Elementary Waveforms Research Articles

Geometrical X-lets for Image Denoising.

There has been a lot of researches allocated to image denoising in recent years. One of the appropriate approaches for image denoising is applying nonlinear thresholding techniques in time-frequency transform domains. These transforms decompose an image to a series of elementary waveforms called basis functions or dictionary atoms. Different directional time-frequency dictionaries provide various geometrical X-let transforms in two or higher dimensions. In this paper, we have a comparative study of geometrical X-let transforms including 2D-Discrete Wavelet (2D-DWT), Dual-Tree Complex Wavelet (DT-CWT), Curvelet, Contourlet, Steerable Pyramid (STP) and Circlet Transform (CT) in application of image denoising. Experimental results show that in synthetic images of Optical Coherence Tomography (OCT), the Steerable Pyramid outperforms other geometrical X-lets in terms of Peak Signal-to-Noise Ratio (PSNR), while DT-CWT is superior in terms of Structural Similarity Index (SSIM). Moreover, in real images of OCT which consist of retinal layers, Curvelet Transform has better results in terms of Contrast-to-Noise Ratio (CNR) and 2D-DWT is better in Edge Preservation (EP) and Texture Preservation (TP) which indicate various X-lets can be effective due to different criteria and different images.

Design and evaluation of a parametric model for cardiac sounds

Heart sound analysis plays an important role in the auscultative diagnosis process to detect the presence of cardiovascular diseases. In this paper we propose a novel parametric heart sound model that accurately represents normal and pathological cardiac audio signals, also known as phonocardiograms (PCG). The proposed model considers that the PCG signal is formed by the sum of two parts: one of them is deterministic and the other one is stochastic. The first part contains most of the acoustic energy. This part is modeled by the Matching Pursuit (MP) algorithm, which performs an analysis-synthesis procedure to represent the PCG signal as a linear combination of elementary waveforms. The second part, also called residual, is obtained after subtracting the deterministic signal from the original heart sound recording and can be accurately represented as an autoregressive process using the Linear Predictive Coding (LPC) technique. We evaluate the proposed heart sound model by performing subjective and objective tests using signals corresponding to different pathological cardiac sounds. The results of the objective evaluation show an average Percentage of Root-Mean-Square Difference of approximately 5% between the original heart sound and the reconstructed signal. For the subjective test we conducted a formal methodology for perceptual evaluation of audio quality with the assistance of medical experts. Statistical results of the subjective evaluation show that our model provides a highly accurate approximation of real heart sound signals. We are not aware of any previous heart sound model rigorously evaluated as our proposal.

Three dimensional data-driven multi scale atomic representation of optical coherence tomography.

In this paper, we discuss about applications of different methods for decomposing a signal over elementary waveforms chosen in a family called a dictionary (atomic representations) in optical coherence tomography (OCT). If the representation is learned from the data, a nonparametric dictionary is defined with three fundamental properties of being data-driven, applicability on 3D, and working in multi-scale, which make it appropriate for processing of OCT images. We discuss about application of such representations including complex wavelet based K-SVD, and diffusion wavelets on OCT data. We introduce complex wavelet based K-SVD to take advantage of adaptability in dictionary learning methods to improve the performance of simple dual tree complex wavelets in speckle reduction of OCT datasets in 2D and 3D. The algorithm is evaluated on 144 randomly selected slices from twelve 3D OCTs taken by Topcon 3D OCT-1000 and Cirrus Zeiss Meditec. Improvement of contrast to noise ratio (CNR) (from 0.9 to 11.91 and from 3.09 to 88.9, respectively) is achieved. Furthermore, two approaches are proposed for image segmentation using diffusion. The first method is designing a competition between extended basis functions at each level and the second approach is defining a new distance for each level and clustering based on such distances. A combined algorithm, based on these two methods is then proposed for segmentation of retinal OCTs, which is able to localize 12 boundaries with unsigned border positioning error of 9.22 ±3.05 μm, on a test set of 20 slices selected from 13 3D OCTs.

