Search results for: 2D Gabor wavelet transform

Authors: Shahriar Farzam, Maryam Rastgarpour

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Image denoising plays extremely important role in digital image processing. Enhancement of clinical image research based on Curvelet has been developed rapidly in recent years. In this paper, we present a method for image contrast enhancement for cone beam CT (CBCT) images based on fast discrete curvelet transforms (FDCT) that work through Unequally Spaced Fast Fourier Transform (USFFT). These transforms return a table of Curvelet transform coefficients indexed by a scale parameter, an orientation and a spatial location. Accordingly, the coefficients obtained from FDCT-USFFT can be modified in order to enhance contrast in an image. Our proposed method first uses a two-dimensional mathematical transform, namely the FDCT through unequal-space fast Fourier transform on input image and then applies thresholding on coefficients of Curvelet to enhance the CBCT images. Consequently, applying unequal-space fast Fourier Transform leads to an accurate reconstruction of the image with high resolution. The experimental results indicate the performance of the proposed method is superior to the existing ones in terms of Peak Signal to Noise Ratio (PSNR) and Effective Measure of Enhancement (EME).

Keywords: curvelet transform, CBCT, image enhancement, image denoising

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Authors: Ali Seddiki, Mohamed Djebbouri, Driss Guerchi

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Medical imaging produces human body pictures in digital form. Since these imaging techniques produce prohibitive amounts of data, compression is necessary for storage and communication purposes. In some areas in medicine, it may be sufficient to maintain high image quality only in region of interest (ROI). This paper discusses a contribution to quality purpose compression in the region of interest of scintigraphic images based on dual tree complex wavelet transform (DT-CWT) using Run-Length coding (RLE) and Huffman coding (HC).

Keywords: DT-CWT, region of interest, run length coding, Scintigraphic images

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Authors: Joon-Hoon Park

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In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

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Authors: Rajkumar Kolangarakandy

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Feature extraction and selection is the primary part of any mammogram classification algorithms. The choice of feature, attribute or measurements have an important influence in any classification system. Discrete Wavelet Transformation (DWT) coefficients are one of the prominent features for representing images in frequency domain. The features obtained after the decomposition of the mammogram images using wavelet transformations have higher dimension. Even though the features are higher in dimension, they were highly correlated and redundant in nature. The dimensionality reduction techniques play an important role in selecting the optimum number of features from the higher dimension data, which are highly correlated. PCA is a mathematical tool that reduces the dimensionality of the data while retaining most of the variation in the dataset. In this paper, a multilevel classification of mammogram images using reduced discrete wavelet transformation coefficients and lazy classifiers is proposed. The classification is accomplished in two different levels. In the first level, mammogram ROIs extracted from the dataset is classified as normal and abnormal types. In the second level, all the abnormal mammogram ROIs is classified into benign and malignant too. A further classification is also accomplished based on the variation in structure and intensity distribution of the images in the dataset. The Lazy classifiers called Kstar, IBL and LWL are used for classification. The classification results obtained with the reduced feature set is highly promising and the result is also compared with the performance obtained without dimension reduction.

Keywords: PCA, wavelet transformation, lazy classifiers, Kstar, IBL, LWL

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Authors: Cherifi Mehdi, Lahdir Mourad, Ameur Soltane

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Image compression is used to reduce the number of bits required to represent an image. The Meteosat Second Generation satellite (MSG) allows the acquisition of 12 image files every 15 minutes. Which results a large databases sizes. The transform selected in the images compression should contribute to reduce the data representing the images. The Radon transform retrieves the Radon points that represent the sum of the pixels in a given angle for each direction. Linear predictive coding (LPC) with filtering provides a good decorrelation of Radon points using a Predictor constitute by the Symmetric Nearest Neighbor filter (SNN) coefficients, which result losses during decompression. Finally, Run Length Coding (RLC) gives us a high and fixed compression ratio regardless of the input image. In this paper, a novel image compression method based on the Radon transform and linear predictive coding (LPC) for MSG images is proposed. MSG image compression based on the Radon transform and the LPC provides a good compromise between compression and quality of reconstruction. A comparison of our method with other whose two based on DCT and one on DWT bi-orthogonal filtering is evaluated to show the power of the Radon transform in its resistibility against the quantization noise and to evaluate the performance of our method. Evaluation criteria like PSNR and the compression ratio allows showing the efficiency of our method of compression.

