Showing papers on "Harmonic wavelet transform published in 2010"

Multifocus Image Fusion and Restoration With Sparse Representation

Abstract: To obtain an image with every object in focus, we always need to fuse images taken from the same view point with different focal settings. Multiresolution transforms, such as pyramid decomposition and wavelet, are usually used to solve this problem. In this paper, a sparse representation-based multifocus image fusion method is proposed. In the method, first, the source image is represented with sparse coefficients using an overcomplete dictionary. Second, the coefficients are combined with the choose-max fusion rule. Finally, the fused image is reconstructed from the combined sparse coefficients and the dictionary. Furthermore, the proposed fusion scheme can simultaneously resolve the image restoration and fusion problem by changing the approximate criterion in the sparse representation algorithm. The proposed method is compared with spatial gradient (SG)-, morphological wavelet transform (MWT)-, discrete wavelet transform (DWT)-, stationary wavelet transform (SWT)-, curvelet transform (CVT)-, and nonsubsampling contourlet transform (NSCT)-based methods on several pairs of multifocus images. The experimental results demonstrate that the proposed approach performs better in both subjective and objective qualities.

Asymmetric cryptosystem based on phase-truncated Fourier transforms.

Abstract: We propose an asymmetric cryptosystem based on a phase-truncated Fourier transform. With phase truncation in Fourier transform, one is able to produce an asymmetric ciphertext as real-valued and stationary white noise by using two random phase keys as public keys, while a legal user can retrieve the plaintext using another two different private phase keys in the decryption process. Owing to the nonlinear operation of phase truncation, high robustness against existing attacks could be achieved. A set of simulation results shows the validity of proposed asymmetric cryptosystem.

Wavelets: Theory and Applications for Manufacturing

Abstract: Why wavelets.- From fourier transform to wavelet transform.- Wavelet integrated with fourier transform: a spectral post-processing technique.- Wavelet-based multi-sensor data fusion.- Integration of wavelet with fuzzy logic for machine defect severity classification.- Wavelet-based multi-fractal singularity spectrum.- Wavelet-based ultrasonic pulse detection and differentiation.- Wavelet-based multi-scale enveloping spectrogram.- Wavelet packet decomposition for cross-term interference suppression in wigner-ville distribution.- Optimal wavelet packet transform for discriminable feature extraction.- Wavelet selection criteria.- Customized wavelet design.

Short-Time Fractional Fourier Transform and Its Applications

Abstract: The fractional Fourier transform (FRFT) is a potent tool to analyze the chirp signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. The short-time fractional Fourier transform (STFRFT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the short-time fractional Fourier domain (STFRFD). Two aspects of its performance are considered: the 2-D resolution and the STFRFD support. The time-FRFD-bandwidth product (TFBP) is defined to measure the resolvable area and the STFRFD support. The optimal STFRFT is obtained with the criteria that maximize the 2-D resolution and minimize the STFRFD support. Its inverse transform, properties and computational complexity are presented. Two applications are discussed: the estimations of the time-of-arrival (TOA) and pulsewidth (PW) of chirp signals, and the STFRFD filtering. Simulations verify the validity of the proposed algorithms.

On the Analytic Wavelet Transform

Abstract: An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of nonnegligible amplitude and frequency modulation. The analytic signal is first locally represented as a modulated oscillation, demodulated by its own instantaneous frequency, and then Taylor-expanded at each point in time. The terms in this expansion, called the instantaneous modulation functions, are time-varying functions which quantify, at increasingly higher orders, the local departures of the signal from a uniform sinusoidal oscillation. Closed-form expressions for these functions are found in terms of Bell polynomials and derivatives of the signal's instantaneous frequency and bandwidth. The analytic wavelet transform is shown to depend upon the interaction between the signal's instantaneous modulation functions and frequency-domain derivatives of the wavelet, inducing a hierarchy of departures of the transform away from a perfect representation of the signal. The form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal, in which case our expressions simplify considerably. One may then quantify the time-varying bias associated with signal estimation via wavelet ridge analysis, and choose wavelets to minimize this bias.