Detection and Classification of Power Quality Disturbances Using Sparse Signal Decomposition on Hybrid Dictionaries

Several methods have been proposed for detection and classification of power quality (PQ) disturbances using wavelet, Hilbert transform, Gabor transform, Gabor-Wigner transform, S transform, and Hilbert-Haung transform. This paper presents a new method for detection and classification of single and combined PQ disturbances using a sparse signal decomposition (SSD) on overcomplete hybrid dictionary (OHD) matrix. The method first decomposes a PQ signal into detail and approximation signals using the proposed SSD technique with an OHD matrix containing impulse and sinusoidal elementary waveforms. The output detail signal adequately captures morphological features of transients (impulsive and oscillatory) and waveform distortions (harmonics and notching). Whereas the approximation signal contains PQ features of fundamental, flicker, dc-offset, and short- and long-duration variations (sags, swells, and interruptions). Thus, the required PQ features are extracted from the detail and approximation signals. Then, a hierarchical decision-tree algorithm is used for classification of single and combined PQ disturbances. The proposed method is tested using both synthetic and microgrid simulated PQ disturbances. Results demonstrate the accuracy and robustness of the method in detection and classification of single and combined PQ disturbances under noiseless and noisy conditions. The method can be easily expanded for compressed sensing based PQ monitoring networks.

Iterative Thresholding for Sparse Approximations

Sparse signal expansions represent or approximate a signal using a small number of elements from a large collection of elementary waveforms. Finding the optimal sparse expansion is known to be NP hard in general and non-optimal strategies such as Matching Pursuit, Orthogonal Matching Pursuit, Basis Pursuit and Basis Pursuit De-noising are often called upon. These methods show good performance in practical situations, however, they do not operate on the ℓ 0 penalised cost functions that are often at the heart of the problem. In this paper we study two iterative algorithms that are minimising the cost functions of interest. Furthermore, each iteration of these strategies has computational complexity similar to a Matching Pursuit iteration, making the methods applicable to many real world problems. However, the optimisation problem is non-convex and the strategies are only guaranteed to find local solutions, so good initialisation becomes paramount. We here study two approaches. The first approach uses the proposed algorithms to refine the solutions found with other methods, replacing the typically used conjugate gradient solver. The second strategy adapts the algorithms and we show on one example that this adaptation can be used to achieve results that lie between those obtained with Matching Pursuit and those found with Orthogonal Matching Pursuit, while retaining the computational complexity of the Matching Pursuit algorithm.

Incremental HMM training applied to ECG signal analysis

This work discusses the implementation of incremental hidden Markov model (HMM) training methods for electrocardiogram (ECG) analysis. The HMMs are used to model the ECG signal as a sequence of connected elementary waveforms. Moreover, an adaptation process is implemented to adapt the HMMs to the ECG signal of a particular individual. The adaptation training strategy is based on incremental versions of the expectation–maximization, segmental k-means and Bayesian approaches. Performance of the training methods was assessed through experiments considering the QT and ST–T databases. The results obtained show that the incremental training improves beat segmentation and ischemia detection performance with the advantage of low computational effort.

Optimized search over the Gabor dictionary for note decomposition and recognition

Performing real-time note detection of multiple audio sources, such as guitar signals, is a difficult task due to the complex nature of these signals. For instance, guitar notes are close in pitch and the harmonic overtones of each note are strongly interlaced, thus preventing standard filtering techniques. In order to accomplish note detection, a harmonic matching pursuit algorithm has been used to decompose an audio signal in terms of elementary waveforms called harmonic atoms. These atoms are derived from the standard matching pursuit algorithm, and are part of an extended and overcomplete Gabor dictionary. In this paper, the search over Gabor dictionary is optimized by using signal modeling of the guitar signal in order to pre-calculate a parameter set; therefore avoiding a costly search over the extended Gabor dictionary. The parameter set defined for the proposed algorithm includes time-location, decay rate, frequency, scale and phase, which are calculated at the onset of each note played. This optimized algorithm is demonstrated through synthesized and real guitar signal examples. Considerable computational savings of this proposed algorithm over the harmonic matching pursuit algorithm are achieved.

Design and Analysis of Synthesized Template Waveform for Receiving UWB Signals

Ultra Wideband (UWB) communication system utilizing impulse signals is attractive technique which can achieve high data rate with low complexity and low power consumption. In this impulse based UWB system, lots of different shaped pulses have been considered to represent more information bits per symbol. In order to detect these different shaped UWB signals at the receiver, the synthesized template generation method using several elementary waveforms is effective. In this paper we design and analyze this synthesized template waveform instead of the conventional matched filter technique. The synthesis of UWB template waveform can be achieved as combinations of orthogonalized elementary waveforms with Fourier coefficients. By adjusting the number of elementary waveforms and their coefficients, it is possible to detect several types of UWB signals. The orders of approximation corresponding to different number of elementary waveforms are analyzed and the bit error rate properties are then investigated in AWGN and multipath fading channels. In addition, the proposed system can capture more energy by adjusting its coefficients adaptively under the multipath environment and reduce the effect of Intra-Pulse Interference (IPI) which is occurred when the propagation channel is not separable, that is, multipath components spaced closer than the typical pulse width. We show the design of the adaptive template synthesis method and its performance compared with conventional Rake receiver.

