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The adaptive wavelet Galerkin method for solving linear, elliptic operator equations introduced by Cohen et al. (Math Comp 70:27-75, 2001) is extended to nonlinear equations and is shown to converge with optimal rates without coarsening. Moreover, when an appropriate scheme is available for the approximate evaluation of residuals, the method is shown to have asymptotically optimal computational complexity. The application of this method to solving least-squares formulations of operator equations G(u) = 0, where G : H → K', is studied. For formulations of partial differential equations as first-order least-squares systems, a valid approximate residual evaluation is developed that is easy to implement and quantitatively efficient. Keywords Adaptive wavelet methods * Least-squares formulations of boundary value problems * Optimal convergence rates * Asymptotically optimal computational complexity * Galerkin discretization Mathematics Subject Classification 41A25 * 42C40 * 47J25 * 65J15 * 65N12 * 65T60 * 65N30, 1 Introduction 1.1 Adaptive Wavelet Methods We consider the problem of solving F (u) = 0, where F : H → H', with H being a Hilbert space. As applications, [...]

Upwelling ecosystems are particularly heterogeneous and present intense mesoscale (tens of kilometres) and sub- mesoscale (hundreds of metres to kilometres) activity that are expected to drive the distribution of the organisms and thus their interactions. Here we addressed the impact of the physical forcing in the northern Humboldt Current system off Peru, which is characterized by the presence of an intense and shallow oxygen minimum zone and used the variability of the depth of the oxycline as a proxy of the physical forcing that impacts the epipelagic communities. We analyzed simultaneous high-resolution acoustic observations of the oxycline depth, the biomass in macrozooplankton, and the biomass in pelagic fish. Three complementary methodologies were considered: (i) geostatistical methods and correlation tests, (ii) principal coordinates of neighbour matrices, and (iii) wavelet analysis. Our results highlight the relevance of a multimethod framework to characterize the multiscale relationships between marine ecosystem components. We also provided evidence that the sub-mesoscale-to-mesoscale variability of the oxycline depth drives the distribution of macrozooplankton, which further structures the distribution of forage fish in a bottom-up cascade. Les ecosystemes de zones de remontee d'eau sont particulierement heterogenes et presentent une activite intense tant a l'echelle mesoscopique (de l'ordre de dizaines de kilometres) que submesoscopique (de l'ordre de centaines de metres a quelques kilometres) qui structurerait la distribution des organismes et, de ce fait, leurs interactions. Le present article se penche sur l'effet du forcage physique dans la partie nord du systeme du Courant de Humboldt, le long des cotes peruviennes. Ce systeme est caracterise par la presence d'une intense zone de minimum d'oxygene peu profonde. La variabilite de la profondeur de l'oxycline est utilisee comme indicateur du forcage physique auquel sont assujetties les communautes epipelagiques. Des observations acoustiques simultanees de haute resolution de la profondeur de l'oxycline, de la biomasse de macrozooplancton et de la biomasse de poissons pelagiques sont analysees. Trois methodes complementaires sont prises en consideration : (i) des methodes geostatistiques et des tests de correlation, (ii) la methode des coordonnees principales de matrices de voisinage et (iii) l'analyse en ondelettes. Les resultats obtenus soulignent la pertinence d'une approche faisant appel a plusieurs methodes pour caracteriser les relations a diverses echelles entre les composantes des ecosystemes marins. Ils indiquent egalement que la variabilite aux echelles mesoscopique a sub-mesoscopique de la profondeur de l'oxycline structure la distribution du macrozooplancton et ainsi, par un effet de cascade vers le haut, la distribution du poisson fourrage. [Traduit par la Redaction], Introduction The identification and explanation of the spatial variation of ecological structures is a major issue in ecology (Dale et al. 2002). Populations are spatially structured because of several factors, [...]

