Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

Implementación didáctica de algunos criptosistemas en Maxima

Implementar funciones criptográficas básicas que permitan a los estudiantes experimentar con algunos criptosistemas. Las implementaciones se realizan con el calculador simbólico Maxima.

Multiresolution-based image fusion with additive wavelet decomposition

The standard data fusion methods may not be satisfactory to merge a high-resolution panchromatic image and a low-resolution multispectral image because they can distort the spectral characteristics of the multispectral data. The authors developed a technique, based on multiresolution wavelet decomposition, for the merging and data fusion of such images. The method presented consists of adding the wavelet coefficients of the high-resolution image to the multispectral (low-resolution) data. They have studied several possibilities concluding that the method which produces the best results consists in adding the high order coefficients of the wavelet transform of the panchromatic image to the intensity component (defined as L=(R+G+B)/3) of the multispectral image. The method is, thus, an improvement on standard intensity-hue-saturation (IHS or LHS) mergers. They used the ¿a trous¿ algorithm which allows the use of a dyadic wavelet to merge nondyadic data in a simple and efficient scheme. They used the method to merge SPOT and LANDSATTM images. The technique presented is clearly better than the IHS and LHS mergers in preserving both spectral and spatial information.

A wavelet-based method for the determination of the relative resolution between remotely sensed images

Spatial resolution is a key parameter of all remote sensing satellites and platforms. The nominal spatial resolution of satellites is a well-known characteristic because it is directly related to the area in ground that represents a pixel in the detector. Nevertheless, in practice, the actual resolution of a specific image obtained from a satellite is difficult to know precisely because it depends on many other factors such as atmospheric conditions. However, if one has two or more images of the same region, it is possible to compare their relative resolutions. In this paper, a wavelet-decomposition-based method for the determination of the relative resolution between two remotely sensed images of the same area is proposed. The method can be applied to panchromatic, multispectral, and mixed (one panchromatic and one multispectral) images. As an example, the method was applied to compute the relative resolution between SPOT-3, Landsat-5, and Landsat-7 panchromatic and multispectral images taken under similar as well as under very different conditions. On the other hand, if the true absolute resolution of one of the images of the pair is known, the resolution of the other can be computed. Thus, in the last part of this paper, a spatial calibrator that is designed and constructed to help compute the absolute resolution of a single remotely sensed image is described, and an example of its use is presented.

Introduction of sensor spectral response into image fusion methods. Application to wavelet-based methods

Usual image fusion methods inject features from a high spatial resolution panchromatic sensor into every low spatial resolution multispectral band trying to preserve spectral signatures and improve spatial resolution to that of the panchromatic sensor. The objective is to obtain the image that would be observed by a sensor with the same spectral response (i.e., spectral sensitivity and quantum efficiency) as the multispectral sensors and the spatial resolution of the panchromatic sensor. But in these methods, features from electromagnetic spectrum regions not covered by multispectral sensors are injected into them, and physical spectral responses of the sensors are not considered during this process. This produces some undesirable effects, such as resolution overinjection images and slightly modified spectral signatures in some features. The authors present a technique which takes into account the physical electromagnetic spectrum responses of sensors during the fusion process, which produces images closer to the image obtained by the ideal sensor than those obtained by usual wavelet-based image fusion methods. This technique is used to define a new wavelet-based image fusion method.

Multifractal wavelet filter of natural images

Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this Letter we show that those properties uniquely define an intrinsic wavelet and present a suitable technique to obtain it from an ensemble of images. Once this wavelet is known, images can be represented as expansions in the associated wavelet basis. The resulting code has the remarkable properties that it separates independent features at different resolution level, reducing the redundancy, and remains essentially unchanged under changes in the power spectrum. The possible generalization of this representation to other systems is discussed.

EEG windowed statistical wavelet scoring for evaluation and discrimination of muscular artifacts

EEG recordings are usually corrupted by spurious extra-cerebral artifacts, which should be rejected or cleaned up by the practitioner. Since manual screening of human EEGs is inherently error prone and might induce experimental bias, automatic artifact detection is an issue of importance. Automatic artifact detection is the best guarantee for objective and clean results. We present a new approach, based on the time–frequency shape of muscular artifacts, to achieve reliable and automatic scoring. The impact of muscular activity on the signal can be evaluated using this methodology by placing emphasis on the analysis of EEG activity. The method is used to discriminate evoked potentials from several types of recorded muscular artifacts—with a sensitivity of 98.8% and a specificity of 92.2%. Automatic cleaning ofEEGdata are then successfully realized using this method, combined with independent component analysis. The outcome of the automatic cleaning is then compared with the Slepian multitaper spectrum based technique introduced by Delorme et al (2007 Neuroimage 34 1443–9).