Keywords: image compression, radon transform, linear predictive coding (LPC), run lengthcoding (RLC), meteosat second generation (MSG)

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Authors: A. Biran, P. Sobhe Bidari, K. Raahemifar

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Diabetic Retinopathy (DR) is an eye disease that leads to blindness. The earliest signs of DR are the appearance of red and yellow lesions on the retina called hemorrhages and exudates. Early diagnosis of DR prevents from blindness; hence, many automated algorithms have been proposed to extract hemorrhages and exudates. In this paper, an automated algorithm is presented to extract hemorrhages and exudates separately from retinal fundus images using different image processing techniques including Circular Hough Transform (CHT), Contrast Limited Adaptive Histogram Equalization (CLAHE), Gabor filter and thresholding. Since Optic Disc is the same color as the exudates, it is first localized and detected. The presented method has been tested on fundus images from Structured Analysis of the Retina (STARE) and Digital Retinal Images for Vessel Extraction (DRIVE) databases by using MATLAB codes. The results show that this method is perfectly capable of detecting hard exudates and the highly probable soft exudates. It is also capable of detecting the hemorrhages and distinguishing them from blood vessels.

Keywords: diabetic retinopathy, fundus, CHT, exudates, hemorrhages

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Authors: Devinder Singh, Rajneesh Kumar, Arvind Kumar

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The present investigation deals with the deformation of micropolar generalized thermoelastic solid subjected to thermo-mechanical loading due to a thermal laser pulse. Laplace transform and Fourier transform techniques are used to solve the problem. Thermo-mechanical laser interactions are taken as distributed sources to describe the application of the approach. The closed form expressions of normal stress, tangential stress, coupled stress and temperature are obtained in the domain. Numerical inversion technique of Laplace transform and Fourier transform has been implied to obtain the resulting quantities in the physical domain after developing a computer program. The normal stress, tangential stress, coupled stress and temperature are depicted graphically to show the effect of relaxation times. Some particular cases of interest are deduced from the present investigation.

Keywords: pulse laser, integral transform, thermoelastic, boundary value problem

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Authors: Habiba Ben Abdessalem

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The emergence of giant set of textual data was the push that has encouraged researchers to invest in this field. The purpose of textual data analysis methods is to facilitate access to such type of data by providing various graphic visualizations. Applying these methods requires a corpus pretreatment step, whose standards are set according to the objective of the problem studied. This step determines the forms list contained in contingency table by keeping only those information carriers. This step may, however, lead to noisy contingency tables, so the use of wavelet denoising function. The validity of the proposed approach is tested on a text database that offers economic and political events in Tunisia for a well definite period.

Keywords: textual data, wavelet, denoising, contingency table

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Authors: Neziha Jaouedi, Noureddine Boujnah, Mohamed Salim Bouhlel

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In the framework of human machine interaction systems enhancement, we focus throw this paper on human behavior analysis and action recognition. Human behavior is characterized by actions and reactions duality (movements, psychological modification, verbal and emotional expression). It’s worth noting that many information is hidden behind gesture, sudden motion points trajectories and speeds, many research works reconstructed an information retrieval issues. In our work we will focus on motion extraction, tracking and action recognition using wavelet network approaches. Our contribution uses an analysis of human subtraction by Gaussian Mixture Model (GMM) and body movement through trajectory models of motion constructed from kalman filter. These models allow to remove the noise using the extraction of the main motion features and constitute a stable base to identify the evolutions of human activity. Each modality is used to recognize a human action using wavelets of derived beta distributions approach. The proposed approach has been validated successfully on a subset of KTH and UCF sports database.