The present paper describes the use of Morlet wavelet transform in understanding the stall inception mechanism in a single stage axial flow fan. Unsteady pressure data from wall mounted sensors were used in the wavelet transforms. This paper was carried out under undistorted and distorted inflow conditions as well as for slow throttle closure and throttle ramping. B was observed from the wavelet transforms that the stall inception under clean inflow (undistorted) and counter-rotating inflow distortions (in the direction opposing the rotor rotation) incur through short length-scale disturbances and through long length-scale disturbances under static and co-rotating inflow distortions (in the same direction of rotor rotation). Modal activity was observed to be insignificant under clean inflow while under static inflow distortion, long length-scale disturbances evolved due to interaction between rotor blades and the distorted sector, especially near the trailing edge of the distortion screen. The presence of a strong mode was observed under both co- and counter-rotating inflow distortions. With throttle ramping, stall inception occurs through long and short length-scale disturbances under co- and counter-rotating inflow distortions, respectively. Some preliminary flow characteristics were studied using a seven hole probe. A significant increase in flow angle and decrease in axial flow coefficient close to the rotor tip were observed under co-rotating inflow distortion as compared with counter-rotating inflow distortion. [DOI: 10.1115/1.4002921] Keywords: flow instability, rotating stall, static inflow distortion, dynamic inflow distortion, stall inception

A new method for improving fingerprint detections by a compression-based joint transform correlator (JTC) via wavelet filter is proposed. The simulation results show that the proposed method has advantages over the conventional compression-based JTC in that detection performance can be maximized to be higher than a classical JTC by using a smaller file size for the compressed-reference images. OCIS codes: 070.4550, 100.7410.

Pattern discovery algorithms based on the computational mechanics (CM) method have been shown to succinctly describe underlying patterns in data through the reconstruction of minimum probabilistic finite state automata (PFSA). We apply the CM approach toward the tracking of human subjects in real time by matching and tracking the underlying color pattern as observed from a fixed camera. Objects are extracted from a video sequence, and then raster scanned, decomposed with a one-dimensional Haar wavelet transform, and symbolized with the aid of a red--green--blue (RGB) color cube. The clustered causal state algorithm is then used to reconstruct the corresponding PFSA. Tracking is accomplished by generating the minimum PFSA for each subsequent frame, followed by matching the PFSAs to the previous frame. Results show that there is an optimum alphabet size and segmentation of the RGB color cube for efficient tracking. OCIS codes: 100.4999, 100.0100, 150.1135, 150.6044.

This paper proposes a multiresolution based wavelet controller for the control of linear time varying systems consisting of a time invariant component and a component with zero mean slowly time varying parameters. The real time discrete wavelet transform controller is based on a time interval from the initial until the current time and is updated at regular time steps. By casting a modified optimal control problem in a linear quadratic regulator (LQR) form constrained to a band of frequency in the wavelet domain, frequency band dependent control gain matrices are obtained. The weighting matrices are varied for different bands of frequencies depending on the emphasis to be placed on the response energy or the control effort in minimizing the cost functional, for the particular band of frequency leading to frequency dependent gains. The frequency dependent control gain matrices of the developed controller are applied to multiresolution analysis (MRA) based filtered time signals obtained until the current time. The use of MRA ensures perfect decomposition to obtain filtered time signals over the finite interval considered, with a fast numerical implementation for control application. The proposed controller developed using the Daubechies wavelet is shown to work effectively for the control of free and forced vibration (both under harmonic and random excitations) responses of linear time varying single-degree-of-freedom and multidegree-of-freedom systems. Even for the cases where the conventional LQR or addition of viscous damping fails to control the vibration response, the proposed controller effectively suppresses the instabilities in the linear time varying systems. DOI: 10.1061/(ASCE)EM.1943-7889.0000162 CE Database subject headings: Wavelet; Structural control; Frequency analysis; Transformation. Author keywords: Wavelet; Structural control; Time-frequency analysis; Transformation.

This paper describes a new wavelet-based anomaly detection technique for a dual-band forward-looking infrared (FLIR) sensor consisting of a coregistered longwave (LW) with a midwave (MW) sensor. The proposed approach, called the wavelet-RX (Reed--Xiaoli) algorithm, consists of a combination of a two-dimensional (2D) wavelet transform and a well-known multivariate anomaly detector called the RX algorithm. In our wavelet-RX algorithm, a 2D wavelet transform is first applied to decompose the input image into uniform subbands. A subband-image cube is formed by concatenating together a number of significant subbands (high-energy subbands). The RX algorithm is then applied to the subband-image cube obtained from a wavelet decomposition of the LW or MW sensor data. In the case of the dual band, the RX algorithm is applied to a subband-image cube constructed by concatenating together the high-energy subbands of the LW and MW subband-image cubes. Experimental results are presented for the proposed wavelet-RX and the classical constant false alarm rate (CFAR) algorithm for detecting anomalies (targets) in a single broadband FLIR (LW or MW) or in a coregistered dual-band FLIR sensor. The results show that the proposed wavelet-RX algorithm outperforms the classical CFAR detector for both single-band and dual-band FLIR sensors. [c] 2010 Optical Society of America OCIS codes: 100.5010, 100.4994, 100.3008.

