Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow for the recovery of topological information. We present an easy to implement, computationally efficient pre-processing algorithm to prepare noisy point cloud ...

A few different approaches exist for computing undecimated wavelet transform. In this work we construct three undecimated schemes and evaluate their performance for image noise reduction. We use standard wavelet based de-noising techniques and compare the performance of our algorithms with the original undecimated wavelet transform, as well as with the decimated wavelet transform. The experimen...

This paper describes an approach for accomplishing sub-octave wavelet analysis and its discrete implementation for noise reduction and feature enhancement. Sub-octave wavelet transforms allow us to more closely characterize features within distinct frequency bands. By dividing each octave into sub-octave components, we demonstrate a superior ability to capture transient activities in a signal o...

Shallow depth geophysical data from archaeological sites contain various levels and types of noise that hinters the valuable information of the subsurface architectural relics. Wavelet transform techniques were tested as a method for decomposition of the original geophysical data in order to eliminate the noise levels inherent to the geophysical measurements. In addition to the above, unsupervi...

Electrocardiogram (ECG) is a non-invasive tool that monitors the electrical activity of the heart. An ECG signal is highly prone to the disturbances such as noise contamination, artifacts and other signals interference. So, an ECG signal has to be de-noised so that the distortions can be eliminated from the original signal for the perfect diagnosing of the condition and performance of the heart...

Recently, kernel Principal Component Analysis is becoming a popular technique for feature extraction. It enables us to extract nonlinear features and therefore performs as a powerful preprocessing step for classification. There is one drawback, however, that extracted feature components are sensitive to outliers contained in data. This is a characteristic common to all PCA-based techniques. In ...

Wavelet Shrinkage de-noi si ng i s appl i ed to El ect rophoret i c Nucl ear Magnet i c Resonance (ENMR) data. Both threshol d rul es for removi ng noi se, namel y sof t and hard, proposed i n Donoho's Vi suShri nk are used simul t aneousl y. Sof t t hreshol di ng i s appl i ed to ne l evel s of wavel et decomposi t i on coe ci ent s and hard threshol di ng to coarse l evel s. Thi s impl ementa...

Wavelets provide a powerful and remarkably flexible set of tools for handling fundamental problems in science and engineering, such as audio de-noising, signal compression, object detection and fingerprint compression, image de-noising, image enhancement, image recognition, diagnostic heart trouble and speech recognition, to name a few. Here, we are going to concentrate on wavelet application i...

Clinical MRI data is normally corrupted by random noise from the measurement process which reduces the accuracy and reliability of any automatic analysis. For this reason, de-noising methods are often applied to increase the SNR and improve image quality. Most of these methods work on single channel images by correcting each grey level using an implicit model of the surrounding region, but with...

A new de-noising and compression method for ECG signals has been developed based on the wavelet transform. It has been designed for mobile telecardiology scenarios, where reliability as well as spectral efficiency are essential. The signal is segmented into beats and a beat template is subtracted to them. Beat templates as well as residual signals are coded with a wavelet expansion. De-noising ...