International Science Index
Sparsity-Based Unsupervised Unmixing of Hyperspectral Imaging Data Using Basis Pursuit
Mixing in the hyperspectral imaging occurs due to the low spatial resolutions of the used cameras. The existing pure materials “endmembers” in the scene share the spectra pixels with different amounts called “abundances”. Unmixing of the data cube is an important task to know the present endmembers in the cube for the analysis of these images. Unsupervised unmixing is done with no information about the given data cube. Sparsity is one of the recent approaches used in the source recovery or unmixing techniques. The l1-norm optimization problem “basis pursuit” could be used as a sparsity-based approach to solve this unmixing problem where the endmembers is assumed to be sparse in an appropriate domain known as dictionary. This optimization problem is solved using proximal method “iterative thresholding”. The l1-norm basis pursuit optimization problem as a sparsity-based unmixing technique was used to unmix real and synthetic hyperspectral data cubes.
3D Object Model Reconstruction Based on Polywogs Wavelet Network Parametrization
This paper presents a technique for compact three
dimensional (3D) object model reconstruction using wavelet
networks. It consists to transform an input surface vertices
into signals,and uses wavelet network parameters for signal
approximations. To prove this, we use a wavelet network architecture
founded on several mother wavelet families. POLYnomials
WindOwed with Gaussians (POLYWOG) wavelet families are used
to maximize the probability to select the best wavelets which
ensure the good generalization of the network. To achieve a better
reconstruction, the network is trained several iterations to optimize the
wavelet network parameters until the error criterion is small enough.
Experimental results will shown that our proposed technique can
effectively reconstruct an irregular 3D object models when using
the optimized wavelet network parameters. We will prove that an
accurateness reconstruction depends on the best choice of the mother
Effects of Various Wavelet Transforms in Dynamic Analysis of Structures
Time history dynamic analysis of structures is considered as an exact method while being computationally intensive. Filtration of earthquake strong ground motions applying wavelet transform is an approach towards reduction of computational efforts, particularly in optimization of structures against seismic effects. Wavelet transforms are categorized into continuum and discrete transforms. Since earthquake strong ground motion is a discrete function, the discrete wavelet transform is applied in the present paper. Wavelet transform reduces analysis time by filtration of non-effective frequencies of strong ground motion. Filtration process may be repeated several times while the approximation induces more errors. In this paper, strong ground motion of earthquake has been filtered once applying each wavelet. Strong ground motion of Northridge earthquake is filtered applying various wavelets and dynamic analysis of sampled shear and moment frames is implemented. The error, regarding application of each wavelet, is computed based on comparison of dynamic response of sampled structures with exact responses. Exact responses are computed by dynamic analysis of structures applying non-filtered strong ground motion.
Automatic Detection of Defects in Ornamental Limestone Using Wavelets
A methodology based on wavelets is proposed for the automatic location and delimitation of defects in limestone plates. Natural defects include dark colored spots, crystal zones trapped in the stone, areas of abnormal contrast colors, cracks or fracture lines, and fossil patterns. Although some of these may or may not be considered as defects according to the intended use of the plate, the goal is to pair each stone with a map of defects that can be overlaid on a computer display. These layers of defects constitute a database that will allow the preliminary selection of matching tiles of a particular variety, with specific dimensions, for a requirement of N square meters, to be done on a desktop computer rather than by a two-hour search in the storage park, with human operators manipulating stone plates as large as 3 m x 2 m, weighing about one ton. Accident risks and work times are reduced, with a consequent increase in productivity. The base for the algorithm is wavelet decomposition executed in two instances of the original image, to detect both hypotheses – dark and clear defects. The existence and/or size of these defects are the gauge to classify the quality grade of the stone products. The tuning of parameters that are possible in the framework of the wavelets corresponds to different levels of accuracy in the drawing of the contours and selection of the defects size, which allows for the use of the map of defects to cut a selected stone into tiles with minimum waste, according the dimension of defects allowed.
Calcification Classification in Mammograms Using Decision Trees
Cancer affects people globally with breast cancer being a leading killer. Breast cancer is due to the uncontrollable multiplication of cells resulting in a tumour or neoplasm. Tumours are called ‘benign’ when cancerous cells do not ravage other body tissues and ‘malignant’ if they do so. As mammography is an effective breast cancer detection tool at an early stage which is the most treatable stage it is the primary imaging modality for screening and diagnosis of this cancer type. This paper presents an automatic mammogram classification technique using wavelet and Gabor filter. Correlation feature selection is used to reduce the feature set and selected features are classified using different decision trees.