Two-dimensional refractive index profiles of ion exchanged channel waveguides in glass have been obtained from the analysis of interferometer data. To obtain depth data, a shallow bevel is produced in the glass by polishing. The refractive index profile information that is contained within the derivative of the phase data is extracted directly using a continuous wavelet transform algorithm. The algorithm used to characterize and smooth the wavelet ridge is discussed in detail. OCIS codes: 100.5070, 100.7410, 180.3170, 230.7380.

Problem statement: The aim of this study was to report the human emotion assessment using Electroencephalogram (EEG). Approach: An audio-visual induction based protocol was designed for inducing five different emotions (happy, surprise, fear, disgust and neutral) on 20 subjects in the age group of 19~39 years. EEG signals are recorded from 64 channels placed over entire scalp according to International 10-10 system. We firstly applied Spatial Filtering technique to remove the noises and artifacts from the EEG signals. Three wavelet functions ('db8', 'sym8' and 'coif5') were used to decompose the EEG signal into five different frequency bands namely: delta, theta, alpha, beta and gamma. A set of new statistical features related to energy were extracted from the EEG frequency bands to construct the feature vector for classifying the emotions. Two simple linear classifiers (K Nearest Neighbor (KNN) and Linear Discriminant Analysis (LDA)) were used for mapping the feature vector into corresponding emotions. Furthermore, we compared the efficacy of emotion classification with a reduced set of channels (24 channels) for evaluating the reliability of the emotion recognition system. Results: In this study, 62 channels outperform 24 channels by giving the maximum average classification accuracy of 79.65% using KNN and 78.52% using LDA. Conclusion: In this study we presented an approach to discrete emotion recognition based on the processing of EEG signals. The preliminary results resented in this study address the classifiability of human emotions using original and reduced set of EEG channels. The results presented in this study indicated that, statistical features extracted from time-frequency analysis (wavelet transform) works well in the context of discrete emotion classification. Key words: EEG, discrete wavelet transform, k-Nearest Neighbor (kNN), Linear Discriminant Analysis (LDA), INTRODUCTION The information retrieval from the brain signals related to human emotion is one of the key steps towards emotional intelligence. Our emotional state plays an important role in how [...]

An application of the continuous wavelet transform to modulation extraction of additive moire fringes and time-average patterns is proposed. We present numerical studies of the influence of various parameters of the wavelet transformation itself and a fringe pattern under study on the demodulation results. To facilitate the task of demodulating a signal with zero crossing values, a two-frame approach for wavelet ridge extraction is proposed. Experimental studies of vibration mode patterns by time-average interferometry provide excellent verification of numerical findings. They compare very well with the results of our previous investigations using the temporal phase-shifting method widely considered as the most accurate one. No need of performing phase shifting represents significant simplification of the experimental procedure. [c] 2010 Optical Society of America OCIS codes: 120.2650, 120.3180, 120.4120, 120.7280, 100.7410.

Problem statement: This study proposed an approach for classification of placental tissues development using ultrasound images. Approach: This approach is based to the selection of tissues, feature extraction by discrete wavelet transform and classification by neural network and especially the Multi Layer Perceptron (MLP). Results: The proposed approach is tested for ultrasound placental images; resulting in 95% success rate. Conclusion/Recommendations: The method showed a good recognition for placental tissues and will be useful for detection of the placental anomalies those concerning the premature birth and the intrauterine growth retardation. Key words: Placenta, wavelet transform, neural network, MLP, INTRODUCTION An ultrasound diagnostic system has become an important and popular diagnostic tool since it has a wide range of applications. Specifically, due to its noninvasive and non-destructive nature, the [...]

