The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator-theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet-type frames and wavelet-type bases, obtained by acting ...

In this paper, we propose a 3D geometry compression technique for densely sampled surface meshes. Based on a 3D multiresolution analysis (performed by a 3D Discrete Wavelet Transform for semi-regular meshes), this scheme includes a model-based bit allocation process across the wavelet subbands and an efficient surface adapted weighted criterion for 3D wavelet coefficient coordinates. This permi...

Recently, several extensions of classical Shannon sampling theory to wavelet subspaces have been reported. This paper is devoted to uniform and periodic nonuniform oversampling in wavelet subspaces. Specifically, we provide a stability analysis and we introduce a technique for calculating the condition number of wavelet subspace sampling operators. It is shown that oversampling results in impro...

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding constant for the algorithm, which depends on the shape parameter of the generalized Gaussian distribution. We also quantify the optimal number of steps which h...

In audio applications it is often necessary to process the signal in “real time”. The method of segmented wavelet transform (SegWT) makes it possible to compute the discrete-time wavelet transform of a signal segment-by-segment, not using the classical “windowing”. This means that the method could be utilized for wavelettype processing of an audio signal in real time, or alternatively in case w...

This work compares a few attempts based on Wavelet and Neural networks, for extracting the Jominy hardness pro les of steels directly from the chemical composition. That is essentially a black-box modeling problem: Wavelet and Neural networks seem powerful, especially when compared with classical methods commonly found in literature. In particular, the paper proposes a multi-network architectur...

We present two strategies for detecting patterns and clusters in high-dimensional timedependent functional data. The use on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster ...

In this paper we study a generalization of the Donoho-Johnstone denoising model for the case of the translation invariant wavelet transform. Instead of soft-thresholding coeecients of the classical orthogonal discrete wavelet transform, we study soft-thresholding of the co-eecients of the translation invariant discrete wavelet transform. This latter transform is not an orthogonal transformation...

This talk concerns about mathematical mechanism for transmission error concealment. The previous methods involve concealing the transmission error for DCT (Discrete Cosine Transform) based compression line (e.g. MPEG and JEPG adopted by ISO/IEC). In this talk, we consider the mechanism to recover the transmission error of DWT(Discrete Wavelet Transform) based compression process. Also operation...

An analytic wavelet transform, based on Hilbert wavelet pairs, is applied to bivariate time-varying spectral estimation for neurophysiological time series. Under the assumption of an underlying block stationary process, both single-trial and ensemble studies are amenable to this method. A bootstrap procedure, which samples with replacement blocks centered around the events of interest, is propo...