A Numerical Solution Based On Operational Matrix of Differentiation of Shifted Second Kind Chebyshev Wavelets for a Stefan Problem
In this study, one dimensional phase change problem
(a Stefan problem) is considered and a numerical solution of this
problem is discussed. First, we use similarity transformation to
convert the governing equations into ordinary differential equations
with its boundary conditions. The solutions of ordinary differential
equation with the associated boundary conditions and interface
condition (Stefan condition) are obtained by using a numerical
approach based on operational matrix of differentiation of shifted
second kind Chebyshev wavelets. The obtained results are compared
with existing exact solution which is sufficiently accurate.
Wavelet Based Residual Method of Detecting GSM Signal Strength Fading
In this paper, GSM signal strength was measured in
order to detect the type of the signal fading phenomenon using onedimensional
multilevel wavelet residual method and neural network
clustering to determine the average GSM signal strength received in
the study area. The wavelet residual method predicted that the GSM
signal experienced slow fading and attenuated with MSE of 3.875dB.
The neural network clustering revealed that mostly -75dB, -85dB and
-95dB were received. This means that the signal strength received in
the study is a weak signal.
Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices
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
Optimal Control of Volterra Integro-Differential Systems Based On Legendre Wavelets and Collocation Method
In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential
(VID) equation is considered. The method is developed by means
of the Legendre wavelet approximation and collocation method. The
properties of Legendre wavelet together with Gaussian integration
method are utilized to reduce the problem to the solution of nonlinear
programming one. Some numerical examples are given to confirm the
accuracy and ease of implementation of the method.
Feature Level Fusion of Multimodal Images Using Haar Lifting Wavelet Transform
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.)
A Comparative Study between Discrete Wavelet Transform and Maximal Overlap Discrete Wavelet Transform for Testing Stationarity
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.
Automatic Detection of Breast Tumors in Sonoelastographic Images Using DWT
Breast Cancer is the most common malignancy in women and the second leading cause of death for women all over the world. Earlier the detection of cancer, better the treatment. The diagnosis and treatment of the cancer rely on segmentation of Sonoelastographic images. Texture features has not considered for Sonoelastographic segmentation. Sonoelastographic images of 15 patients containing both benign and malignant tumorsare considered for experimentation.The images are enhanced to remove noise in order to improve contrast and emphasize tumor boundary. It is then decomposed into sub-bands using single level Daubechies wavelets varying from single co-efficient to six coefficients. The Grey Level Co-occurrence Matrix (GLCM), Local Binary Pattern (LBP) features are extracted and then selected by ranking it using Sequential Floating Forward Selection (SFFS) technique from each sub-band. The resultant images undergo K-Means clustering and then few post-processing steps to remove the false spots. The tumor boundary is detected from the segmented image. It is proposed that Local Binary Pattern (LBP) from the vertical coefficients of Daubechies wavelet with two coefficients is best suited for segmentation of Sonoelastographic breast images among the wavelet members using one to six coefficients for decomposition. The results are also quantified with the help of an expert radiologist. The proposed work can be used for further diagnostic process to decide if the segmented tumor is benign or malignant.
Numerical Solution of a Laminar Viscous Flow Boundary Layer Equation Using Uniform Haar Wavelet Quasi-linearization Method
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.
The Utility of Wavelet Transform in Surface Electromyography Feature Extraction -A Comparative Study of Different Mother Wavelets
Electromyography (EMG) signal processing has been investigated remarkably regarding various applications such as in rehabilitation systems. Specifically, wavelet transform has served as a powerful technique to scrutinize EMG signals since wavelet transform is consistent with the nature of EMG as a non-stationary signal. In this paper, the efficiency of wavelet transform in surface EMG feature extraction is investigated from four levels of wavelet decomposition and a comparative study between different mother wavelets had been done. To recognize the best function and level of wavelet analysis, two evaluation criteria, scatter plot and RES index are recruited. Hereupon, four wavelet families, namely, Daubechies, Coiflets, Symlets and Biorthogonal are studied in wavelet decomposition stage. Consequently, the results show that only features from first and second level of wavelet decomposition yields good performance and some functions of various wavelet families can lead to an improvement in separability class of different hand movements.
Evaluation of Haar Cascade Classifiers Designed for Face Detection
In the past years a lot of effort has been made in the
field of face detection. The human face contains important features
that can be used by vision-based automated systems in order to
identify and recognize individuals. Face location, the primary step of
the vision-based automated systems, finds the face area in the input
image. An accurate location of the face is still a challenging task.
