1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

Introduction to Wavelets and Wavelet Transforms: A Primer

Introduction to linear and nonlinear programming

The article provides arguments in favor of an alternative approach that uses splines, which is equally justifiable on a theoretical basis, and which offers many practical advantages. To reassure the reader who may be afraid to enter new territory, it is emphasized that one is not losing anything because the traditional theory is retained as a particular case (i.e., a spline of infinite degree). The basic computational tools are also familiar to a signal processing audience (filters and recursive algorithms), even though their use in the present context is less conventional. The article also brings out the connection with the multiresolution theory of the wavelet transform. This article attempts to fulfil three goals. The first is to provide a tutorial on splines that is geared to a signal processing audience. The second is to gather all their important properties and provide an overview of the mathematical and computational tools available; i.e., a road map for the practitioner with references to the appropriate literature. The third goal is to give a review of the primary applications of splines in signal and image processing.

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Splines: a perfect fit for signal and image processing

HPVs (human papillomaviruses) infect epithelial cells and cause a variety of lesions ranging from common warts/verrucas to cervical neoplasia and cancer. Over 100 different HPV types have been identified so far, with a subset of these being classified as high risk. High-risk HPV DNA is found in almost all cervical cancers (>99.7%), with HPV16 being the most prevalent type in both low-grade disease and cervical neoplasia. Productive infection by high-risk HPV types is manifest as cervical flat warts or condyloma that shed infectious virions from their surface. Viral genomes are maintained as episomes in the basal layer, with viral gene expression being tightly controlled as the infected cells move towards the epithelial surface. The pattern of viral gene expression in low-grade cervical lesions resembles that seen in productive warts caused by other HPV types. High-grade neoplasia represents an abortive infection in which viral gene expression becomes deregulated, and the normal life cycle of the virus cannot be completed. Most cervical cancers arise within the cervical transformation zone at the squamous/columnar junction, and it has been suggested that this is a site where productive infection may be inefficiently supported. The high-risk E6 and E7 proteins drive cell proliferation through their association with PDZ domain proteins and Rb (retinoblastoma), and contribute to neoplastic progression, whereas E6-mediated p53 degradation prevents the normal repair of chance mutations in the cellular genome. Cancers usually arise in individuals who fail to resolve their infection and who retain oncogene expression for years or decades. In most individuals, immune regression eventually leads to clearance of the virus, or to its maintenance in a latent or asymptomatic state in the basal cells.

Molecular biology of human papillomavirus infection and cervical cancer.

We propose the concept of a generalized assorted pixel (GAP) camera, which enables the user to capture a single image of a scene and, after the fact, control the tradeoff between spatial resolution, dynamic range and spectral detail. The GAP camera uses a complex array (or mosaic) of color filters. A major problem with using such an array is that the captured image is severely under-sampled for at least some of the filter types. This leads to reconstructed images with strong aliasing. We make four contributions in this paper: 1) we present a comprehensive optimization method to arrive at the spatial and spectral layout of the color filter array of a GAP camera. 2) We develop a novel algorithm for reconstructing the under-sampled channels of the image while minimizing aliasing artifacts. 3) We demonstrate how the user can capture a single image and then control the tradeoff of spatial resolution to generate a variety of images, including monochrome, high dynamic range (HDR) monochrome, RGB, HDR RGB, and multispectral images. 4) Finally, the performance of our GAP camera has been verified using extensive simulations that use multispectral images of real world scenes. A large database of these multispectral images has been made available at http://wwwl.cs.columbia.edu/ CAVE/projects/gap_camera/ for use by the research community.

/pdf/generalized-assorted-pixel-camera-postcapture-control-of-4mrfe9pr06.pdf

Generalized Assorted Pixel Camera: Postcapture Control of Resolution, Dynamic Range, and Spectrum

Recent algorithms developed in the field of color vision make assumptions based on the spectral reflectance curves of Munsell chips and natural materials Some of them rely on data collected many years ago which is partially incomplete in the visible spectrum or contains many occurrences of the same material in it In this article we present a set of new measurements of different materials In particular we measured the spectral reflectance of Munsell chips, paints and various natural materials in the 390–730-nm range In addition, we have analyzed through principal-component analysis, the possibility of representing the data collected with a set of basis functions We show the implications of varying the number of principal components used (from 7 down to 3) on the errors introduced using this method

Measurement and Analysis of Object Reflectance Spectra

The three-dimensional structure of bovine papillomavirus has been determined to 9 A resolution by reconstruction of high resolution, low dose cryo-electron micrographs of quench-frozen virions. Although hexavalent and pentavalent capsomeres form star-shaped pentamers of the major capsid protein L1, they have distinct high-resolution structures. Most prominently, a 25 A hole in the centre of hexavalent capsomeres is occluded in the pentavalent capsomeres. This raises the possibility that the L2 minor capsid protein is located in the centre of the pentavalent capsomeres. Inter-capsomere connections approximately 10 A in diameter were clearly resolved. These link adjacent capsomeres and are reminiscent of the helical connections that stabilize polyomavirus.

Novel structural features of bovine papillomavirus capsid revealed by a three-dimensional reconstruction to 9 Å resolution

The problem of color correction for changes in illumination is briefly reviewed. A new method using the spectral reflectance distribution in the image is introduced and compared to a white-point mapping method. The new method is based on principal component analysis and thus is dependent upon the characteristics of the images that are to be viewed. These two methods are compared using chromaticity plots and the CIE L*a*b* ΔE measurement, for test samples which include color copiers, thermal writers, ink-jet printers, and lithography.

Color correction using principal components

The mathematical formulation of calibrating color image reproduction and recording devices is presented. This formulation provides a foundation for future research in areas of characterization of devices and display of color images. The importance of calibration is demonstrated by real examples. The procedure outlined in this paper should become standard for displaying color images for the image processing community.

https://www.eecis.udel.edu/~barner/courses/eleg675/papers/Color%20Image%20Processing/Color%20_Device_Calibration_A_Mathematical_Formulation.pdf

Color device calibration: a mathematical formulation

The quality of color correction is dependent on the filters used to scan the image. This paper introduces a method of selecting the color filters using a priori information about the viewing illuminants. Color correction results using the derived filters are compared with color correction results using filters that are optimal for individual viewing and recording illuminants. The comparison is performed using the CIE PEL/sub L*a*b*/ perceptual color difference measure. Applications of this work are found in the design of scanners, copiers, and television systems. >

Michael J. Vrhel

Papers

Measurement and Analysis of Object Reflectance Spectra

Novel structural features of bovine papillomavirus capsid revealed by a three-dimensional reconstruction to 9 Å resolution

Color correction using principal components

Color device calibration: a mathematical formulation

Filter considerations in color correction