Search results for: Fast Haar Transform

Authors: Phang Chang, Phang Piau

Abstract:

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.

Keywords: Fast Haar Transform, Haar transform, Wavelet analysis.

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Authors: Sudipta Majumdar, Jayant Bharadwaj

Abstract:

This paper presents feature level image fusion using Haar lifting wavelet transform. Feature fused is edge and boundary information, which is obtained using wavelet transform modulus maxima criteria. Simulation results show the superiority of the result as entropy, gradient, standard deviation are increased for fused image as compared to input images. The proposed methods have the advantages of simplicity of implementation, fast algorithm, perfect reconstruction, and reduced computational complexity. (Computational cost of Haar wavelet is very small as compared to other lifting wavelets.)

Keywords: Lifting wavelet transform, wavelet transform modulus maxima.

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Authors: Abdelkader Magdy, Magdy Saeb, A. Baith Mohamed, Ahmed Khadragi

Abstract:

The Deoxyribonucleic Acid (DNA) which is a doublestranded helix of nucleotides consists of: Adenine (A), Cytosine (C), Guanine (G) and Thymine (T). In this work, we convert this genetic code into an equivalent digital signal representation. Applying a wavelet transform, such as Haar wavelet, we will be able to extract details that are not so clear in the original genetic code. We compare between different organisms using the results of the Haar wavelet Transform. This is achieved by using the trend part of the signal since the trend part bears the most energy of the digital signal representation. Consequently, we will be able to quantitatively reconstruct different biological families.

Keywords: Digital Signal, DNA, Fluctuation part, Haar wavelet, Nucleotides, Trend part.

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Authors: Mohamed I. Mahmoud, Moawad I. M. Dessouky, Salah Deyab, Fatma H. Elfouly

Abstract:

Recently, the Field Programmable Gate Array (FPGA) technology offers the potential of designing high performance systems at low cost. The discrete wavelet transform has gained the reputation of being a very effective signal analysis tool for many practical applications. However, due to its computation-intensive nature, current implementation of the transform falls short of meeting real-time processing requirements of most application. The objectives of this paper are implement the Haar and Daubechies wavelets using FPGA technology. In addition, the comparison between the Haar and Daubechies wavelets is investigated. The Bit Error Rat (BER) between the input audio signal and the reconstructed output signal for each wavelet is calculated. It is seen that the BER using Daubechies wavelet techniques is less than Haar wavelet. The design procedure has been explained and designed using the stat-of-art Electronic Design Automation (EDA) tools for system design on FPGA. Simulation, synthesis and implementation on the FPGA target technology has been carried out.

Keywords: Daubechies wavelet, discrete wavelet transform, Haar wavelet, Xilinx FPGA.

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Authors: Fituri H Belgassem, Abdulbasit Nigrat, Seddeeq Ghrari

Abstract:

In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

Keywords: Piece wise linear transforms, Fast transforms, Fast algorithms.

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Authors: G.Hariharan, K.Kannan

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In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

Keywords: FitzHugh-Nagumo equation, Haar wavelet method, adomain decomposition method, computationally attractive.

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Authors: S. Al Wadi, Mohd Tahir Ismail, Samsul Ariffin Abdul Karim

Abstract:

It is well known that during the developments in the economic sector and through the financial crises occur everywhere in the whole world, volatility measurement is the most important concept in financial time series. Therefore in this paper we discuss the volatility for Amman stocks market (Jordan) for certain period of time. Since wavelet transform is one of the most famous filtering methods and grows up very quickly in the last decade, we compare this method with the traditional technique, Fast Fourier transform to decide the best method for analyzing the volatility. The comparison will be done on some of the statistical properties by using Matlab program.

Keywords: Fast Fourier transforms, Haar wavelet transform, Matlab (Wavelet tools), stocks market, Volatility.

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Authors: Fatma H. Elfouly, Mohamed I. Mahmoud, Moawad I. M. Dessouky, Salah Deyab

Abstract:

Recently, the Field Programmable Gate Array (FPGA) technology offers the potential of designing high performance systems at low cost. The discrete wavelet transform has gained the reputation of being a very effective signal analysis tool for many practical applications. However, due to its computation-intensive nature, current implementation of the transform falls short of meeting real-time processing requirements of most application. The objectives of this paper are implement the Haar and Daubechies wavelets using FPGA technology. In addition, the Bit Error Rate (BER) between the input audio signal and the reconstructed output signal for each wavelet is calculated. From the BER, it is seen that the implementations execute the operation of the wavelet transform correctly and satisfying the perfect reconstruction conditions. The design procedure has been explained and designed using the stat-ofart Electronic Design Automation (EDA) tools for system design on FPGA. Simulation, synthesis and implementation on the FPGA target technology has been carried out.