Problem statement: The objective of prosody modification is to change the amplitude, duration and pitch ([F.sub.0]) of speech segments without altering their spectral envelop. Applications are numerous, including, Text-To-Speech synthesis, transformation of voice characteristics and foreign language learning. Several approaches have been developed in the literature to achieve this goal. The main restrictions of these latter are in the modification range, the synthesized speech quality and naturalness of spoken language. The latest research studies provide evidence that the first Formant ([F.sub.1]) and [F.sub.0] are dependent; suggesting that in order to preserve high quality and naturalness of the speech signal, any change to one of these parameters must be accompanied by a suitable modification of the other. Approach: This study introduced a prosody modification method using combining Synchronous Overlap and Add with Fixed-Synthesis (SOLAFS) algorithm and a multi level decomposition based on Discrete Wavelet Transform (DWT) to overcome the limitations cited above. It uses Standard Arabic (SA) sounds. For a purpose of comparison, two techniques based on frame by frame processing are proposed. The first one consists in a pitch synchronous processing of the mth approximation level time segments used in SOLAFS algorithm. It was aimed to modify the prosody of the input speech without affecting the spectral envelop. The second one explores the correlation between [F.sub.1] and [F.sub.0] in the corresponding approximation level of SA sounds and modifies duration and both [F.sub.0] and [F.sub.1] scales. It is based on a re-sampling method using FFT interpolation. The use of multi level analysis was aimed to provide independent control over the spectral envelope. In both techniques, the decomposition level depends on the chosen sampling Frequency ([F.sub.S]). [F.sub.0] marking is based on multi level peaks comparison. Both techniques use an automatic speech classification algorithm based on modified version of the Johnson algorithm. Results: The performances of the proposed techniques are evaluated by listening tests using sentences in SA language sampled at an [F.sub.S] of 16 kHz. It has been found that manipulation in the third approximation level of [F.sub.0] in conjunction with the local [F.sub.1] improves significantly the naturalness of the modified speech compared to the classical prosody modification. Conclusion: This improvement was most suitable for high [F.sub.0] scales from the fact that speaker generally increases [F.sub.1] as they increase their [F.sub.0]. Further, the technique can be used in the manipulation of the remained formant structure. Key words: Prosody modification, SOLAFS, PSOLA, intelligibility, naturalness, distortion, INTRODUCTION The purpose of prosody modification is to change the amplitude, duration and pitch ([F.sub.0]) of a speech segment without affecting the timbre of the speaker voice. Amplitude modification can [...]

Flash ladar systems are compact devices with high frame rates that hold promise for robotics applications, but these devices suffer from poor spatial resolution. This work develops a wavelet preprocessing stage to enhance registration of multiple frames and applies super-resolution to improve the resolution of flash ladar range imagery. The triangle orientation discrimination methodology was used for a subjective evaluation of the effectiveness of super-resolution for flash ladar. Results show statistically significant increases in the probability of target discrimination at all target ranges, as well as a reduction in subject response times for super-resolved imagery. OCIS codes: 100.6640, 110.3000.

This paper presents a statistical measure for the identification of the presence, the location, and the calibration of the strength of singularity in a signal or in any of its derivatives in the presence of measurement noise without the requirement of a baseline using a wavelet based detection technique. For this proposed wavelet based detection of singularities present in a signal, the problem of false alarm and its significant reduction by use of multiple measurements is presented. The importance of the proposed measure on baseline and nonbaseline damage calibration has been discussed from the aspect of structural health monitoring. The findings in this paper can also be used for crosschecking of background noise level in an observed signal. The detection of the existence, location, and extent of an open crack from the first fundamental modeshape of a simply supported beam is presented as an example problem. [DOI: 10.1115/1.3142880] Keywords: singularity detection, wavelet analysis, false alarm, signal to noise ratio, open crack

We describe a numerical reconstruction technique for digital holography by means of the two-dimensional Gabor wavelet transform (2D-GWT). Applying the 2D-GWT to digital holography, the object wave can be reconstructed by calculating the wavelet coefficients of the hologram at the peak of the 2D-GWT automatically. At the same time the effect of the zero-order diffraction image and the twin image are eliminated without spatial filtering. Comparing the numerical reconstruction of a holographic image by the analysis of the one-dimensional Gabor wavelet transform (1D-GWT) with the 2D-GWT, we show that the 2D-GWT method is superior to the 1D-GWT method, especially when the fringes of the hologram are not just along the y direction. The theory and the results of a simulation and experiments are shown. OCIS codes: 090.1995, 100.7410, 120.5050.