Viola-Jones framework has been widely used by researchers in order
to detect the location of faces and objects in a given image. Face
detection classifiers are shared by public communities, such as
OpenCV. An evaluation of these classifiers will help researchers to
choose the best classifier for their particular need. This work focuses
of the evaluation of face detection classifiers minding facial
Investigation on Feature Extraction and Classification of Medical Images
In this paper we present the deep study about the Bio-
Medical Images and tag it with some basic extracting features (e.g.
color, pixel value etc). The classification is done by using a nearest
neighbor classifier with various distance measures as well as the
automatic combination of classifier results. This process selects a
subset of relevant features from a group of features of the image. It
also helps to acquire better understanding about the image by
describing which the important features are. The accuracy can be
improved by increasing the number of features selected. Various
types of classifications were evolved for the medical images like
Support Vector Machine (SVM) which is used for classifying the
Bacterial types. Ant Colony Optimization method is used for optimal
results. It has high approximation capability and much faster
convergence, Texture feature extraction method based on Gabor
Optic Disc Detection by Earth Mover's Distance Template Matching
This paper presents a method for the detection of OD in the retina which takes advantage of the powerful preprocessing techniques such as the contrast enhancement, Gabor wavelet transform for vessel segmentation, mathematical morphology and Earth Mover-s distance (EMD) as the matching process. The OD detection algorithm is based on matching the expected directional pattern of the retinal blood vessels. Vessel segmentation method produces segmentations by classifying each image pixel as vessel or nonvessel, based on the pixel-s feature vector. Feature vectors are composed of the pixel-s intensity and 2D Gabor wavelet transform responses taken at multiple scales. A simple matched filter is proposed to roughly match the direction of the vessels at the OD vicinity using the EMD. The minimum distance provides an estimate of the OD center coordinates. The method-s performance is evaluated on publicly available DRIVE and STARE databases. On the DRIVE database the OD center was detected correctly in all of the 40 images (100%) and on the STARE database the OD was detected correctly in 76 out of the 81 images, even in rather difficult pathological situations.
Speckle Reducing Contourlet Transform for Medical Ultrasound Images
Speckle noise affects all coherent imaging systems
including medical ultrasound. In medical images, noise suppression
is a particularly delicate and difficult task. A tradeoff between noise
reduction and the preservation of actual image features has to be made
in a way that enhances the diagnostically relevant image content.
Even though wavelets have been extensively used for denoising
speckle images, we have found that denoising using contourlets gives
much better performance in terms of SNR, PSNR, MSE, variance and
correlation coefficient. The objective of the paper is to determine the
number of levels of Laplacian pyramidal decomposition, the number
of directional decompositions to perform on each pyramidal level and
thresholding schemes which yields optimal despeckling of medical
ultrasound images, in particular. The proposed method consists of the
log transformed original ultrasound image being subjected to contourlet
transform, to obtain contourlet coefficients. The transformed
image is denoised by applying thresholding techniques on individual
band pass sub bands using a Bayes shrinkage rule. We quantify the
achieved performance improvement.
Nonstational Dual Wavelet Frames in Sobolev Spaces
In view of the good properties of nonstationary wavelet frames and the better flexibility of wavelets in Sobolev spaces, the nonstationary dual wavelet frames in a pair of dual Sobolev spaces are studied in this paper. We mainly give the oblique extension principle and the mixed extension principle for nonstationary dual wavelet frames in a pair of dual Sobolev spaces Hs(Rd) and H-s(Rd).
A New Voting Approach to Texture Defect Detection Based on Multiresolutional Decomposition
Wavelets have provided the researchers with
significant positive results, by entering the texture defect detection domain. The weak point of wavelets is that they are one-dimensional
by nature so they are not efficient enough to describe and analyze two-dimensional functions. In this paper we present a new method to
detect the defect of texture images by using curvelet transform.
Simulation results of the proposed method on a set of standard
texture images confirm its correctness. Comparing the obtained results indicates the ability of curvelet transform in describing
discontinuity in two-dimensional functions compared to wavelet
Performance Evaluation of ROI Extraction Models from Stationary Images
In this paper three basic approaches and different
methods under each of them for extracting region of interest (ROI)
from stationary images are explored. The results obtained for each of
the proposed methods are shown, and it is demonstrated where each
method outperforms the other. Two main problems in ROI
extraction: the channel selection problem and the saliency reversal
problem are discussed and how best these two are addressed by
various methods is also seen. The basic approaches are 1) Saliency
based approach 2) Wavelet based approach 3) Clustering based
approach. The saliency approach performs well on images containing
objects of high saturation and brightness. The wavelet based
approach performs well on natural scene images that contain regions
of distinct textures. The mean shift clustering approach partitions the
image into regions according to the density distribution of pixel
intensities. The experimental results of various methodologies show
that each technique performs at different acceptable levels for
various types of images.
Haar Wavelet Method for Solving Fitz Hugh-Nagumo Equation
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.
Peakwise Smoothing of Data Models using Wavelets
Smoothing or filtering of data is first preprocessing step
for noise suppression in many applications involving data analysis.
Moving average is the most popular method of smoothing the data,
generalization of this led to the development of Savitzky-Golay filter.