Keywords: Daubechies wavelet, discrete wavelet transform, Haar wavelet, Xilinx FPGA.

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Authors: K. Sakthivel, R. Nallusamy, C. Kavitha

Abstract:

The system is designed to show images which are related to the query image. Extracting color, texture, and shape features from an image plays a vital role in content-based image retrieval (CBIR). Initially RGB image is converted into HSV color space due to its perceptual uniformity. From the HSV image, Color features are extracted using block color histogram, texture features using Haar transform and shape feature using Fuzzy C-means Algorithm. Then, the characteristics of the global and local color histogram, texture features through co-occurrence matrix and Haar wavelet transform and shape are compared and analyzed for CBIR. Finally, the best method of each feature is fused during similarity measure to improve image retrieval effectiveness and accuracy.

Keywords: Color Histogram, Haar Wavelet Transform, Fuzzy C-means, Co-occurrence matrix; Similarity measure.

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Authors: S. Piramu Kailasam

Abstract:

This study is expected to compress true color image with compression algorithms in color spaces to provide high compression rates. The need of high compression ratio is to improve storage space. Alternative aim is to rank compression algorithms in a suitable color space. The dataset is sequence of true color images with size 128 x 128. HAAR Wavelet is one of the famous wavelet transforms, has great potential and maintains image quality of color images. HAAR wavelet Transform using Set Partitioning in Hierarchical Trees (SPIHT) algorithm with different color spaces framework is applied to compress sequence of images with angles. Embedded Zerotrees of Wavelet (EZW) is a powerful standard method to sequence data. Hence the proposed compression frame work of HAAR wavelet, xyz color space, morphological gradient and applied image with EZW compression, obtained improvement to other methods, in terms of Compression Ratio, Mean Square Error, Peak Signal Noise Ratio and Bits Per Pixel quality measures.

Keywords: Color Spaces, HAAR Wavelet, Morphological Gradient, Embedded Zerotrees Wavelet Compression.

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Authors: Cuong Nguyen Khac, Ju H. Park, Ho-Youl Jung

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This paper proposes a new approach to perform the problem of real-time face detection. The proposed method combines primitive Haar-Like feature and variance value to construct a new feature, so-called Variance based Haar-Like feature. Face in image can be represented with a small quantity of features using this new feature. We used SVM instead of AdaBoost for training and classification. We made a database containing 5,000 face samples and 10,000 non-face samples extracted from real images for learning purposed. The 5,000 face samples contain many images which have many differences of light conditions. And experiments showed that face detection system using Variance based Haar-Like feature and SVM can be much more efficient than face detection system using primitive Haar-Like feature and AdaBoost. We tested our method on two Face databases and one Non-Face database. We have obtained 96.17% of correct detection rate on YaleB face database, which is higher 4.21% than that of using primitive Haar-Like feature and AdaBoost.

Keywords: AdaBoost, Haar-Like feature, SVM, variance, Variance based Haar-Like feature.

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Authors: Abdulnasir Hossen, Ulrich Heute

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In 1990 [1] the subband-DFT (SB-DFT) technique was proposed. This technique used the Hadamard filters in the decomposition step to split the input sequence into low- and highpass sequences. In the next step, either two DFTs are needed on both bands to compute the full-band DFT or one DFT on one of the two bands to compute an approximate DFT. A combination network with correction factors was to be applied after the DFTs. Another approach was proposed in 1997 [2] for using a special discrete wavelet transform (DWT) to compute the discrete Fourier transform (DFT). In the first step of the algorithm, the input sequence is decomposed in a similar manner to the SB-DFT into two sequences using wavelet decomposition with Haar filters. The second step is to perform DFTs on both bands to obtain the full-band DFT or to obtain a fast approximate DFT by implementing pruning at both input and output sides. In this paper, the wavelet-based DFT (W-DFT) with Haar filters is interpreted as SB-DFT with Hadamard filters. The only difference is in a constant factor in the combination network. This result is very important to complete the analysis of the W-DFT, since all the results concerning the accuracy and approximation errors in the SB-DFT are applicable. An application example in spectral analysis is given for both SB-DFT and W-DFT (with different filters). The adaptive capability of the SB-DFT is included in the W-DFT algorithm to select the band of most energy as the band to be computed. Finally, the W-DFT is extended to the two-dimensional case. An application in image transformation is given using two different types of wavelet filters.

