Showing papers on "Multiresolution analysis published in 2013"

SVM-Based Characterization of Liver Ultrasound Images Using Wavelet Packet Texture Descriptors

Abstract: A system to characterize normal liver, cirrhotic liver and hepatocellular carcinoma (HCC) evolved on cirrhotic liver is proposed in this paper. The study is performed with 56 real ultrasound images (15 normal, 16 cirrhotic and 25 HCC liver images) taken from 56 subjects. A total of 180 nonoverlapping regions of interest (ROIs), i.e. 60 from each image class, are extracted by an experienced participating radiologist. The multiresolution wavelet packet texture descriptors, i.e. mean, standard deviation and energy features, are computed from all 180 ROIs by using various compact support wavelet filters including Haar, Daubechies (db4 and db6), biorthogonal (bior3.1,bior3.3 and bior4.4), symlets (sym3 and sym5) and coiflets (coif1 and coif2). It is observed that a combined texture descriptor feature vector of length 48 consisting of 16 mean, 16 standard deviation and 16 energy features estimated from all 16 subband feature images (wavelet packets) obtained by second-level decomposition with two-dimensional wavelet packet transform by using Haar wavelet filter gives the best characterization performance of 86.6 %. Feature selection by genetic algorithm-support vector machine method increased the classification accuracy to 88.8 % with sensitivity of 90 % for detecting normal and cirrhotic cases and sensitivity of 86.6 % for HCC cases. Considering limited sensitivity of B-mode ultrasound for detecting HCCs evolved on cirrhotic liver, the sensitivity of 86.6 % for HCC lesions obtained by the proposed computer-aided diagnostic system is quite promising and suggests that the proposed system can be used in a clinical environment to support radiologists in lesion interpretation.

Discrete Wavelet Transform and Data Expansion Reduction in Homomorphic Encrypted Domain

Abstract: Signal processing in the encrypted domain is a new technology with the goal of protecting valuable signals from insecure signal processing. In this paper, we propose a method for implementing discrete wavelet transform (DWT) and multiresolution analysis (MRA) in homomorphic encrypted domain. We first suggest a framework for performing DWT and inverse DWT (IDWT) in the encrypted domain, then conduct an analysis of data expansion and quantization errors under the framework. To solve the problem of data expansion, which may be very important in practical applications, we present a method for reducing data expansion in the case that both DWT and IDWT are performed. With the proposed method, multilevel DWT/IDWT can be performed with less data expansion in homomorphic encrypted domain. We propose a new signal processing procedure, where the multiplicative inverse method is employed as the last step to limit the data expansion. Taking a 2-D Haar wavelet transform as an example, we conduct a few experiments to demonstrate the advantages of our method in secure image processing. We also provide computational complexity analyses and comparisons. To the best of our knowledge, there has been no report on the implementation of DWT and MRA in the encrypted domain.

Classification of masses in mammographic image using wavelet domain features and polynomial classifier

Abstract: Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98+/-0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms.

Multiresolution analysis over simple graphs for brain computer interfaces

Abstract: Objective. Multiresolution analysis (MRA) offers a useful framework for signal analysis in the temporal and spectral domains, although commonly employed MRA methods may not be the best approach for brain computer interface (BCI) applications. This study aims to develop a new MRA system for extracting tempo-spatial-spectral features for BCI applications based on wavelet lifting over graphs. Approach. This paper proposes a new graph-based transform for wavelet lifting and a tailored simple graph representation for electroencephalography (EEG) data, which results in an MRA system where temporal, spectral and spatial characteristics are used to extract motor imagery features from EEG data. The transformed data is processed within a simple experimental framework to test the classification performance of the new method. Main Results. The proposed method can significantly improve the classification results obtained by various wavelet families using the same methodology. Preliminary results using common spatial patterns as feature extraction method show that we can achieve comparable classification accuracy to more sophisticated methodologies. From the analysis of the results we can obtain insights into the pattern development in the EEG data, which provide useful information for feature basis selection and thus for improving classification performance. Significance. Applying wavelet lifting over graphs is a new approach for handling BCI data. The inherent flexibility of the lifting scheme could lead to new approaches based on the hereby proposed method for further classification performance improvement.

A review of wavelet denoising in medical imaging

Abstract: In this tutorial, we review recent wavelet denoising techniques for medical ultrasound and for magnetic resonance images. We evaluate their implementation via MATLAB package and discuss their performances in terms of SNR (signal-to-noise ratio) or PSNR (peak signal-to-noise ratio) and visual aspects of image quality. Image denoising using wavelet-based multiresolution analysis requires a delicate compromise between noise reduction and preserving significant image details. Hence, some subtleties associated with these denoising techniques will be explained in detail.