Many window smoothing methods were developed by convolving
the data with different window functions for different applications;
most widely used window functions are Gaussian or Kaiser. Function
approximation of the data by polynomial regression or Fourier
expansion or wavelet expansion also gives a smoothed data. Wavelets
also smooth the data to great extent by thresholding the wavelet
coefficients. Almost all smoothing methods destroys the peaks and
flatten them when the support of the window is increased. In certain
applications it is desirable to retain peaks while smoothing the data
as much as possible. In this paper we present a methodology called
as peak-wise smoothing that will smooth the data to any desired level
without losing the major peak features.
Speaker Identification Using Admissible Wavelet Packet Based Decomposition
Mel Frequency Cepstral Coefficient (MFCC) features
are widely used as acoustic features for speech recognition as well
as speaker recognition. In MFCC feature representation, the Mel frequency
scale is used to get a high resolution in low frequency region,
and a low resolution in high frequency region. This kind of processing
is good for obtaining stable phonetic information, but not suitable
for speaker features that are located in high frequency regions. The
speaker individual information, which is non-uniformly distributed
in the high frequencies, is equally important for speaker recognition.
Based on this fact we proposed an admissible wavelet packet based
filter structure for speaker identification. Multiresolution capabilities
of wavelet packet transform are used to derive the new features.
The proposed scheme differs from previous wavelet based works,
mainly in designing the filter structure. Unlike others, the proposed
filter structure does not follow Mel scale. The closed-set speaker
identification experiments performed on the TIMIT database shows
improved identification performance compared to other commonly
used Mel scale based filter structures using wavelets.
Denoising and Compression in Wavelet Domainvia Projection on to Approximation Coefficients
We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.
Union is Strength in Lossy Image Compression
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
A New Method for Image Classification Based on Multi-level Neural Networks
In this paper, we propose a supervised method for
color image classification based on a multilevel sigmoidal neural
network (MSNN) model. In this method, images are classified into
five categories, i.e., “Car", “Building", “Mountain", “Farm" and
“Coast". This classification is performed without any segmentation
processes. To verify the learning capabilities of the proposed method,
we compare our MSNN model with the traditional Sigmoidal Neural
Network (SNN) model. Results of comparison have shown that the
MSNN model performs better than the traditional SNN model in the
context of training run time and classification rate. Both color
moments and multi-level wavelets decomposition technique are used
to extract features from images. The proposed method has been
tested on a variety of real and synthetic images.
Robust Detection of R-Wave Using Wavelet Technique
Electrocardiogram (ECG) is considered to be the
backbone of cardiology. ECG is composed of P, QRS & T waves and
information related to cardiac diseases can be extracted from the
intervals and amplitudes of these waves. The first step in extracting
ECG features starts from the accurate detection of R peaks in the
QRS complex. We have developed a robust R wave detector using
wavelets. The wavelets used for detection are Daubechies and
Symmetric. The method does not require any preprocessing therefore,
only needs the ECG correct recordings while implementing the
detection. The database has been collected from MIT-BIH arrhythmia
database and the signals from Lead-II have been analyzed. MatLab
7.0 has been used to develop the algorithm. The ECG signal under
test has been decomposed to the required level using the selected
wavelet and the selection of detail coefficient d4 has been done based
on energy, frequency and cross-correlation analysis of decomposition
structure of ECG signal. The robustness of the method is apparent
from the obtained results.
Improved Approximation to the Derivative of a Digital Signal Using Wavelet Transforms for Crosstalk Analysis
The information revealed by derivatives can help to
better characterize digital near-end crosstalk signatures with the
ultimate goal of identifying the specific aggressor signal.
Unfortunately, derivatives tend to be very sensitive to even low
levels of noise. In this work we approximated the derivatives of both
quiet and noisy digital signals using a wavelet-based technique. The
results are presented for Gaussian digital edges, IBIS Model digital
edges, and digital edges in oscilloscope data captured from an actual
printed circuit board. Tradeoffs between accuracy and noise
immunity are presented. The results show that the wavelet technique
can produce first derivative approximations that are accurate to
within 5% or better, even under noisy conditions. The wavelet
technique can be used to calculate the derivative of a digital signal
edge when conventional methods fail.
Image Compression Using Multiwavelet and Multi-Stage Vector Quantization
The existing image coding standards generally degrades at low bit-rates because of the underlying block based Discrete Cosine Transform scheme. Over the past decade, the success of wavelets in solving many different problems has contributed to its unprecedented popularity. Due to implementation constraints scalar wavelets do not posses all the properties such as orthogonality, short support, linear phase symmetry, and a high order of approximation through vanishing moments simultaneously, which are very much essential for signal processing. New class of wavelets called 'Multiwavelets' which posses more than one scaling function overcomes this problem. This paper presents a new image coding scheme based on non linear approximation of multiwavelet coefficients along with multistage vector quantization. The performance of the proposed scheme is compared with the results obtained from scalar wavelets.