Keywords: feautures extraction, human action classifier, wavelet neural network, beta wavelet

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Authors: Michael Zimba

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A novel set of features for copy-move image forgery, CMIF, detection method is proposed. The proposed set presents a new approach which relies on electrostatic field theory, EFT. Solely for the purpose of reducing the dimension of a suspicious image, firstly performs discrete wavelet transform, DWT, of the suspicious image and extracts only the approximation subband. The extracted subband is then bijectively mapped onto a virtual electrostatic field where concepts of EFT are utilised to extract robust features. The extracted features are shown to be invariant to additive noise, JPEG compression, and affine transformation. The proposed features can also be used in general object matching.

Keywords: virtual electrostatic field, features, affine transformation, copy-move image forgery

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Saurabh Farkya, Govinda Surampudi

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Optical Character Recognition is one of the current major research areas. This paper is focussed on recognition of Devanagari script and its sound generation. This Paper consists of two parts. First, Optical Character Recognition of Devnagari handwritten Script. Second, speech synthesis of the recognized text. This paper shows an implementation of support vector machines for the purpose of Devnagari Script recognition. The Support Vector Machines was trained with Multi Domain features; Transform Domain and Spatial Domain or Structural Domain feature. Transform Domain includes the wavelet feature of the character. Structural Domain consists of Distance Profile feature and Gradient feature. The Segmentation of the text document has been done in 3 levels-Line Segmentation, Word Segmentation, and Character Segmentation. The pre-processing of the characters has been done with the help of various Morphological operations-Otsu's Algorithm, Erosion, Dilation, Filtration and Thinning techniques. The Algorithm was tested on the self-prepared database, a collection of various handwriting. Further, Unicode was used to convert recognized Devnagari text into understandable computer document. The document so obtained is an array of codes which was used to generate digitized text and to synthesize Hindi speech. Phonemes from the self-prepared database were used to generate the speech of the scanned document using concatenation technique.

Keywords: Character Recognition (OCR), Text to Speech (TTS), Support Vector Machines (SVM), Library of Support Vector Machines (LIBSVM)

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Authors: Mohmmad A. Obeidat, Amjed Al Fahoum, Ayman M. Mansour

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The recognition of an abnormal activity of the brain functionality is a vital issue. To determine the type of the abnormal activity either a brain image or brain signal are usually considered. Imaging localizes the defect within the brain area and relates this area with somebody functionalities. However, some functions may be disturbed without affecting the brain as in epilepsy. In this case, imaging may not provide the symptoms of the problem. A cheaper yet efficient approach that can be utilized to detect abnormal activity is the measurement and analysis of the electroencephalogram (EEG) signals. The main goal of this work is to come up with a new method to facilitate the classification of the abnormal and disorder activities within the brain directly using EEG signal processing, which makes it possible to be applied in an on-line monitoring system.

Keywords: EEG, wavelet, epilepsy, detection

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Authors: Manoj Gupta, Nirmendra Singh Bhadauria

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Most of the applications in image processing require high spatial and high spectral resolution in a single image. For example satellite image system, the traffic monitoring system, and long range sensor fusion system all use image processing. However, most of the available equipment is not capable of providing this type of data. The sensor in the surveillance system can only cover the view of a small area for a particular focus, yet the demanding application of this system requires a view with a high coverage of the field. Image fusion provides the possibility of combining different sources of information. In this paper, we have decomposed the image using DTCWT and then fused using average and hybrid of (maxima and average) pixel level techniques and then compared quality of both the images using PSNR.

Keywords: image fusion, DWT, DT-CWT, PSNR, average image fusion, hybrid image fusion

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Authors: Chia Jui Hsieh, Jyh Cheng Chen, Chih Wei Kuo, Ruei Teng Wang, Woei Chyn Chu