Keywords: Image Transform, Spectral Analysis, Sub-Band DFT, Wavelet DFT.

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Authors: Amel Abdoullah Ahmed Dghais, Mohd Tahir Ismail

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In this paper the core objective is to apply discrete wavelet transform and maximal overlap discrete wavelet transform functions namely Haar, Daubechies2, Symmlet4, Coiflet2 and discrete approximation of the Meyer wavelets in non stationary financial time series data from Dow Jones index (DJIA30) of US stock market. The data consists of 2048 daily data of closing index from December 17, 2004 to October 23, 2012. Unit root test affirms that the data is non stationary in the level. A comparison between the results to transform non stationary data to stationary data using aforesaid transforms is given which clearly shows that the decomposition stock market index by discrete wavelet transform is better than maximal overlap discrete wavelet transform for original data.

Keywords: Discrete wavelet transform, maximal overlap discrete wavelet transform, stationarity, autocorrelation function.

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Authors: S.G.Venkatesh, S.K.Ayyaswamy, G.Hariharan

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In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.

Keywords: Haar wavelet method, Bratu's problem, boundary value problems, initial value problems, adomain decomposition method.

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Authors: Wen-Chi Hou, Cheng Luo, Zhewei Jiang, Feng Yan

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In this research, we propose to use the discrete cosine transform to approximate the cumulative distributions of data cube cells- values. The cosine transform is known to have a good energy compaction property and thus can approximate data distribution functions easily with small number of coefficients. The derived estimator is accurate and easy to update. We perform experiments to compare its performance with a well-known technique - the (Haar) wavelet. The experimental results show that the cosine transform performs much better than the wavelet in estimation accuracy, speed, space efficiency, and update easiness.

Keywords: DCT, Data Cube

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Authors: Mario Mastriani

Abstract:

In this work, we present a comparison between different techniques of image compression. First, the image is divided in blocks which are organized according to a certain scan. Later, several compression techniques are applied, combined or alone. Such techniques are: wavelets (Haar's basis), Karhunen-Loève Transform, etc. Simulations show that the combined versions are the best, with minor Mean Squared Error (MSE), and higher Peak Signal to Noise Ratio (PSNR) and better image quality, even in the presence of noise.

Keywords: Haar's basis, Image compression, Karhunen-LoèveTransform, Morton's scan, row-rafter scan.

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Authors: Mario Mastriani, Juliana Gambini

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In this work, we present a comparison between two techniques of image compression. In the first case, the image is divided in blocks which are collected according to zig-zag scan. In the second one, we apply the Fast Cosine Transform to the image, and then the transformed image is divided in blocks which are collected according to zig-zag scan too. Later, in both cases, the Karhunen-Loève transform is applied to mentioned blocks. On the other hand, we present three new metrics based on eigenvalues for a better comparative evaluation of the techniques. Simulations show that the combined version is the best, with minor Mean Absolute Error (MAE) and Mean Squared Error (MSE), higher Peak Signal to Noise Ratio (PSNR) and better image quality. Finally, new technique was far superior to JPEG and JPEG2000.

Keywords: Fast Cosine Transform, image compression, JPEG, JPEG2000, Karhunen-Loève Transform, zig-zag scan.

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Authors: Sungji Han, Youngjoon Han, Hernsoo Hahn

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This paper presents a robust vehicle detection approach using Haar-like feature. It is possible to get a strong edge feature from this Haar-like feature. Therefore it is very effective to remove the shadow of a vehicle on the road. And we can detect the boundary of vehicles accurately. In the paper, the vehicle detection algorithm can be divided into two main steps. One is hypothesis generation, and the other is hypothesis verification. In the first step, it determines vehicle candidates using features such as a shadow, intensity, and vertical edge. And in the second step, it determines whether the candidate is a vehicle or not by using the symmetry of vehicle edge features. In this research, we can get the detection rate over 15 frames per second on our embedded system.