The infiltrative nature of lesions is a significant feature of malignant breast lesion on ultrasound image. Characterizing the infiltrative nature of lesions with computationally inexpensive and highly efficacious features is crucial for the realization of a computer-aided diagnosis system. In this study, the infiltrative nature is regarded as an energy that produces irregularly and considerably local variances in a 1-D signal. The local variances can be characterized by a few high octave energies (i.e., the channel energies close to low-frequency bands) in a 1-D discrete periodic wavelet transform. For computational cost reduction, high octave decomposition is performed by a reversible round-off 1-D nonrecursive discrete periodic wavelet transform. A test dataset of breast sonograms with the lesion contour delineated by an experienced physician and two inexperienced persons is built for feature efficacy evaluation. High individual performance results imply that the proposed feature is well correlated with the diagnosis of the experienced physician. Experimental results also reveal that with a great performance improvement, the proposed feature is suitable for the combination with some morphometric parameters. Index Terms--Breast lesion classification, octave energy, reversible round-off 1-D nonrecursive discrete periodic wavelet transform (RRO-NRDPWT), roughness description.

Driven by the demands on healthcare resulting from the shift toward more sedentary lifestyles, considerable effort has been devoted to the monitoring and classification of human activity. In previous studies, various classification schemes and feature extraction methods have been used to identify different activities from a range of different datasets. In this paper, we present a comparison of 14 methods to extract classification features from accelerometer signals. These are based on the wavelet transform and other well-known time- and frequency-domain signal characteristics. To allow an objective comparison between the different features, we used two datasets of activities collected from 20 subjects. The first set comprised three commonly used activities, namely, level walking, stair ascent, and stair descent, and the second a total of eight activities. Furthermore, we compared the classification accuracy for each feature set across different combinations of three different accelerometer placements. The classification analysis has been performed with robust subject-based cross-validation methods using a nearest-neighbor classifier. The findings show that, although the wavelet transform approach can be used to characterize nonstationary signals, it does not perform as accurately as frequency-based features when classifying dynamic activities performed by healthy subjects. Overall, the best feature sets achieved over 95% intersubject classification accuracy. Index Terms--Activity classification, ambulatory monitoring, machine learning, wavelet transform.

Ultrawideband (UWB) communications involve very sparse channels, because the bandwidth increase results in a better time resolution. This property is used in this paper to propose an efficient algorithm that jointly estimates the channel and the transmitted symbols. More precisely, this paper introduces an expectation-maximization (EM) algorithm within a wavelet-domain Bayesian framework for semiblind channel estimation of multiband orthogonal frequency division multiplexing based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding 'insignificant' wavelet coefficients from the estimation process. Simulation results using UWB channels that were issued from both models and measurements show that, under sparseness conditions, the proposed algorithm outperforms pilot-based channel estimation in terms of the mean square error (MSE) and bit error rate (BER). Moreover, the estimation accuracy is improved, whereas the computational complexity is reduced compared with traditional semiblind methods. Index Terms--Bayesian channel estimation, expectation-maximization (EM) algorithm, iterative (turbo) detection, orthogonal frequency-division multiplexing (OFDM), sparse-wavelet-domain representation, ultrawideband (UWB).

Wavelet analyses of tunable diode laser absorption spectroscopy signals were performed. The absorption spectroscopy data were obtained by repeatedly scanning the beams from a tunable diode laser operating in the near infrared across absorption lines of gaseous N[H.sub.3] contained within a windowed glass tube. The laser was modulated and wavelet analyses of the absorption data were performed. It was observed that harmonic wavelets could simultaneously extract the 1f and 2f harmonics as well as higher-order harmonics from the direct absorption data. OCIS codes: 300.6260, 350.6980.

