Single-trial multiwavelet coherence in application to neurophysiological time series

A method of single-trial coherence analysis is presented, through the application of continuous muldwavelets. Multiwavelets allow the construction of spectra and bivariate statistics such as coherence within single trials. Spectral estimates are made consistent through optimal time-frequency localization and smoothing. The use of multiwavelets is considered along with an alternative single-trial method prevalent in the literature, with the focus being on statistical, interpretive and computational aspects. The multiwavelet approach is shown to possess many desirable properties, including optimal conditioning, statistical descriptions and computational efficiency. The methods. are then applied to bivariate surrogate and neurophysiological data for calibration and comparative study. Neurophysiological data were recorded intracellularly from two spinal motoneurones innervating the posterior,biceps muscle during fictive locomotion in the decerebrated cat

Wavelet pooling for convolutional neural networks

Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Petia Radeva,[en] Wavelets are mathematical functions that are currently used in many computer vision problems, such as image denoising or image compression. In this work, first we will study all the basic theory about wavelets, in order to understand them and build a basic knowledge that allows us to develop another application. For such purpose, we propose two pooling methods based on wavelets: one based on simple wavelet basis and one that combines two basis working in parallel. We will test them and show that they can be used at the same level of performance as max and average pooling

Wavelet Neural Networks: A Practical Guide

Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications

Image Steganography by Using Multiwavelet Transform

Steganography is the art of secret communication. Its purpose is to hide the presence of information, using, for example, images as covers. The frequency domain is well suited for embedding in image, since hiding in this frequency domain coefficients is robust to many attacks. This paper proposed hiding a secret image of size equal to quarter of the cover one. Set Partitioning in Hierarchal Trees (SPIHT) codec is used to code the secret image to achieve security. The proposed method applies Discrete Multiwavelet Transform (DMWT) for cover image. The coded bit stream of the secret image is embedded in the high frequency subbands of the transformed cover one. A scaling factors ? and ? in frequency domain control the quality of the stego images. The proposed algorithm is compared with wavelet based algorithm which shows a favorable results in terms of PSNR reaches to 18 dB