A General Description of Linear Time-Frequency Transforms and Formulation of a Fast, Invertible Transform That Samples the Continuous S-Transform Spectrum Nonredundantly

Abstract: Examining the frequency content of signals is critical in many applications, from neuroscience to astronomy. Many techniques have been proposed to accomplish this. One of these, the S-transform, provides simultaneous time and frequency information similar to the wavelet transform, but uses sinusoidal basis functions to produce frequency and globally referenced phase measurements. It has shown promise in many medical imaging applications but has high computational requirements. This paper presents a general transform that describes Fourier-family transforms, including the Fourier, short-time Fourier, and S- transforms. A discrete, nonredundant formulation of this transform, as well as algorithms for calculating the forward and inverse transforms are also developed. These utilize efficient sampling of the time-frequency plane and have the same computational complexity as the fast Fourier transform. When configured appropriately, this new algorithm samples the continuous S-transform spectrum efficiently and nonredundantly, allowing signals to be transformed in milliseconds rather than days, as compared to the original S-transform algorithm. The new and efficient algorithms make practical many existing signal and image processing techniques, both in biomedical and other applications.

Cluster expansion and the configurational theory of alloys

Abstract: A rigorous mathematical foundation for the cluster-expansion method is presented It is shown that the cluster basis developed by Sanchez et al [Physica A 128, 334 (1984)] is a multidimensional discrete Fourier transform while the general formalism of Sanchez [Phys Rev B 48, 14013 (1993)] corresponds to a multidimensional discrete wavelet transform For functions that depend nonlinearly on the concentration, it is shown that the cluster basis corresponding to a multidimensional discrete Fourier transform does not converge, as it is usually assumed, to a finite cluster expansion or to an Ising-type model representation of the energy of formation of alloys The multidimensional wavelet transform, based on a variable basis cluster expansion, is shown to provide a satisfactory solution to the deficiencies of the discrete Fourier-transform approach Several examples aimed at illustrating the main findings and conclusions of this work are given

Medical image enhancement algorithm based on wavelet transform

Abstract: Low contrast and poor quality are main problems in the production of medical images. By using the wavelet transform and Haar transform, a novel image enhancement approach is proposed. First, a medical image was decomposed with wavelet transform. Secondly, all high-frequency sub-images were decomposed with Haar transform. Thirdly, noise in the frequency field was reduced by the soft-threshold method. Fourthly, high-frequency coefficients were enhanced by different weight values in different sub-images. Then, the enhanced image was obtained through the inverse wavelet transform and inverse Haar transform. Lastly, the image's histogram was stretched by nonlinear histogram equalisation. Experiments showed that this method can not only enhance an image's details but can also preserve its edge features effectively.

Time-Frequency Representation Based on an Adaptive Short-Time Fourier Transform

Abstract: In this paper, a new concise algorithm about time-frequency representation (TFR) based on an adaptive short-time Fourier transform (ASTFT) is presented. In this algorithm, the analysis window width is equal to the local stationary length which is measured by the instantaneous frequency gradient (IFG) of the signal. And the instantaneous frequency (IF) of the signal is obtained by detecting the ridge of wavelet transform (WT). The ASTFT provides much better performance than conventional TFR algorithms. Furthermore, the algorithm is simpler and more computational efficient than some of other adaptive TFR algorithms proposed previously. Several examples are presented to illustrate its behavior on different kinds of signals and demonstrate its validity.

Dual-Tree Complex Wavelet Transform Based SAR Despeckling Using Interscale Dependence

Abstract: In this paper, a dual-tree complex wavelet transform (DTCWT) based despeckling algorithm is proposed for synthetic aperture radar (SAR) images, considering the significant dependences of the wavelet coefficients across different scales. The DTCWT has the advantage of improved directional selectivity, approximate shift invariance, and perfect reconstruction over the discrete wavelet transform. The wavelet coefficients in each subband are modeled with a bivariate Cauchy probability density function (PDF) which takes into account the statistical dependence among the wavelet coefficients. Mellin transform of two dependent random variables is utilized to estimate the dispersion parameter of the bivariate Cauchy PDF from the noisy observations. This method is faster and effective when compared to that of the earlier techniques on numerical integration. Within this framework, we propose a new method for despeckling SAR images employing a maximum a posteriori estimator. Experimental results show that the proposed method based on bivariate Cauchy prior achieves better performance in terms of equivalent number of looks, peak signal-to-noise ratio, and Pratt's figure of merit.

Comparison of Wavelet and Short Time Fourier Transform Methods in the Analysis of EMG Signals

Abstract: The electromyographic (EMG) signal observed at the surface of the skin is the sum of thousands of small potentials generated in the muscle fiber. There are many approaches to analyzing EMG signals with spectral techniques. In this study, the short time Fourier Transform (STFT) and wavelet transform (WT) were applied to EMG signals and coefficients were obtained. In these studies, MATLAB 7.01 program was used. According to obtained results, it was determined that WT is more useful than STFT in the fields of eliminating of resolution problem and providing of changeable resolution during analyze.

