Representations. For the purposes of this paper a representation of G over C is a matrix-valued function ρ : G → Cdρ×dρ such that ρ(x)ρ(y) = ρ(xy) for any x, y ∈ G. We call dρ the order or the dimensionality of ρ. Note that ρ(e) = I for any representation. Two representations ρ1 and ρ2 of the same dimensionality d are said to be equivalent if for some invertible T ∈ Cd×d, ρ1(x) = Tρ2(x)T for an...

A study is presented for the use of multiresolution analysis-based onset detection in the complex domain. It shows that using variable time-resolution across frequency bands generates sharper detection functions for higher bands and more accurate detection functions for lower bands. The resulting method improves the localisation of onsets on fixed-resolution schemes, by favouring the increased ...

The rise of frame theory in appled mathematics is due to the flexibility and redundancy of frames. Structured frames are much easier to construct than Structured orthonormal bases. In this work, the notion of the ternary generalized multiresolution structure (TGMS) of subspace 2 3 ( ) L R is proposed, which is the generalization of the ternary frame multiresolution analysis. The biorthogonality...

The paper is concerned with the introduction and study of multiresolution analysis based on the up function, which is an infinitely differentiable function supported on [0, 2]. Such analysis is, necessarily, nonstationary. It is shown that the approximation orders associated with the corresponding spaces are spectral, thus making the spaces attractive for the approximation of very smooth functi...

Transmission of large terrain databases across the Internet is still worrying. A large terrain database requires a big number of polygons and textures, and that represents a problem with current bandwidth and resource limitations. Multiresolution models permit progressive transmission, that is the transmission of a simple model followed by successive refinements. In this work we present a new m...

In this paper, we outline a method for constructing nonnegative scaling vectors on the interval. Scaling vectors for the interval have been constructed in [1–3]. The approach here is different in that the we start with an existing scaling vector Φ that generates a multi-resolution analysis for L(R) to create a scaling vector for the interval. If desired, the scaling vector can be constructed so...

Many multiresolution methods have been proposed. Most of them emphasize accuracy and hence are slow. Some methods may be fast, but they may not preserve the geometry of the model. Although there are a few real-time multiresolution methods available, they are developed mainly for handling large terrain models. In this paper, we present a very efficient multiresolution method for continuously red...

T h i s paper presen t s a n e w computat ional s cheme based o n mult iresolut ion decomposition for extracting t h e features of interest f r o m t h e oceanographic images by suppressing t h e noise. T h e multiresolution analysis f r o m t h e m e d i a n presented by Starck-Murtagh-Bijaoui [4][5] is used for t h e noise suppression. A parallel approach is presented f o r this computat iona...

In this paper, we introduce two new methods for face recognition of frontal images. The methods combine the well known Karhunen-Loeve transform with morphological and subband analysis. The use of this kind of analysis contributes to better discrimination between different images. Morphological and subband approaches are compared while the former is a non linear method and the latter a linear on...