Keywords: vehicle detection, haar-like feauture, single camera, real time

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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, image enhancement, CBCT, image denoising.

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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, single-path delay feedback, 3GPP-LTE.

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Authors: Harpreet Kaur, Vinod Mishra, R. C. Mittal

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In this paper, we have proposed a Haar wavelet quasilinearization method to solve the well known Blasius equation. The method is based on the uniform Haar wavelet operational matrix defined over the interval [0, 1]. In this method, we have proposed the transformation for converting the problem on a fixed computational domain. The Blasius equation arises in the various boundary layer problems of hydrodynamics and in fluid mechanics of laminar viscous flows. Quasi-linearization is iterative process but our proposed technique gives excellent numerical results with quasilinearization for solving nonlinear differential equations without any iteration on selecting collocation points by Haar wavelets. We have solved Blasius equation for 1≤α ≤ 2 and the numerical results are compared with the available results in literature. Finally, we conclude that proposed method is a promising tool for solving the well known nonlinear Blasius equation.

Keywords: Boundary layer Blasius equation, collocation points, quasi-linearization process, uniform haar wavelets.

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Authors: Varun Setia, Vinod Kumar

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In present paper we proposed a simple and effective method to compress an image. Here we found success in size reduction of an image without much compromising with it-s quality. Here we used Haar Wavelet Transform to transform our original image and after quantization and thresholding of DWT coefficients Run length coding and Huffman coding schemes have been used to encode the image. DWT is base for quite populate JPEG 2000 technique.

Keywords: Lossy compression, DWT, quantization, Run length coding, Huffman coding, JPEG2000.

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Authors: Liang-Ta Cheng, Ching-Yu Yang

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Based on fast discrete cosine transform (FDCT), the authors present a high capacity and high perceived quality method for electrocardiogram (ECG) signal. By using a simple adjusting policy to the 1-dimentional (1-D) DCT coefficients, a large volume of secret message can be effectively embedded in an ECG host signal and be successfully extracted at the intended receiver. Simulations confirmed that the resulting perceived quality is good, while the hiding capability of the proposed method significantly outperforms that of existing techniques. In addition, our proposed method has a certain degree of robustness. Since the computational complexity is low, it is feasible for our method being employed in real-time applications.

Keywords: Data hiding, ECG steganography, fast discrete cosine transform, 1-D DCT bundle, real-time applications.

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Authors: Maan M. Shaker

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The electroencephalograph (EEG) signal is one of the most widely signal used in the bioinformatics field due to its rich information about human tasks. In this work EEG waves classification is achieved using the Discrete Wavelet Transform DWT with Fast Fourier Transform (FFT) by adopting the normalized EEG data. The DWT is used as a classifier of the EEG wave's frequencies, while FFT is implemented to visualize the EEG waves in multi-resolution of DWT. Several real EEG data sets (real EEG data for both normal and abnormal persons) have been tested and the results improve the validity of the proposed technique.

Keywords: Bioinformatics, DWT, EEG waves, FFT.

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Authors: Monika Garg, Lillie Dewan

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Three novel and significant contributions are made in this paper Firstly, non-recursive formulation of Haar connection coefficients, pioneered by the present authors is presented, which can be computed very efficiently and avoid stack and memory overflows. Secondly, the generalized approach for state analysis of singular bilinear time-invariant (TI) and time-varying (TV) systems is presented; vis-˜a-vis diversified and complex works reported by different authors. Thirdly, a generalized approach for parameter estimation of bilinear TI and TV systems is also proposed. The unified framework of the proposed method is very significant in that the digital hardware once-designed can be used to perform the complex tasks of state analysis and parameter estimation of different types of bilinear systems single-handedly. The simplicity, effectiveness and generalized nature of the proposed method is established by applying it to different types of bilinear systems for the two tasks.

Keywords: Bilinear Systems, Haar Wavelet, Haar ConnectionCoefficients, Parameter Estimation, Singular Bilinear Systems, StateAnalysis.