The seismic P phase first arrival identification is a fundamental problem in seismology. The accurate identification of the P-wave first arrival is not a trivial process, particularly when the seismograms present a very low signal-to-noise ratio (SNR) or are contaminated with artificial transients that could produce false alarms. In this paper, a new approach based on higher order statistics and the stationary wavelet transform is presented. The P onset is obtained under a statistical criterion applied in the time--frequency domain. The results have been compared to those estimated by another P phase picking algorithm and P onsets picked by expert analysts. The comparison shows that our proposed method efficiently provides a good estimate of the P onset picks that are consistent with analyst picks, particularly in cases of very low SNR. Index Terms--Kurtosis, P phase identification, seismic signal processing, stationary wavelet transform (SWT).

The relatively new field of framelets shows promise in removing some of the limitations of wavelets. Several applications have benefited from the use of frames, for example, denoising and signal coding. In this research, Fast 1D-2D Framlet Transform algorithm for computing advance transforms are proposed. For a 2D framelet transformation, the algorithm is applied in x-direction first and then in y-direction. The propose method reduces heavily processing time for decomposition of video sequences keeping or overcoming the quality of reconstructed sequences In addition, it cuts heavily the memory demands. Also, the inverse procedures of all the above transform for multidimensional cases are verified. Keywords: Fast computing, framelet transform, filter banks, inverse framelet transform, INTRODUCTION Though standard DWT is a powerful tool for analysis and processing of many real-world signals and images, it suffers from three major disadvantages, Shift- sensitivity, Poor directionality and Lack [...]

We evaluate a method based on the two-dimensional directional wavelet transform and the introduction of a spatial carrier to retrieve optical phase distributions in singular scalar light fields. The performance of the proposed phase-retrieval method is compared with an approach based on Fourier transform. The advantages and limitations of the proposed method are discussed. OCIS codes: 100.5070, 120.5050, 120.6150.

We present the continuous wavelet transform (CWT) method for determining the dispersion curves of the refractive index and extinction coefficient of absorbing thin films by using the transmittance spectrum in the visible and near infrared regions at room temperature. The CWT method is performed on the transmittance spectrum of an a - [Si.sub.1-x][C.sub.x]:H film, and the refractive index and extinction coefficient of the film are continuously determined and compared with the results of the envelope and fringe counting methods. Also the noise filter property of the method is depicted on a theoretically generated noisy signal. Finally, the error analyses of the CWT, envelope, and fringe counting methods are performed. OCIS codes: 070.4560, 310.6860, 070.4790.

In this paper, we propose an automatic method to detect microaneurysms in retina photographs. Microaneurysms are the most frequent and usually the first lesions to appear as a consequence of diabetic retinopathy. So, their detection is necessary for both screening the pathology and follow up (progression measurement). Automating this task, which is currently performed manually, would bring more objectivity and reproducibility. We propose to detect them by locally matching a lesion template in sub-bands of wavelet transformed images. To improve the method performance, we have searched for the best adapted wavelet within the lifting scheme framework. The optimization process is based on a genetic algorithm followed by Powell's direction set descent. Results are evaluated on 120 retinal images analyzed by an expert and the optimal wavelet is compared to different conventional mother wavelets. These images are of three different modalities: there are color photographs, green filtered photographs, and angiographs. Depending on the imaging modality, microaneurysms were detected with a sensitivity of respectively 89.62%, 90.24%, and 93.74% and a positive predictive value of respectively 89.50%, 89.75%, and 91.67%, which is better than previously published methods. Index Terms--Diabetic retinopathy, genetic algorithm, microaneurysms, optimal wavelet transform, template matching.

Speckle noise is an inherent nature of ultrasound images, which may have negative effect on image interpretation and diagnostic tasks. In this paper, we propose several multiscale nonlinear thresholding methods for ultrasound speckle suppression. The wavelet coefficients of the logarithm of image are modeled as the sum of a noise-free component plus an independent noise. Assuming that the noise-free component has some local mixture distribution (MD), and the noise is either Gaussian or Rayleigh, we derive the minimum mean squared error (MMSE) and the averaged maximum a posteriori (AMAP) estimators for noise reduction. We use Gaussian and Laplacian MD for each noise-free wavelet coefficient to characterize their heavy-tailed property. Since we estimate the parameters of the MD using the expectation maximization (EM) algorithm and local neighbors, the proposed MD incorporates some information about the intrascale dependency of the wavelet coefficients. To evaluate our spatially adaptive despeckling methods, we use both real medical ultrasound and synthetically introduced speckle images for speckle suppression. The simulation results show that our method outperforms several recently and the state-of-the-art techniques qualitatively and quantitatively. Index Terms--Averaged maximum a posteriori estimator, complex wavelet transform, image enhancement, mixture priors, MMSE, speckle reduction, ultrasound imaging.