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Compressed sensing (CS) based computed tomographic (CT) reconstruction algorithm utilizes total variation (TV) to transform CT image into sparse domain and minimizes L1-norm of sparse image for reconstruction. Different from the traditional CS based reconstruction which only calculates x-coordinate and y-coordinate TV to transform CT images into sparse domain, we propose a multi-directional TV to transform tomographic image into sparse domain for low-dose reconstruction. Our method considers all possible directions of TV calculations around a pixel, so the sparse transform for CS based reconstruction is more accurate. In 2D CT reconstruction, we use eight-directional TV to transform CT image into sparse domain. Furthermore, we also use 26-directional TV for 3D reconstruction. This multi-directional sparse transform method makes CS based reconstruction algorithm more powerful to reduce noise and increase image quality. To validate and evaluate the performance of this multi-directional sparse transform method, we use both Shepp-Logan phantom and a head phantom as the targets for reconstruction with the corresponding simulated sparse projection data (angular sampling interval is 5 deg and 6 deg, respectively). From the results, the multi-directional TV method can reconstruct images with relatively less artifacts compared with traditional CS based reconstruction algorithm which only calculates x-coordinate and y-coordinate TV. We also choose RMSE, PSNR, UQI to be the parameters for quantitative analysis. From the results of quantitative analysis, no matter which parameter is calculated, the multi-directional TV method, which we proposed, is better.

Keywords: compressed sensing (CS), low-dose CT reconstruction, total variation (TV), multi-directional gradient operator

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Authors: Ines Elouedi, Atef Hammouda

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This paper presents a new fast version of the generalized Multi-Directional Radon Transform method. The new method uses the inverse Fast Fourier Transform to lead to a faster Generalized Radon projections. We prove in this paper that the fast algorithm leads to almost the same results of the eldest one but with a considerable lower time computation cost. The projection end result of the fast method is a parameterized Radon space where a high valued pixel allows the detection of a curve from the original image. The proposed fast inversion algorithm leads to an exact reconstruction of the initial image from the Radon space. We show examples of the impact of this algorithm on the pattern recognition domain.

Keywords: fast generalized multi-directional Radon transform, curve, exact reconstruction, pattern recognition

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Authors: M. A. Ben Messaoud, A. Bouzid, N. Ellouze

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Speech Segmentation is the measure of the change point detection for partitioning an input speech signal into regions each of which accords to only one speaker. In this paper, we apply two features based on multi-scale product (MP) of the clean speech, namely the spectral centroid of MP, and the zero crossings rate of MP. We focus on multi-scale product analysis as an important tool for segmentation extraction. The multi-scale product is based on making the product of the speech wavelet transform coefficients at three successive dyadic scales. We have evaluated our method on the Keele database. Experimental results show the effectiveness of our method presenting a good performance. It shows that the two simple features can find word boundaries, and extracted the segments of the clean speech.

Keywords: multiscale product, spectral centroid, speech segmentation, zero crossings rate

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: N. Dahraoui, M. Boulakroune, D. Benatia

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In this paper, the improvement by deconvolution of the depth resolution in Secondary Ion Mass Spectrometry (SIMS) analysis is considered. Indeed, we have developed a new Tikhonov-Miller deconvolution algorithm where a priori model of the solution is included. This is a denoisy and pre-deconvoluted signal obtained from: firstly, by the application of wavelet shrinkage algorithm, secondly by the introduction of the obtained denoisy signal in an iterative deconvolution algorithm. In particular, we have focused the light on the effect of the iterations number on the evolution of the deconvoluted signals. The SIMS profiles are multilayers of Boron in Silicon matrix.

Keywords: DRF, in-depth resolution, multiresolution deconvolution, SIMS, wavelet shrinkage

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Authors: Manoel Pereira, Alvaro Veiga, Camila Epprecht, Renato Costa

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This paper introduces an empirical version of the Esscher transform for risk-neutral option pricing. Traditional parametric methods require the formulation of an explicit risk-neutral model and are operational only for a few probability distributions for the returns of the underlying. In our proposal, we make only mild assumptions on the pricing kernel and there is no need for the formulation of the risk-neutral model for the returns. First, we simulate sample paths for the returns under the physical distribution. Then, based on the empirical Esscher transform, the sample is reweighted, giving rise to a risk-neutralized sample from which derivative prices can be obtained by a weighted sum of the options pay-offs in each path. We compare our proposal with some traditional parametric pricing methods in four experiments with artificial and real data.

