This paper examines wavelet analyses for detecting and characterizing printing defects. Positive wavelet features for this application include localized space-frequency properties for characterizing defects of limited spatial support (in contrast with the Fourier analysis, which has no spatial localization over the analysis region). In addition, the scale based analyses of wavelets mimic proper...

This paper shows how to design good biorthogonal FIR filters for wavelet image compression by balancing the space and frequency dispersions of analysis and synthesis lowpass filters. A quality metric is proposed which can be computed directly from the filter coefficients. By optimizing over the space of FIR filter coefficients, a filter bank can be found which minimizes the metric in about 60 s...

We study regularity properties of solutions to operator equations on patchwise smooth manifolds ∂Ω such as, e.g., boundaries of polyhedral domains Ω ⊂ R3. Using suitable biorthogonal wavelet bases Ψ, we introduce a new class of Besov-type spaces Bα Ψ,q(Lp(∂Ω)) of functions u : ∂Ω → C. Special attention is paid on the rate of convergence for best n–term wavelet approximation to functions in thes...

A key ingredient of the construction of biorthogonal wavelet bases for Sobolev spaces on manifolds from [DS], which is based on topological isomorphisms [CF], is the Hestenes extension operator. Here we firstly investigate whether this particular extension operator can be replaced by another extension operator. Our main theoretical result states that an important class of extension operators ba...

In the first part of this paper we construct an algorithm for implementing the discrete wavelet transform by means of matrices in SO2(R) for orthonormal compactly supported wavelets and matrices in SLm(R),m ≥ 2, for compactly supported biorthogonal wavelets. We show that in 1 dimension the total operation count using this algorithm can be reduced to about 50% of the conventional convolution and...

IMAGE COMPRESSION Jan E. Odegard C. Sidney Burrus Department of Electrical and Computer Engineering Rice University, Houston, Texas 77005-1892, USA [email protected], [email protected] http: www-dsp.rice.edu ABSTRACT In this paper we introduce a new family of smooth, symmetric biorthogonal wavelet basis. The new wavelets are a generalization of the Cohen, Daubechies and Feauveau (CDF) biorthogonal wa...

We investigate the lifting scheme as a method for constructing compactly supported biorthogonal scaling functions and wavelets. A well-known issue arising with the use of this scheme is that the resulting functions are only formally biorthogonal. It is not guaranteed that the new wavelet bases actually exist in an acceptable sense. To verify that these bases do exist one must test an associated...

This paper deals with the application of the wavelet transform to hierarchical texture analysis. The main goal is the design of texture-matched FIR-filterbanks as the dyadic (2-channel) orthogonal and the M-channel biorthogonal wavelet filterbanks. The new approach represents a generalization of the already known purely mathematically-oriented design methods for multirate and wavelet filterbank...

We introduce a new locally adaptive wavelet transform, called Easy Path Wavelet Transform (EPWT), that works along pathways through the array of function values and exploits the local correlations of the data in a simple appropriate manner. The usual discrete orthogonal and biorthogonal wavelet transform can be formulated in this approach. The EPWT can be incorporated into a multiresolution ana...

The wavelet transform has been employed as an efficient method in image denoising via wavelet thresholding and shrinkage. The ridgelet transform was recently introduced as an alternative to the wavelet representation of two dimensional signals and image data. In this paper, a BayesShrink ridgelet denoising technique is proposed and its denoising performance is compared with a previous VisuShrin...