Signal De-noising method based on particle swarm algorithm and Wavelet transform

Wavelet analiza je novi alat za analizu odnosa vrijeme-frekvencija, razvijen na temelju Fourierove analize s dobrim svojstvom lokaliziranja vremena i frekvencije i mogućnosti donošenja višestrukih rješenja. Koristi se u cijelom nizu primjena u području obrade signala. U ovom se radu analizira primjena wavelet transforma u filtriranju signala korištenjem poboljšane optimalizacije roja čestica i predlaže inteligentna metoda uklanjanja šuma iz signala zasnovana na wavelet analizi. Metoda koristi Center Based Particle Swarm Algorithm (CBPSO) za izbor optimalnog praga za svaki pod-pojas u različitim mjerilima, inteligentno razaznavajući vrstu šuma iz samog signala, što ne zahtijeva nikakvo prethodno poznavanje šuma. Poboljšani algoritam roja čestica koristi se da potakne optimalni izbor različitih mjerila praga wavelet domena, što je dovelo do uklanjanja šuma iz signala kod različitih tipova pozadinskog šuma, i povećane brzine wavelet transforma i wavelet konstrukcije te ima veću fleksibilnost. Eksperimentalni rezultati su pokazali da se CBPSO algoritmom može postići bolji učinak uklanjanja šuma.Wavelet analysis is a new time-frequency analysis tool developed on the basis of Fourier analysis with good time-frequency localization property and multi-resolution characteristics, which is in a wide range of applications in the field of signal processing. This paper studies the application of wavelet transform in signal filtering, by using an improved particle swarm optimization, proposes an intelligent signal de-noising method based on wavelet analysis. The method uses a Center Based Particle Swarm Algorithm (CBPSO) to select the optimal threshold for each sub-band in different scales, learning the type of noise from the signal itself intelligently, which does not require any prior knowledge of the noise. The improved particle swarm algorithm is used to enhance the optimal choice of the different scales of the wavelet domain threshold, which realized the signal De-noising under different types of noise background, and improved the speed of wavelet transform and wavelet construction, and has greater flexibility. The experimental results showed that CBPSO algorithm can get better De-noising effect

Wavelet transform-based de-noising for two-photon imaging of synaptic Ca2+ transients.

PublishedJournal ArticleResearch Support, Non-U.S. Gov'tThis is an open access article.Postsynaptic Ca(2+) transients triggered by neurotransmission at excitatory synapses are a key signaling step for the induction of synaptic plasticity and are typically recorded in tissue slices using two-photon fluorescence imaging with Ca(2+)-sensitive dyes. The signals generated are small with very low peak signal/noise ratios (pSNRs) that make detailed analysis problematic. Here, we implement a wavelet-based de-noising algorithm (PURE-LET) to enhance signal/noise ratio for Ca(2+) fluorescence transients evoked by single synaptic events under physiological conditions. Using simulated Ca(2+) transients with defined noise levels, we analyzed the ability of the PURE-LET algorithm to retrieve the underlying signal. Fitting single Ca(2+) transients with an exponential rise and decay model revealed a distortion of τ(rise) but improved accuracy and reliability of τ(decay) and peak amplitude after PURE-LET de-noising compared to raw signals. The PURE-LET de-noising algorithm also provided a ∼30-dB gain in pSNR compared to ∼16-dB pSNR gain after an optimized binomial filter. The higher pSNR provided by PURE-LET de-noising increased discrimination accuracy between successes and failures of synaptic transmission as measured by the occurrence of synaptic Ca(2+) transients by ∼20% relative to an optimized binomial filter. Furthermore, in comparison to binomial filter, no optimization of PURE-LET de-noising was required for reducing arbitrary bias. In conclusion, the de-noising of fluorescent Ca(2+) transients using PURE-LET enhances detection and characterization of Ca(2+) responses at central excitatory synapses.C.M.T. and J.R.M. were supported by the Wellcome Trust, and K.T.-A. was supported by grant No. EP/I018638/1 from the Engineering and Physical Sciences Research Council

Extracting fetal heart beats from maternal abdominal recordings: Selection of the optimal principal components

This study presents a systematic comparison of different approaches to the automated selection of the principal components (PC) which optimise the detection of maternal and fetal heart beats from non-invasive maternal abdominal recordings. A public database of 75 4-channel non-invasive maternal abdominal recordings was used for training the algorithm. Four methods were developed and assessed to determine the optimal PC: (1) power spectral distribution, (2) root mean square, (3) sample entropy, and (4) QRS template. The sensitivity of the performance of the algorithm to large-amplitude noise removal (by wavelet de-noising) and maternal beat cancellation methods were also assessed. The accuracy of maternal and fetal beat detection was assessed against reference annotations and quantified using the detection accuracy score F1 [2*PPV*Se / (PPV + Se)], sensitivity (Se), and positive predictive value (PPV). The best performing implementation was assessed on a test dataset of 100 recordings and the agreement between the computed and the reference fetal heart rate (fHR) and fetal RR (fRR) time series quantified. The best performance for detecting maternal beats (F1 99.3%, Se 99.0%, PPV 99.7%) was obtained when using the QRS template method to select the optimal maternal PC and applying wavelet de-noising. The best performance for detecting fetal beats (F1 89.8%, Se 89.3%, PPV 90.5%) was obtained when the optimal fetal PC was selected using the sample entropy method and utilising a fixed-length time window for the cancellation of the maternal beats. The performance on the test dataset was 142.7 beats2/min2 for fHR and 19.9 ms for fRR, ranking respectively 14 and 17 (out of 29) when compared to the other algorithms presented at the Physionet Challenge 2013

Bayesian wavelet de-noising with the caravan prior

According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising approach that takes into account such a feature of the signal may in practice outperform other, more vanilla methods, both in terms of the estimation error and visual appearance of the estimates. Motivated by this observation, we present a Bayesian approach to wavelet de-noising, where dependencies between neighbouring wavelet coefficients are a priori modelled via a Markov chain-based prior, that we term the caravan prior. Posterior computations in our method are performed via the Gibbs sampler. Using representative synthetic and real data examples, we conduct a detailed comparison of our approach with a benchmark empirical Bayes de-noising method (due to Johnstone and Silverman). We show that the caravan prior fares well and is therefore a useful addition to the wavelet de-noising toolbox.Comment: 32 pages, 15 figures, 4 table

N-body simulations with two-orders-of-magnitude higher performance using wavelets

Noise is a problem of major concern for N-body simulations of structure formation in the early Universe, of galaxies and plasmas. Here for the first time we use wavelets to remove noise from N-body simulations of disc galaxies, and show that they become equivalent to simulations with two orders of magnitude more particles. We expect a comparable improvement in performance for cosmological and plasma simulations. Our wavelet code will be described in a following paper, and will then be available on request.Comment: Mon. Not. R. Astron. Soc., in press. The interested reader is strongly recommended to ignore the low-resolution Fig. 3 (and Fig. 4), and to download the full-resolution paper (700 kb) from http://www.oso.chalmers.se/~romeo/Paper_VI.ps.g