Time Domain Signal Analysis Using Wavelet Packet Decomposition Approach

Abstract: This paper explains a study conducted based on wavelet packet transform techniques. In this paper the key idea underlying the construction of wavelet packet analysis (WPA) with various wavelet basis sets is elaborated. Since wavelet packet decomposition can provide more precise frequency resolution than wavelet decomposition the implementation of one dimensional wavelet packet transform and their usefulness in time signal analysis and synthesis is illustrated. A mother or basis wavelet is first chosen for five wavelet filter families such as Haar, Daubechies (Db4), Coiflet, Symlet and dmey. The signal is then decomposed to a set of scaled and translated versions of the mother wavelet also known as time and frequency parameters. Analysis and synthesis of the time signal is performed around 8 seconds to 25 seconds. This was conducted to determine the effect of the choice of mother wavelet on the time signals. Results are also prepared for the comparison of the signal at each decomposition level. The physical changes that are occurred during each decomposition level can be observed from the results. The results show that wavelet filter with WPA are useful for analysis and synthesis purpose. In terms of signal quality and the time required for the analysis and synthesis, the Haar wavelet has been seen to be the best mother wavelet. This is taken from the analysis of the signal to noise ratio (SNR) value which is around 300 dB to 315 dB for the four decomposition levels.

Gabor Transform, SPWVD, Gabor-Wigner Transform and Wavelet Transform - Tools For Power Quality Monitoring

Abstract: The one-dimension frequency analysis based on DFT (Discrete FT ) is sufficient in many cases in detecting power disturbances and evaluating power quality (PQ). To illustrate in a more comprehensive manner the character of the signal, time-frequency analyses are p erformed. The most common known time-frequency representations (TFR) are spectrogram (SPEC) and Gabor Transform (GT). However, the method has a relatively low time-frequency resolution. The other TF R: Discreet Dyadic Wavelet Transform (DDWT), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) and new Gabor-Wigner Transform (GWT) are described in the paper. The main features of the transforms, on the basis of testing signals, are presented.

Fast linear canonical transforms

Abstract: The linear canonical transform provides a mathematical model of paraxial propagation though quadratic phase systems. We review the literature on numerical approximation of this transform, including discretization, sampling, and fast algorithms, and identify key results. We then propose a frequency-division fast linear canonical transform algorithm comparable to the Sande-Tukey fast Fourier transform. Results calculated with an implementation of this algorithm are presented and compared with the corresponding analytic functions.

A Space-Vector Discrete Fourier Transform for Unbalanced and Distorted Three-Phase Signals

Abstract: In this paper, a space-vector discrete-time Fourier transform is proposed for fast and precise detection of the fundamental-frequency and harmonic positive- and negative-sequence vector components of three-phase input signals. The discrete Fourier transform is applied to the three-phase signals represented by Clarke's αβ vector. It is shown that the complex numbers output from the Fourier transform are the instantaneous values of the positive- and negative-sequence harmonic component vectors of the input three-phase signals. The method allows the computation of any desired positive- or negative-sequence fundamental-frequency or harmonic vector component of the input signal. A recursive algorithm for low-effort online implementation is also presented. The detection performance for variable-frequency and interharmonic input signals is discussed. The proposed and other usual method performances are compared through simulations and experiments.

Harmonic wavelet approximation of random, fractal and high frequency signals

Abstract: The analysis of a periodic signal with localized random (or high frequency) noise is given by using harmonic wavelets. Since they are orthogonal to the Fourier basis, by defining a projection wavelet operator the signal is automatically decomposed into the localized pulse and the periodic function. An application to the analysis of a self-similar non-stationary noise is also given.