The phase space representation of imaging with optical fields in any state of spatial coherence is developed by using spatial coherence wavelets. It leads to new functions for describing the optical transfer and response of imaging systems when the field is represented by Wigner distribution functions. Specific imaging cases are analyzed in this context, and special attention is devoted to the imaging of two point sources. OCIS codes: 030.1640, 260.1960.

A new scheme for the comparison of wavelet features from images taken at different resolutions is discussed.

This paper proposes a new approach based on auxiliary mass spatial probing by stationary wavelet transform (SWT) to provide a method for crack detection in beamlike structure. SWT can provide accurate estimation of the variances at each scale and facilitate the identification of salient features in a signal. The natural frequencies of a damaged beam with a traversing auxiliary mass change due to the change in flexibility and inertia of the beam as the auxiliary mass is traversed along the beam. Therefore, the auxiliary mass can enhance the effects of the crack on the dynamics of the beam and, therefore, facilitate the identification and location of damage in the beam. That is, the auxiliary mass can be used to probe the dynamic characteristic of the beam by traversing the mass from one end of the beam to the other. However, it is difficult to locate the crack directly from the graphical plot of the natural frequency versus axial location of auxiliary mass. This curve of the natural frequencies can be decomposed by SWT into a smooth, low order curve, called approximation coefficient, and a wavy, high order curve called the detail coefficient, which includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams with auxiliary mass used are computed using the finite element method (FEM). Sixty-four cases are studied using FEM and SWT. The efficiency and practicability of the proposed method is illustrated via experimental testing. The effects of crack depth, crack location, auxiliary mass, and spatial probing interval are investigated. From the simulated and experimental results, the efficiency of the proposed method is demonstrated. [DOI: 10.1115/1.2891242] Keywords: crack detection, beam, stationary wavelet transform, auxiliary mass spatial probing

A discrete diffraction transform (DDT) is a novel discrete wavefield propagation model that is aliasing free for a pixelwise invariant object distribution. For this class of distribution, the model is precise and has no typical discretization effects because it corresponds to accurate calculation of the diffraction integral. A spatial light modulator (SLM) is a good example of a system where a pixelwise invariant distribution appears. Frequency domain regularized inverse algorithms are developed for reconstruction of the object wavefield distribution from the distribution given in the sensor plane. The efficiency of developed frequency domain algorithms is demonstrated by simulation. OCIS codes: 070.2025, 100.3010, 100.3190.

The phase unwrapping algorithm plays a very important role in many noncontact optical profilometries based on triangular measurement theory. Here we focus on discussing how to diminish the phase error caused by incorrect unwrapping path in wavelet transform profilometry. We employ the amplitude value map of wavelet transform coefficients at the wavelet-ridge position to identify the reliability of the phase data and the path of phase unwrapping. This means that the wrapped phase located at the pixel with the highest amplitude value will be selected as the starting point of the phase unwrapping, and that pixels with higher amplitude value will be unwrapped earlier. So the path of phase unwrapping is always in the direction of the pixel with highest amplitude value to the one with lowest amplitude value. Making full use of the amplitude information of wavelet coefficients at the wavelet-ridge position keeps the phase unwrapping error limited to local minimum areas even in the worst case. Computer simulations and experiments verify our theory. OCIS codes: 100.5088, 100.2650, 100.7410, 120.3180.

Author(s): Davide Castelvecchi French mathematician Yves Meyer has won the 2017 Abel Prize for his 'pivotal role' in establishing the theory of wavelets - data-analysis tools used in everything from [...]

The article presents computational efficiency of the Stein's unbiased risk estimate (SURE), a new approach to image denoising.

The article discusses a simple method for building oversampled filter banks and tight frames. Findings reveal that the frames build by the proposed method generate low redundancy and complexity.

