In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Abstract Proteomics aims at determining the structure, function and expression of… (More)
Constructions of wavelets and prewavelets over triangulations with an emphasis of the continuous piecewise polynomial setting are discussed. Some recent results on piecewise linear prewavelets and orthogonal wavelets are presented.
A method for compressing surfaces associated with C 1 cubic splines defined on triangulated quadr-angulations is described. The method makes use of hierarchical bases, and does not require the construction of wavelets.
MOTIVATION Mass spectrometry (MS) can generate high-throughput protein profiles for biomedical research to discover biologically related protein patterns/biomarkers. The noisy functional MS data collected by current technologies, however, require consistent, sensitive and robust data-processing techniques for successful biomedical application. Therefore, it… (More)
Scattered data collected at sample points may be used to determine simple functions to best fit the data. An ideal choice for these simple functions is bivariate splines. Triangulation of the sample points creates partitions over which the bivariate splines may be defined. But the optimality of the approximation is dependent on the choice of triangulation.… (More)
We consider solutions of a system of refinement equations with a 4 × 1 function vector and three nonzero 4 × 4 coefficient matrices. We give explicit expressions of coefficient matrices such that the refinement function vector and the corresponding wavelet vector have properties of short support [0, 2], symmetry or antisymmetry, and orthogonality. The… (More)
Proteomics is the study of and the search for information about proteins. The development of mass spectrometry (MS) such as matrix-assisted laser desorption ionization (MALDI) time-of-flight (TOF) MS and imaging mass spectrometry (IMS), greatly speeds up proteomics studies. At the same time, the MS and IMS applications in medical science give rise to many… (More)
This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar sim-plex is introduced, new formulations of smoothness conditions of… (More)
Over the past decade, hyperspectral imaging has quickly grown into a powerful and versatile technology. It generates images of narrow spectral bands over a continuous spectral range, and produces the spectra of all the pixels in the scene. Using hyperspectral imaging data allows for the comparison of spectral similarity and the extraction of sub-pixel scale… (More)