Divergence-Free Wavelets and High Order Regularization

Abstract: Expanding on a wavelet basis the solution of an inverse problem provides several advantages. Wavelet bases yield a natural and efficient multiresolution analysis. The continuous representation of the solution with wavelets enables analytical calculation of regularization integrals over the spatial domain. By choosing differentiable wavelets, high-order derivative regularizers can be designed, either taking advantage of the wavelet differentiation properties or via the basis's mass and stiffness matrices. Moreover, differential constraints on vector solutions, such as the divergence-free constraint in physics, can be handled with biorthogonal wavelet bases. This paper illustrates these advantages in the particular case of fluid flows motion estimation. Numerical results on synthetic and real images of incompressible turbulence show that divergence-free wavelets and high-order regularizers are particularly relevant in this context.

Properties of Discrete Framelet Transforms

Abstract: As one of the major directions in applied and computational harmonic analysis, the classical theory of wavelets and framelets has been extensively investigated in the function setting, in particular, in the function space L 2 (ℝd ). A discrete wavelet transform is often regarded as a byproduct in wavelet analysis by decomposing and reconstructing functions in L 2 (ℝd ) via nested subspaces of L 2 (ℝd ) in a multiresolution analysis. However, since the input/output data and all filters in a discrete wavelet transform are of discrete nature, to understand better the performance of wavelets and framelets in applications, it is more natural and fundamental to directly study a discrete framelet/wavelet transform and its key properties. The main topic of this paper is to study various properties of a discrete framelet transform purely in the discrete/digital setting without involving the function space L 2 (ℝd ). We shall develop a comprehensive theory of discrete framelets and wavelets using an algorithmic approach by directly studying a discrete framelet transform. The connections between our algorithmic approach and the classical theory of wavelets and framelets in the function setting will be addressed. Using tensor product of univariate complex-valued tight framelets, we shall also present an example of directional tight framelets in this paper.

Adaptive multiresolution discontinuous Galerkin schemes for conservation laws

Abstract: A multiresolution-based adaptation concept is proposed that aims at accelerating Discontinuous Galerkin schemes applied to nonlinear hyperbolic conservation laws. Opposite to standard adaptation concepts no error estimates are needed to tag mesh elements for refinement. Instead of this, a multiresolution analysis is performed on a hierarchy of nested grids for the data given on a uniformly refined mesh. This provides difference information between successive refinement levels, that may become negligibly small in regions where the solution is locally smooth. Applying hard thresholding the data are highly compressed and local grid adaptation is triggered by the remaining significant coefficients. A central mathematical problem addressed in this work is then to show that the adaptive solution is of the same accuracy as the reference solution on a uniformly refined mesh. Numerical comparisons demonstrate the efficiency of the concept and provide reliable estimates of the actual error in the numerical solution.

Idealizing Ion Channel Recordings by a Jump Segmentation Multiresolution Filter

Abstract: Based on a combination of jump segmentation and statistical multiresolution analysis for dependent data, a new approach called J-SMURF to idealize ion channel recordings has been developed. It is model-free in the sense that no a-priori assumptions about the channel's characteristics have to be made; it thus complements existing methods which assume a model for the channel's dynamics, like hidden Markov models. The method accounts for the effect of an analog filter being applied before the data analysis, which results in colored noise, by adapting existing muliresolution statistics to this situation. J-SMURF's ability to denoise the signal without missing events even when the signal-to-noise ratio is low is demonstrated on simulations as well as on ion current traces obtained from gramicidin A channels reconstituted into solvent-free planar membranes. When analyzing a newly synthesized acylated system of a fatty acid modified gramicidin channel, we are able to give statistical evidence for unknown gating characteristics such as subgating.

Adaptive Inpainting Algorithm Based on DCT Induced Wavelet Regularization

Abstract: In this paper, we propose an image inpainting optimization model whose objective function is a smoothed l1 norm of the weighted nondecimated discrete cosine transform (DCT) coefficients of the underlying image. By identifying the objective function of the proposed model as a sum of a differentiable term and a nondifferentiable term, we present a basic algorithm inspired by Beck and Teboulle's recent work on the model. Based on this basic algorithm, we propose an automatic way to determine the weights involved in the model and update them in each iteration. The DCT as an orthogonal transform is used in various applications. We view the rows of a DCT matrix as the filters associated with a multiresolution analysis. Nondecimated wavelet transforms with these filters are explored in order to analyze the images to be inpainted. Our numerical experiments verify that under the proposed framework, the filters from a DCT matrix demonstrate promise for the task of image inpainting.

Tight wavelet frames on local fields

Abstract: Summary In this paper, some algorithms for constructing tight wavelet frames on local fields using the unitary extension principles are suggested. We present a sufficient condition for finite number of functions to form a tight wavelet frame and establish general principles for constructing tight wavelet frames on local fields

An economic prediction of refinement coefficients in wavelet‐based adaptive methods for electron structure calculations

Abstract: The wave function of a many electron system contains inhomogeneously distributed spatial details, which allows to reduce the number of fine detail wavelets in multiresolution analysis approximations. Finding a method for decimating the unnecessary basis functions plays an essential role in avoiding an exponential increase of computational demand in wavelet-based calculations. We describe an effective prediction algorithm for the next resolution level wavelet coefficients, based on the approximate wave function expanded up to a given level. The prediction results in a reasonable approximation of the wave function and allows to sort out the unnecessary wavelets with a great reliability.