Despite of the decent development of the pattern recognition science applications in the last decade of the twentieth century and this century, text recognition remains one of the most important problems in pattern recognition. To the best of our knowledge, little work has been done in the area of Arabic text recognition compared with those for Latin, Chins and Japanese text. The main difficulty encountered when dealing with Arabic text is the cursive nature of Arabic writing in both printed and handwritten forms. An Automatic Arabic Hand-Written Text Recognition (AHTR) System is proposed. An efficient segmentation stage is required in order to divide a cursive word or sub-word into its constituting characters. After a word has been extracted from the scanned image, it is thinned and its base line is calculated by analysis of horizontal density histogram. The pattern is then followed through the base line and the segmentation points are detected. Thus after the segmentation stage, the cursive word is represented by a sequence of isolated characters. The recognition problem thus reduces to that of classifying each character. A set of features extracted from each individual characters. A minimum distance classifier is used. Some approaches are used for processing the characters and post processing added to enhance the results. Recognized characters will be appended directly to a word file which is editable form. Key words: Arabic character, classification, discrete wavelet transform, features selection, INTRODUCTION An optical character recognition system typically consists of the following processing steps: digitization, preprocessing, segmentation, feature extraction, recognition using one or more classifiers and contextual verification or post-processing. Recognition [...]

This paper describes an area and power-efficient VLSI approach for implementing the discrete wavelet transform on streaming multielectrode neurophysiological data in real time. The VLSI implementation is based on the lifting scheme for wavelet computation using the symmlet4 basis with quantized coefficients and integer fixed-point data precision to minimize hardware demands. The proposed design is driven by the need to compress neural signals recorded with high-density microelectrode arrays implanted in the cortex prior to data telemetry. Our results indicate that signal integrity is not compromised by quantization down to 5-bit filter coefficient and 10-bit data precision at intermediate stages. Furthermore, results from analog simulation and modeling show that a hardware-minimized computational core executing filter steps sequentially is advantageous over the pipeline approach commonly used in DWT implementations. The design is compared to that of a B-spline approach that minimizes the number of multipliers at the expense of increasing the number of adders. The performance demonstrates that in vivo real-time DWT computation is feasible prior to data telemetry, permitting large savings in bandwidth requirements and communication costs given the severe limitations on size, energy consumption and power dissipation of an implantable device. Index Terms--B-spline, brain machine interface, lifting, microelectrode arrays, neural signal processing, neuroprosthetic devices, wavelet transform.

Abstract: This article presents some comments on the article recently published by Prazenica and Kurdila under the title 'Volterra Kernel Identification Using Triangular Wavelets'. First some common misconceptions in the [...]

Two of the most expected objectives of transmission line protection are: 1) differentiating precisely the internal faults from external and 2) indicating exactly the fault type using one end data only. This paper proposes an improved solution based on wavelet transform and self-organized neural network. The measured voltage and current signals are preprocessed first and then decomposed using wavelet multiresolution analysis to obtain the high frequency details and low frequency approximations. The patterns formed based on high frequency signal components are arranged as inputs of neural network #1, whose task is to indicate whether the fault is internal or external. The patterns formed using low frequency approximations are arranged as inputs of neural network #2, whose task is to indicate the exact fault type. The new method uses both low and high frequency information of the fault signal to achieve an advanced line protection scheme. The proposed approach is verified using frequency-dependent transmission line model and the test results prove its enhanced performance. A discussion of the application issues for the proposed approach is provided at the end where the generality of the proposed approach and guidance for future study are pointed out. Index Terms--Adaptive resonance theory, boundary protection, fault classification, neural network, pattern recognition, power system faults, power system protection, wavelet transform.

The paper proposes a joint probability density function to model the video wavelet coefficients of any two neighboring frames and then applies this statistical model for denoising. The parameter of the density function that measures the correlation between the wavelet coefficients of the two frames is used as an index for the motion. The joint density function is employed for spatial filtering of the noisy wavelet coefficients by developing a bivariate maximum a posteriori estimator. A recursive time averaging of the spatially filtered wavelet coefficients is adopted for further noise reduction. Simulation results on test video sequences show an improved performance both in terms of the peak signal-to-noise ratio and the perceptual quality compared to that of the other denoising algorithms. Index Terms--Bivariate Gaussian density function, bivariate maximum a posteriori (MAP) estimation, bivariate maximum likelihood (ML) estimation, video denoising, wavelet coefficients.