first uses the Golub–Kahan Householder algorithm for reducing A to upper bidiagonal form....

Sets of orthogonal basis functions over circular areas – pupils in optical applications – are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. Here, an orthogonal set is proposed if the area is two non-overlapping circles of equal size. The geometric master parameter is the ratio of the pupil radii over the distance between both circles. Increasingly ...

We study the algebraic aspects of equivariant quantum cohomology algebra of the flag manifold. We introduce and study the quantum double Schubert polynomials S̃w(x, y), which are the Lascoux– Schützenberger type representatives of the equivariant quantum cohomology classes. Our approach is based on the quantum Cauchy identity. We define also quantum Schubert polynomials S̃w(x) as the Gram–Schmidt...

A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model n...

Lattice reduction is fundamental in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra–Lenstra–Lovász reduction algorithm (called LLL or L) has been improved in many ways through the past decades and remains one of the central tool for reducing lattice basis. In particular, its floating-point variants — where the long-integer arithmetic requi...

The Lenstra–Lenstra–Lovász lattice basis reduction algorithm (called LLL or L3) is a fundamental tool in computational number theory and theoretical computer science, which can be viewed as an efficient algorithmic version of Hermite’s inequality on Hermite’s constant. Given an integer d-dimensional lattice basis with vectors of Euclidean norm less than B in an ndimensional space, the L3 algori...

The Lenstra, Lenstra, and Lovász (abbreviated as LLL) basis reduction algorithm computes a basis of a lattice consisting of short, and near orthogonal vectors. The quality of an LLL reduced basis is expressed by three fundamental inequalities, and it is natural to ask, whether these have a common generalization. In this note we find unifying inequalities. Our main result is Theorem 1. Let b1, ....

Abstract—We present a general theory of entanglementassisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the CalderbankShor-Steane structure as in previous work. We provide two significant advances for quantum convolut...

—— This paper describes an evaluation of Inhibition/Enhancement (In/En) network for robust automatic speech recognition (ASR). In distinctive phonetic features (DPFs) based speech recognition using neural network, In/En network is needed to discriminate whether the DPFs dynamic patterns of trajectories are convex or concave. The network is used to achieve categorical DPFs movement by enhancing ...