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Register a new userImage Analysis Using a Dual-Tree $M$-Band Wavelet Transform
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We propose a 2D generalization to the $M$-band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (textit{i}) the construction of the dual basis and (textit{ii}) the resulting directional analysis. We also revisit the necessary pre-processing stage in the $M$-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed $M$-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various $M$-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.
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Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will first be shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform by the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axis. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized, this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a non parametric bootstrap based procedure is described, that provides confidence interval in addition to the estimates themselves and enables to construct an isotropy test procedure, that can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis is illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed.
Image-based jet analysis is built upon the jet image representation of jets that enables a direct connection between high energy physics and the fields of computer vision and deep learning. Through this connection, a wide array of new jet analysis techniques have emerged. In this text, we survey jet image based classification models, built primarily on the use of convolutional neural networks, examine the methods to understand what these models have learned and what is their sensitivity to uncertainties, and review the recent successes in moving these models from phenomenological studies to real world application on experiments at the LHC. Beyond jet classification, several other applications of jet image based techniques, including energy estimation, pileup noise reduction, data generation, and anomaly detection, are discussed.
Submission withdrawn because the authors erroneously submitted a revised version as a new submission, see nlin.CD/0002028.
The continuous wavelet transform may be enhanced by deconvolution with the wavelet response function. After correcting for the cone-of-influence, the power spectral density of the solar magnetic record as given by the derectified yearly sunspot number is calculated, revealing a spectrum of odd harmonics of the fundamental Hale cycle, and the integrated instant power is compared to a reconstruction of global temperature in a normalized scatter plot displaying a positive correlation after the turn of the twentieth century. Comparison of the spectrum with that obtained from the Central England Temperature record suggests that some features are shared while others are not, and the scatter plot again indicates a possible correlation.
A tetra of sets which elements are time series of interbeats has been obtained from the databank Physionet-MIT-BIH, corresponding to the following failures at the humans heart: Obstructive Sleep Apnea, Congestive Heart Failure, and Atrial Fibrillation. Those times series has been analyzed statistically using an already known technique based on the Wavelet and Hilbert Transforms. That technique has been applied to the time series of interbeats for 87 patients, in order to find out the dynamics of the heart. The size of the times series varies around 7 to 24 h. while the kind of wavelet selected for this study has been any one of: Daubechies, Biortoghonal, and Gaussian. The analysis has been done for the complet set of scales ranging from: 1-128 heartbeats. Choosing the Biorthogonal wavelet: bior3.1, it is observed: (a) That the time series hasnt to be cutted in shorter periods, with the purpose to obtain the collapsing of the data, (b) An analytical, universal behavior of the data, for the first and second diseases, but not for the third.
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