High capacity audio watermarking using the high frequency band of the wavelet domain

This paper proposes a novel high capacity robust audio watermarking algorithm by using the high frequency band of the wavelet decomposition at which the human auditory system (HAS) is not very sensitive to alteration. The main idea is to divide the high frequency band into frames and, for embedding, to change the wavelet samples depending on the average of relevant frame¿s samples. The experimental results show that the method has a very high capacity (about 11,000 bps), without significant perceptual distortion (ODG in [¿1 ,0] and SNR about 30dB), and provides robustness against common audio signal processing such as additive noise, filtering, echo and MPEG compression (MP3).

SAR Interferometric phase noise reduction using wavelet transform

The problem of synthetic aperture radar interferometric phase noise reduction is addressed. A new technique based on discrete wavelet transforms is presented. This technique guarantees high resolution phase estimation without using phase image segmentation. Areas containing only noise are hardly processed. Tests with synthetic and real interferograms are reported.

The continuous wavelet transform as a maximum entropy solution of the corresponding inverse problem

The continuous wavelet transform is obtained as a maximumentropy solution of the corresponding inverse problem. It is well knownthat although a signal can be reconstructed from its wavelet transform,the expansion is not unique due to the redundancy of continuous wavelets.Hence, the inverse problem has no unique solution. If we want to recognizeone solution as "optimal", then an appropriate decision criterion hasto be adopted. We show here that the continuous wavelet transform is an"optimal" solution in a maximum entropy sense.

On wideband deconvolution using wavelet transform

A discussion on the expression proposed in [1]–[3]for deconvolving the wideband density function is presented. Weprove here that such an expression reduces to be proportionalto the wideband correlation receiver output, or continuous wavelettransform of the received signal with respect to the transmittedone. Moreover, we show that the same result has been implicitlyassumed in [1], when the deconvolution equation is derived. Westress the fact that the analyzed approach is just the orthogonalprojection of the density function onto the image of the wavelettransform with respect to the transmitted signal. Consequently,the approach can be considered a good representation of thedensity function only under the prior knowledge that the densityfunction belongs to such a subspace. The choice of the transmittedsignal is thus crucial to this approach.

EEG Windowed statitical wavelet deviation for estimation of muscular artifacts

Electroencephalographic (EEG) recordings are, most of the times, corrupted by spurious artifacts, which should be rejected or cleaned by the practitioner. As human scalp EEG screening is error-prone, automatic artifact detection is an issue of capital importance, to ensure objective and reliable results. In this paper we propose a new approach for discrimination of muscular activity in the human scalp quantitative EEG (QEEG), based on the time-frequency shape analysis. The impact of the muscular activity on the EEG can be evaluated from this methodology. We present an application of this scoring as a preprocessing step for EEG signal analysis, in order to evaluate the amount of muscular activity for two set of EEG recordings for dementia patients with early stage of Alzheimer’s disease and control age-matched subjects.

Image registration techniques with multiresolution analysis in satellite oceanography

En aquest article es fa una descripció dels procediments realitzats per enregistrar dues imatges geomètricament, de forma automàtica, si es pren la primera com a imatge de referència. Es comparen els resultats obtinguts mitjançant tres mètodes. El primer mètode és el d’enregistrament clàssic en domini espacial maximitzant la correlació creuada (MCC)[1]. El segon mètode es basa en aplicar l’enregistrament MCC conjuntament amb un anàlisi multiescala a partir de transformades wavelet [2]. El tercer mètode és una variant de l’anterior que es situa a mig camí dels dos. Per cada un dels mètodes s’obté una estimació dels coeficients de la transformació que relaciona les dues imatges. A continuació es transforma per cada cas la segona imatge i es georeferencia respecte la primera. I per acabar es proposen unes mesures quantitatives que permeten discutir i comparar els resultats obtinguts amb cada mètode.

BOI 2.0: disseny d'una implementació de JPEG 2000

JPEG 2000 és un estàndard de compressió d'imatges que utilitza tècniques estat de l’art basades en la transformada wavelet. Els principals avantatges són la millor compressió, la possibilitat d’operar amb dades comprimides i que es pot comprimir amb i sense pèrdua amb el mateix mètode. BOI és la implementació de JPEG 2000 del Grup de Compressió Interactiva d’Imatges del departament d’Enginyeria de la Informació i les Comunicacions, pensada per entendre, criticar i millorar les tecnologies de JPEG 2000. La nova versió intenta arribar a tots els extrems de l’estàndard on la versió anterior no va arribar.