Keywords: esscher transform, generalized autoregressive Conditional Heteroscedastic (GARCH), nonparametric option pricing

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Authors: T. Damak, S. Houidi, M. A. Ben Ayed, N. Masmoudi

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The Versatile Video Coding standard (VVC) is actually under development by the Joint Video Exploration Team (or JVET). An Adaptive Multiple Transforms (AMT) approach was announced. It is based on different transform modules that provided an efficient coding. However, the AMT solution raises several issues especially regarding the complexity of the selected set of transforms. This can be an important issue, particularly for a future industrial adoption. This paper proposed an efficient hardware implementation of the most used transform in AMT approach: the DCT II. The developed circuit is adapted to different block sizes and can reach a minimum frequency of 192 MHz allowing an optimized execution time.

Keywords: adaptive multiple transforms, AMT, DCT II, hardware, transform, versatile video coding, VVC

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Authors: Kritika Bansal, Akwinder Kaur, Shruti Gujral

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In this paper, the approach of denoising is solved by using a new hybrid technique which associates the different denoising methods. Wavelet thresholding and anisotropic diffusion filter are the two different filters in our hybrid techniques. The Wavelet thresholding removes the noise by removing the high frequency components with lesser edge preservation, whereas an anisotropic diffusion filters is based on partial differential equation, (PDE) to remove the speckle noise. This PDE approach is used to preserve the edges and provides better smoothing. So our new method proposes a combination of these two filtering methods which performs better results in terms of peak signal to noise ratio (PSNR), coefficient of correlation (COC) and equivalent no of looks (ENL).

Keywords: denoising, anisotropic diffusion filter, multiplicative noise, speckle, wavelets

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Authors: Mohammad H. Fattahi

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Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. The noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

Keywords: chaotic behavior, wavelet, noise reduction, river flow

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Authors: Nadia Ben Youssef, Aicha Bouzid

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Gradient estimation is one of the most fundamental tasks in the field of image processing in general, and more particularly for color images since that the research in color image gradient remains limited. The widely used gradient method is Di Zenzo’s gradient operator, which is based on the measure of squared local contrast of color images. The proposed gradient mechanism, presented in this paper, is based on the principle of the Di Zenzo’s approach using quaternion representation. This edge detector is compared to a marginal approach based on multiscale product of wavelet transform and another vector approach based on quaternion convolution and vector gradient approach. The experimental results indicate that the proposed color gradient operator outperforms marginal approach, however, it is less efficient then the second vector approach.

Keywords: gradient, edge detection, color image, quaternion

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Authors: Ahmet Karagoz, Irfan Karagoz

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Synthetic Aperture Radar (SAR) is a radar mechanism that can be integrated into manned and unmanned aerial vehicles to create high-resolution images in all weather conditions, regardless of day and night. In this study, SAR images of military vehicles with different azimuth and descent angles are pre-processed at the first stage. The main purpose here is to reduce the high speckle noise found in SAR images. For this, the Wiener adaptive filter, the mean filter, and the median filters are used to reduce the amount of speckle noise in the images without causing loss of data. During the image segmentation phase, pixel values are ordered so that the target vehicle region is separated from other regions containing unnecessary information. The target image is parsed with the brightest 20% pixel value of 255 and the other pixel values of 0. In addition, by using appropriate parameters of statistical region merging algorithm, segmentation comparison is performed. In the step of feature extraction, the feature vectors belonging to the vehicles are obtained by using Gabor filters with different orientation, frequency and angle values. A number of Gabor filters are created by changing the orientation, frequency and angle parameters of the Gabor filters to extract important features of the images that form the distinctive parts. Finally, images are classified by sparse representation method. In the study, l₁ norm analysis of sparse representation is used. A joint database of the feature vectors generated by the target images of military vehicle types is obtained side by side and this database is transformed into the matrix form. In order to classify the vehicles in a similar way, the test images of each vehicle is converted to the vector form and l₁ norm analysis of the sparse representation method is applied through the existing database matrix form. As a result, correct recognition has been performed by matching the target images of military vehicles with the test images by means of the sparse representation method. 97% classification success of SAR images of different military vehicle types is obtained.

