We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1, · · · , ψn with n > 3 such that {2ψj(2x − `, 2ky − m), k, `,m ∈ Z, j = 1, . . . , n} ...

We describe extensions to the \best-basis" method to select orthonormal bases suitable for signal classiica-tion and regression problems from a large collection of orthonormal bases. For classiication problems, we select the basis which maximizes relative entropy of time-frequency energy distributions among classes. For regression problems, we select the basis which tries to minimize the regres...

The mathematical and numerical least squares solution of a general linear system of equations is discussed. Perturbation and differentiability theorems for pseudoinverses are given. Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential proc...

In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and show that it is only true in a subset of all possible orthonormal bases, but that this subset is the natural one to use for physical calculations.

This paper explores the segmentation of tutorial dialogue into cohesive topics. A latent semantic space was created using conversations from human to human tutoring transcripts, allowing cohesion between utterances to be measured using vector similarity. Previous cohesionbased segmentation methods that focus on expository monologue are reapplied to these dialogues to create benchmarks for perfo...

Abstract. In order to get an efficient representation of images which contain orientated edges we construct a directional wavelet basis for L(R). The wavelets basis consists of Haar wavelets with compact support on triangles. In comparison with the classical wavelet transform our functions offer two more directions (diagonal directions). Applying our simple wavelet system to image denoising and...

Paley and Wiener have formulated a criterion for a set of functions {gn} to be "near" a given orthonormal set {/w}. The interest of this criterion is that it guarantees the set {gn} to have expansion properties similar to an orthonormal set. In particular, they show that the set \gn) approximately satisfies Parseval's formula. In the first part of this paper we show that, conversely, if a set {...

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding and quantum teleportation. We describe how to generate fully entangled states in the Hilbert space C N C N starting from a unitary matrix and show that they form an orthonormal basis in this space. Disentanglement is also discussed. Moreover we also calculate the Wi...

There has recently been interest in the use of orthonor-mal bases for the purposes of SISO system identiication. Concurrently, but separately, there has also been vigorous work on estimation of MIMO systems by computa-tionally cheap and reliable schemes. These latter ideas have collectively become known as`4SID' methods. This paper is a contribution overlapping these two schools of thought by s...

The c l a s s i f i c a t i o n o f a s e t o f p a t t e r n s i s a p rob lem t h a t appears i n v e r y many f i e l d s . I n g e n e r a l , the number o f p o s s i b l e c l asses i s unknown. To d e f i n e a d i s t a n c e ( o r s i m i l a r i t y ) m a t r i x on the s e t o f p a t t e r n s , we must summarize the a v a i l a b l e da te i n the fo rm o f a f i n i t e s e t o f ...