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Authors: M.Ghazvini, S. A. Monadjemi, N. Movahhedinia, K. Jamshidi

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In this article, a method has been offered to classify normal and defective tiles using wavelet transform and artificial neural networks. The proposed algorithm calculates max and min medians as well as the standard deviation and average of detail images obtained from wavelet filters, then comes by feature vectors and attempts to classify the given tile using a Perceptron neural network with a single hidden layer. In this study along with the proposal of using median of optimum points as the basic feature and its comparison with the rest of the statistical features in the wavelet field, the relational advantages of Haar wavelet is investigated. This method has been experimented on a number of various tile designs and in average, it has been valid for over 90% of the cases. Amongst the other advantages, high speed and low calculating load are prominent.

Keywords: Defect detection, tile and ceramic quality inspection, wavelet transform, classification, neural networks, statistical features.

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Authors: Jinghui Peng, Shanyu Tang, Jia Li

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Steganalysis seeks to detect the presence of secret data embedded in cover objects, and there is an imminent demand to detect hidden messages in streaming media. This paper shows how a steganalysis algorithm based on Fast Fourier Transform (FFT) can be used to detect the existence of secret data embedded in streaming media. The proposed algorithm uses machine parameter characteristics and a network sniffer to determine whether the Internet traffic contains streaming channels. The detected streaming data is then transferred from the time domain to the frequency domain through FFT. The distributions of power spectra in the frequency domain between original VoIP streams and stego VoIP streams are compared in turn using t-test, achieving the p-value of 7.5686E-176 which is below the threshold. The results indicate that the proposed FFT-based steganalysis algorithm is effective in detecting the secret data embedded in VoIP streaming media.

Keywords: Steganalysis, security, fast Fourier transform, streaming media.

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Authors: Harpreet Kaur, Sudipta Majumdar

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In this paper a method for image dehazing is proposed in lifting wavelet transform domain. Lifting Daubechies (D4) wavelet has been used to obtain the approximate image and detail images.  As the haze is contained in low frequency part, only the approximate image is used for further processing. This region is processed by dehazing algorithm based on dark channel prior (DCP). The dehazed approximate image is then recombined with the detail images using inverse lifting wavelet transform. Implementation of lifting wavelet transform has the advantage of auxiliary memory saving, fast implementation and simplicity. Also, the proposed method deals with near white scene problem, blue horizon issue and localized light sources in a way to enhance image quality and makes the algorithm robust. Simulation results present improvement in terms of visual quality, parameters such as root mean square (RMS) contrast, structural similarity index (SSIM), entropy and execution time.

Keywords: Dark channel prior, image dehazing, lifting wavelet transform.

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Authors: Oğuzhan Urhan

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In this paper, an improved motion estimation (ME) approach based on weighted constrained one-bit transform is proposed for block-based ME employed in video encoders. Binary ME approaches utilize low bit-depth representation of the original image frames with a Boolean exclusive-OR based hardware efficient matching criterion to decrease computational burden of the ME stage. Weighted constrained one-bit transform (WC‑1BT) based approach improves the performance of conventional C-1BT based ME employing 2-bit depth constraint mask instead of a 1-bit depth mask. In this work, the range of constraint mask is further extended to increase ME performance of WC-1BT approach. Experiments reveal that the proposed method provides better ME accuracy compared existing similar ME methods in the literature.

Keywords: Fast motion estimation, low-complexity motion estimation, video coding.

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Authors: Mountassar Maamoun, Mehdi Neggazi, Abdelhamid Meraghni, Daoud Berkani

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This paper presents a VLSI design approach of a highspeed and real-time 2-D Discrete Wavelet Transform computing. The proposed architecture, based on new and fast convolution approach, reduces the hardware complexity in addition to reduce the critical path to the multiplier delay. Furthermore, an advanced twodimensional (2-D) discrete wavelet transform (DWT) implementation, with an efficient memory area, is designed to produce one output in every clock cycle. As a result, a very highspeed is attained. The system is verified, using JPEG2000 coefficients filters, on Xilinx Virtex-II Field Programmable Gate Array (FPGA) device without accessing any external memory. The resulting computing rate is up to 270 M samples/s and the (9,7) 2-D wavelet filter uses only 18 kb of memory (16 kb of first-in-first-out memory) with 256×256 image size. In this way, the developed design requests reduced memory and provide very high-speed processing as well as high PSNR quality.

Keywords: Discrete Wavelet Transform (DWT), Fast Convolution, FPGA, VLSI.

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