Harmonic decomposition of audio signals with matching pursuit

We introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the standard matching pursuit, we define a new pursuit along with a fast algorithm, namely, the fast harmonic matching pursuit, to approximate N-dimensional audio signals with a linear combination of M harmonic atoms. Our algorithm has a computational complexity of O(MKN), where K is the number of partials in a given harmonic atom. The decomposition method is demonstrated on musical recordings, and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations, e.g., very different note durations, lots of reverberation, and overlapping notes.

Normal needle electromyographic insertional activity morphology: a clinical and simulation study.

Needle electromyographic insertional activity waveform morphology, and mechanisms of generation, have received little attention. This study analyzes the individual component waveforms that contribute to the burst of electrical activity known as insertional activity. One hundred monopolar needle insertions were slowly performed and high speed recorded to allow better separation of the contributing individual component waveforms. Analysis of the many waveforms recorded demonstrates several classes of potentials. All of these could be reconstructed by the summation of two basic or elementary waveform patterns: a biphasic initially negative spike with or without a "prepotential" similar to an end-plate spike, and the biphasic initially positive spike with a slowly declining negative phase, similar to a positive sharp wave, though shorter in duration. The relationship between these elementary waveforms and their hypothesized generator sources is discussed.

Time-frequency speech transformation based on an elementary waveform representation

A representation of the speech signal as a sum of elementary waveforms (Elementary Waveform Speech Model or EWSM) is introduced and some of its features for modifying localized time-frequency events are demonstrated. The elementary waveforms model the local spectro-temporal maxima of energy within the speech signal thanks to the use of simple mathematical functions. An automatic analysis-synthesis system allows for waveforms parameters estimation, using frame-by-frame processing: spectral modelling and segmentation using short-time Fourier transform and LPC spectrum, Fourier filtering according to this segmentation, waveform spotting in each channel, waveform modelling using simple functions. The classical theory of speech production proves the validity of the EWSM parameters; their modifications yield well-localized time-frequency transformations, including frequency compression/expansion, pitch, formant and noise modification.

Waveform Analysis in Medicine. An Introduction

The purpose of the book, as stated by the authors, is to serve as a “how-to-do-it” book on waveform analysis for medical personnel and engineering students. They emphasize a conceptual approach, replacing complex mathematical proofs with easy to understand diagrams, and attempt to “close the vocabulary gap between the engineer and the doctor.”The book consists of five parts. Part I introduces the reader to examples of elementary waveforms and their basic functional forms, definitions of technical terms and examples of waveform selection. Part II provides an introduction to differential and integral calculus, the waveform inner product, fourier series, and a discussion of the application of fourier transforms and correlation techniques. Part III gives a method of extracting signals from noise with numerical examples of autocorrelation and cross-correlation and a detailed example of the estimation of lag time between two waveforms. Part IV is an introduction to the basic concepts of the analog computer and the use of orthogonal exponentials in the representation of waveforms.

A note on stationarity of some random processes

It is shown that a band-limited process x(t) = Σ a k F ( t − t k ), where … a k , a k+1 , … is a stationary sequence of random variables and t k 's are equally spaced arrival times of elementary waveforms F(t) , is stationary in the wide sense if and only if an equally spaced interval length between successive arrival times is not larger than Shannon's sampling period ½ W , where W is a maximum frequency of x(t) . This result is utilized for generation by computer of a stationary Gaussian process when power spectrum of the process is band-limited.

Use of digital adaptive filters for measuring prepyriform evoked potentials from cats

A set of techniques is described for making digital measurements on averaged cortical evoked potentials by means of the IBM 7090. The basis for measurement is the selection of a set of elementary wave forms called basis functions, which are scaled by coefficients and added to replicate observed wave forms. Optimization of the coefficients is by nonlinear regression followed by cross-correlation between observed and calculated wave forms. By this means the information contained in the shape of each averaged evoked potential is incorporated into a set of numerical coefficients. Unresolved problems include the need for improved basis functions and for methods for determining confidence intervals for the coefficients.