Keywords: automatic target recognition, sparse representation, image classification, SAR images

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Authors: Xin-Yu Shih, Yue-Qu Liu, Hong-Ru Chou

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This paper presents a low-area and fully-reconfigurable Fast Fourier Transform (FFT) hardware design for 3GPP-LTE communication standard. It can fully support 32 different FFT sizes, up to 2048 FFT points. Besides, a special processing element is developed for making reconfigurable computing characteristics possible, while first-in first-out (FIFO) scheduling scheme design technique is proposed for hardware-friendly FIFO resource arranging. In a synthesis chip realization via TSMC 40 nm CMOS technology, the hardware circuit only occupies core area of 0.2325 mm² and dissipates 233.5 mW at maximal operating frequency of 250 MHz.

Keywords: reconfigurable, fast Fourier transform (FFT), single-path delay feedback (SDF), 3GPP-LTE

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Raquel Ramos López, Anissa El-Khattabi, Ana Lucila Sandoval Orozco, Luis Javier García Villalba

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An increasing number of mobile devices with integrated cameras has meant that most digital video comes from these devices. These digital videos can be made anytime, anywhere and for different purposes. They can also be shared on the Internet in a short period of time and may sometimes contain recordings of illegal acts. The need to reliably trace the origin becomes evident when these videos are used for forensic purposes. This work proposes an algorithm to identify the brand and model of mobile device which generated the video. Its procedure is as follows: after obtaining the relevant video information, a classification algorithm based on sensor noise and Wavelet Transform performs the aforementioned identification process. We also present experimental results that support the validity of the techniques used and show promising results.

Keywords: digital video, forensics analysis, key frame, mobile device, PRNU, sensor noise, source identification

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Authors: Tesfay Mekonnen Weldegerima

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Analysis of precipitation time series is a fundamental undertaking in meteorology and hydrology. The extreme precipitation scenario of the Kulfo River watershed is studied using wavelet analysis and atmospheric transport, a lagrangian trajectory model. Daily rainfall data for the 1991-2020 study periods are collected from the office of the Ethiopian Meteorology Institute. Meteorological fields on a three-dimensional grid at 0.5o x 0.5o spatial resolution and daily temporal resolution are also obtained from the Global Data Assimilation System (GDAS). Wavelet analysis of the daily precipitation processed with the lag-1 coefficient reveals some high power recurred once every 38 to 60 days with greater than 95% confidence for red noise. The analysis also identified inter-annual periodicity in the periods 2002 - 2005 and 2017 - 2019. Back trajectory analysis for 3-day periods up to May 19/2011, indicates the Indian Ocean source; trajectories crossed the eastern African escarpment to arrive at the Kulfo watershed. Atmospheric flows associated with the Western Indian monsoon redirected by the low-level Somali winds and Arabian ridge are responsible for the moisture supply. The time-localization of the wavelet power spectrum yields valuable hydrological information, and the back trajectory approaches provide useful characterization of air mass source.

Keywords: extreme precipitation events, power spectrum, back trajectory, kulfo watershed

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Authors: Sofia M. Karadimitriou, Kostas Triantafyllopoulos, Timothy Heaton

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Reduced dimension Dynamic Spatio-Temporal Models (DSTMs) jointly describe the spatial and temporal evolution of a function observed subject to noise. A basic state space model is adopted for the discrete temporal variation, while a continuous autoregressive structure describes the continuous spatial evolution. Application of such a DSTM relies upon the pre-selection of a suitable reduced set of basic functions and this can present a challenge in practice. In this talk, we propose an online estimation method for high dimensional spatio-temporal data based upon DSTM and we attempt to resolve this issue by allowing the basis to adapt to the observed data. Specifically, we present a wavelet decomposition in order to obtain a parsimonious approximation of the spatial continuous process. This parsimony can be achieved by placing a Laplace prior distribution on the wavelet coefficients. The aim of using the Laplace prior, is to filter wavelet coefficients with low contribution, and thus achieve the dimension reduction with significant computation savings. We then propose a Hierarchical Bayesian State Space model, for the estimation of which we offer an appropriate particle filter algorithm. The proposed methodology is illustrated using real environmental data.

Keywords: multidimensional Laplace prior, particle filtering, spatio-temporal modelling, wavelets

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