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.

Analysis of an iterative deconvolution approach for estimating the source wavelet during waveform inversion of crosshole ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole georadar data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a time-domain waveform inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little-to-no trade-off between the wavelet estimation and the tomographic imaging procedures.

Source-wavelet estimation during full-waveform inversion of ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole ground-penetrating radar (GPR) data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a recently published time-domain inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity of both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little to no trade-off between the wavelet estimation and the tomographic imaging procedures.

Applications of Fourier transform infrared spectroscopy

This article summarizes the basic principles of Fourier Transform Infrared Spectroscopy, with examples of methodologies and applications to different field sciences.

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).

Fourier transform convolution integrals applied to generalized Born molecular volume.

Generalized Born methods are currently among the solvation models most commonly used for biological applications. We reformulate the generalized Born molecular volume method initially described by (Lee et al, 2003, J Phys Chem, 116, 10606; Lee et al, 2003, J Comp Chem, 24, 1348) using fast Fourier transform convolution integrals. Changes in the initial method are discussed and analyzed. Finally, the method is extensively checked with snapshots from common molecular modeling applications: binding free energy computations and docking. Biologically relevant test systems are chosen, including 855-36091 atoms. It is clearly demonstrated that, precision-wise, the proposed method performs as good as the original, and could better benefit from hardware accelerated boards.

Resolução espacial de um modelo digital de elevação definida pela função wavelet

O objetivo deste trabalho foi definir a resolução espacial mais apropriada para representar a variabilidade da elevação, declividade, curvatura em perfil e índice de umidade topográfica de um terreno, por meio de avaliações com a transformada wavelet. Os dados utilizados no estudo têm sua origem em três transectos de 27 km, posicionados em áreas do Planalto, Rebordo do Planalto e Depressão Central na região central do Estado do Rio Grande do Sul. As variáveis - elevação, declividade, curvatura em perfil e índice de umidade topográfica - foram derivadas de um modelo digital de elevação Topodata com resolução de 30 m. A avaliação da resolução com a máxima variabilidade foi realizada pela aplicação da wavelet-mãe, denominada Morlet. Os resultados foram analisados a partir do isograma e do escalograma dos coeficientes wavelet e indicaram que sensores remotos com resolução espacial próxima a 32 e 40 m podem ser utilizados em pesquisas que considerem os atributos de terreno, como declividade, curvatura em perfil e índice de umidade topográfica, ou, ainda, fenômenos ambientais correlacionados a eles. No entanto, não foi possível estabelecer um valor conclusivo para a resolução espacial mais adequada para a variável elevação.

On the inverse windowed Fourier transform

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion.

Lossless compression of hyperspectral images

Technological progress has made a huge amount of data available at increasing spatial and spectral resolutions. Therefore, the compression of hyperspectral data is an area of active research. In somefields, the original quality of a hyperspectral image cannot be compromised andin these cases, lossless compression is mandatory. The main goal of this thesisis to provide improved methods for the lossless compression of hyperspectral images. Both prediction- and transform-based methods are studied. Two kinds of prediction based methods are being studied. In the first method the spectra of a hyperspectral image are first clustered and and an optimized linear predictor is calculated for each cluster. In the second prediction method linear prediction coefficients are not fixed but are recalculated for each pixel. A parallel implementation of the above-mentioned linear prediction method is also presented. Also,two transform-based methods are being presented. Vector Quantization (VQ) was used together with a new coding of the residual image. In addition we have developed a new back end for a compression method utilizing Principal Component Analysis (PCA) and Integer Wavelet Transform (IWT). The performance of the compressionmethods are compared to that of other compression methods. The results show that the proposed linear prediction methods outperform the previous methods. In addition, a novel fast exact nearest-neighbor search method is developed. The search method is used to speed up the Linde-Buzo-Gray (LBG) clustering method.

VariScan Software

VariScan is a software package for the analysis of DNA sequence polymorphisms at the whole genome scale. Among other features, the software:(1) can conduct many population genetic analyses; (2) incorporates a multiresolution wavelet transform-based method that allows capturing relevant information from DNA polymorphism data; and (3) it facilitates the visualization of the results in the most commonly used genome browsers.

Fingermark initial composition and aging using Fourier transform infrared microscopy (μ-FTIR)

This study investigated fingermark residues using Fourier transform infrared microscopy (μ- FTIR) in order to obtain fundamental information about the marks' initial composition and aging kinetics. This knowledge would be an asset for fundamental research on fingermarks, such as for dating purposes. Attenuated Total Reflection (ATR) and single-point reflection modes were tested on fresh fingermarks. ATR proved to be better suited and this mode was subsequently selected for further aging studies. Eccrine and sebaceous material was found in fresh and aged fingermarks and the spectral regions 1000-1850 cm-1 and 2700-3600 cm-1 were identified as the most informative. The impact of substrates (aluminium and glass slides) and storage conditions (storage in the light and in the dark) on fingermark aging was also studied. Chemometric analyses showed that fingermarks could be grouped according to their age regardless of the substrate when they were stored in an open box kept in an air-conditioned laboratory at around 20°C next to a window. On the contrary, when fingermarks were stored in the dark, only specimens deposited on the same substrate could be grouped by age. Thus, the substrate appeared to influence aging of fingermarks in the dark. Furthermore, PLS regression analyses were conducted in order to study the possibility of modelling fingermark aging for potential fingermark dating applications. The resulting models showed an overall precision of ±3 days and clearly demonstrated their capability to differentiate older fingermarks (20 and 34-days old) from newer ones (1, 3, 7 and 9-days old) regardless of the substrate and lighting conditions. These results are promising from a fingermark dating perspective. Further research is required to fully validate such models and assess their robustness and limitations in uncontrolled casework conditions.

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.

Prediction in transformed images

The study is related to lossless compression of greyscale images. The goal of the study was to combine two techniques of lossless image compression, i.e. Integer Wavelet Transform and Differential Pulse Code Modulation to attain better compression ratio. This is an experimental study, where we implemented Integer Wavelet Transform, Differential Pulse Code Modulation and an optimized predictor model using Genetic Algorithm. This study gives encouraging results for greyscale images. We achieved a better compression ration in term of entropy for experiments involving quadrant of transformed image and using optimized predictor coefficients from Genetic Algorithm. In an other set of experiments involving whole image, results are encouraging and opens up many areas for further research work like implementing Integer Wavelet Transform on multiple levels and finding optimized predictor at local levels.

Wavelets in real-time paper web analysis

Online paper web analysis relies on traversing scanners that criss-cross on top of a rapidly moving paper web. The sensors embedded in the scanners measure many important quality variables of paper, such as basis weight, caliper and porosity. Most of these quantities are varying a lot and the measurements are noisy at many different scales. The zigzagging nature of scanning makes it difficult to separate machine direction (MD) and cross direction (CD) variability from one another. For improving the 2D resolution of the quality variables above, the paper quality control team at the Department of Mathematics and Physics at LUT has implemented efficient Kalman filtering based methods that currently use 2D Fourier series. Fourier series are global and therefore resolve local spatial detail on the paper web rather poorly. The target of the current thesis is to study alternative wavelet based representations as candidates to replace the Fourier basis for a higher resolution spatial reconstruction of these quality variables. The accuracy of wavelet compressed 2D web fields will be compared with corresponding truncated Fourier series based fields.