Review: Choice of the wavelet analyzing in the phonocardiogram signal analysis using the discrete and the packet wavelet transform

Abstract: The phonocardiogram signal (PCG) can be utilized more efficiently by medical doctors when they are displayed visually, rather through a conventional stethoscope. This signal provides clinician with valuable diagnostic and prognostic information. Although the PCG signal analysis by auscultation is convenient as clinical tool, heart sound signals are so complex and non-stationary that they have a great difficulty to analyze in time or frequency domain. We have studied the extraction of features out of heart sounds in time-frequency (TF) domain for recognition of heart sounds through TF analysis. This article highlights the importance of the choice of wavelet analyzing wavelet and its order in the phonocardiogram signal analysis using the two versions of the wavelet transform: the discrete wavelet transform (DWT) and the packet wavelet transform (PWT). This analysis is based on the application of a large number of orthogonal and bi-orthogonal wavelets and whenever you measure the value of the average difference (in absolute value) between the original signal and the synthesis signal obtained by multiresolution analysis (AM). The performance of the discrete wavelet transform (DWT) and the packet wavelet transform (PWT) in the PCG signal analysis are evaluated and discussed in this paper. The results we obtain show the clinical usefulness of our extraction methods for recognition of heart sounds (or PCG signal).

Feature extraction of brain mri by stationary wavelet transform and its applications

Abstract: Wavelet transform is widely used in feature extraction of magnetic resonance imaging. However, the traditional discrete wavelet transform (DWT) suffers from translation variant property, which may extract significantly different features from two images of the same subject with only slight movement. In order to solve this problem, this paper utilizes stationary wavelet transform (SWT) to extract features instead of DWT. Experiments on a normal brain MRI demonstrate that wavelet coefficients via SWT are superior to those via DWT, in terms of translation invariant property. In addition, we applied SWT to normal and abnormal brain classification. The results demonstrate that SWT-based classifier is more accurate than that of DWT.

A New Wavelet-based image denoising using undecimated discrete wavelet transform and least squares support vector machine

Abstract: Image denoising is an important image processing task, both as itself, and as a preprocessing in image processing pipeline. The least squares support vector machine (LS-SVM) has shown to exhibit excellent classification performance in many applications. Based on undecimated discrete wavelet transform, a new wavelet-based image denoising using LS-SVM is proposed in this paper. Firstly, the noisy image is decomposed into different subbands of frequency and orientation responses using the undecimated discrete wavelet transform. Secondly, the feature vector for a pixel in a noisy image is formed by the spatial regularity in wavelet domain, and the LS-SVM model is obtained by training. Then the wavelet coefficients are divided into two classes (noisy coefficients and noise-free ones) by LS-SVM training model. Finally, all noisy wavelet coefficients are relatively well denoised by shrink method, in which the adaptive threshold is utilized. Extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state-of-the-art denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.

Investigating advantages and disadvantages of the analysis of a geometrical surface structure with the use of fourier and wavelet transform

Abstract: Nowadays a geometrical surface structure is usually e valuated with the use of Fourier transform. This type of transform allows for accurate analysis of harmonic components of surface profiles. Due to its funda mentals, Fourier transform is particularly efficient when eval uating periodic signals. Wavelets are the small waves that are oscillatory and limited in the range. Wavelets ar e special type of sets of basis functions that are useful in the description of function spaces. They are particularly useful for the description of non-continuous and irregular functions that appear most often as responses of real physical systems. Bases of wavelet functions are usually well located in the frequency and in the time domain. In the case of periodic signals, the Fourier transform is still extremely useful. It allows to obtain accurate inform ation on the analyzed surface. Wavelet analysis does not provide as accurate information about the measured surface as the Fourier tra nsform, but it is a useful tool for detection of irregularities of the profile. Therefore , wavelet analysis is the better way to detect scratches or cracks that sometimes occur on the surface. The pape r presents the fundamentals of both types of transform. It presents also the comparison of an evaluation of the roundness profile by Fourier and wavelet transforms.

Advanced Hough Transform Using A Multilayer Fractional Fourier Method

Abstract: The Hough transform (HT) is a commonly used technique for the identification of straight lines in an image. The Hough transform can be equivalently computed using the Radon transform (RT), by performing line detection in the frequency domain through use of central-slice theorem. In this research, an advanced Radon transform is developed using a multilayer fractional Fourier transform, a Cartesian-to-polar mapping, and 1-D inverse Fourier transforms, followed by peak detection in the sinogram. The multilayer fractional Fourier transform achieves a more accurate sampling in the frequency domain, and requires no zero padding at the stage of Cartesian-to-polar coordinate mapping. Our experiments were conducted on mix-shape images, noisy images, mixed-thickness lines and a large data set consisting of 751 000 handwritten Chinese characters. The experimental results have shown that our proposed method outperforms all known representative line detection methods based on the standard Hough transform or the Fourier transform.