Admissible Diffusion Wavelets and Their Applications in Space-Frequency Processing

Abstract: As signal processing tools, diffusion wavelets and biorthogonal diffusion wavelets have been propelled by recent research in mathematics. They employ diffusion as a smoothing and scaling process to empower multiscale analysis. However, their applications in graphics and visualization are overshadowed by nonadmissible wavelets and their expensive computation. In this paper, our motivation is to broaden the application scope to space-frequency processing of shape geometry and scalar fields. We propose the admissible diffusion wavelets (ADW) on meshed surfaces and point clouds. The ADW are constructed in a bottom-up manner that starts from a local operator in a high frequency, and dilates by its dyadic powers to low frequencies. By relieving the orthogonality and enforcing normalization, the wavelets are locally supported and admissible, hence facilitating data analysis and geometry processing. We define the novel rapid reconstruction, which recovers the signal from multiple bands of high frequencies and a low-frequency base in full resolution. It enables operations localized in both space and frequency by manipulating wavelet coefficients through space-frequency filters. This paper aims to build a common theoretic foundation for a host of applications, including saliency visualization, multiscale feature extraction, spectral geometry processing, etc.

Optical flow estimation in cardiac CT images using the steered Hermite transform

Abstract: This paper describes a new method to estimate the heart's motion in computer tomography images with the inclusion of a bio-inspired image representation model. Our proposal is based on the polynomial decomposition of each of the images using the steered Hermite transform as a representation of the local characteristics of images from an perceptual approach within a multiresolution scheme. The Hermite transform is a model that incorporates some of the more important properties of the first stages of the human visual system, such as the overlapping Gaussian receptive fields, the Gaussian derivative model of early vision and the multiresolution analysis. We propose an approach for optical flow estimation that incorporates image structure information extracted from the steered Hermite coefficients, that is later used as local motion constraints in a differential estimation method that involves several of the constraints seen in the current differential methods, which allows obtaining accurate flows. Considering the importance of understanding the movement of certain structures such as left ventricular and myocardial wall for better medical diagnosis, our main goal is to find an estimation method useful to assist diagnosis tasks in computer tomography images.

Biorthogonal Wavelets on Local Fields of Positive Characteristic

Abstract: We generalize the concept of biorthogonal wavelets to a local field $K$ of positive characteristic We show that if the translates of the scaling functions of two multiresolution analyses are biorthogonal, then the associated wavelet families are also biorthogonal Under mild assumptions on the scaling functions and the wavelets, we also show that the wavelets generate Riesz bases for $L^2(K)$

High Speed Train Bogie Fault Signal Analysis Based on Wavelet Entropy Feature

Abstract: Mechanical behavior of high speed trains bogie seriously impact the reliability of the train system. Performance monitoring and fault diagnosis for the critical component on bogie are very important. Simulation data of high speed train bogie fault signal is selected in data experiment. Based on multiresolution analysis, wavelet entropy features are extracted to reflect the uncertainty level of the vibration signal on scales. In the high dimension space composed by several wavelet entropy features, the dates from four fault patterns are classified and the result is satisfactory. Result show that wavelet entropy feature is effective for fault signal analysis of high speed train bogie.

Hyperbolic Wavelets and Multiresolution in the Hardy Space of the Upper Half Plane

Abstract: A multiresolution analysis in the Hardy space of the unit disc was introduced recently (see Pap in J. Fourier Anal. Appl. 17(5):755–776, 2011). In this paper we will introduce an analogous construction in the Hardy space of the upper half plane. The levels of the multiresolution are generated by localized Cauchy kernels on a special hyperbolic lattice in the upper half plane. This multiresolution has the following new aspects: the lattice which generates the multiresolution is connected to the Blaschke group, the Cayley transform and the hyperbolic metric. The second: the nth level of the multiresolution has finite dimension (in classical affine multiresolution this is not the case) and still we have the density property, i.e. the closure in norm of the reunion of the multiresolution levels is equal to the Hardy space of the upper half plane. The projection operator to the nth resolution level is a rational interpolation operator on a finite subset of the lattice points. If we can measure the values of the function on the points of the lattice the discrete wavelet coefficients can be computed exactly. This makes our multiresolution approximation very useful from the point of view of the computational aspects.

A scale space multiresolution method for extraction of time series features

Abstract: A scale space multiresolution feature extraction method is proposed for time series data The method detects intervals where time series features differ from their surroundings, and it produces a multiresolution analysis of the series as a sum of scale-dependent components These components are obtained from differences of smooths The relevant sequence of smoothing levels is determined using derivatives of smooths with respect to the logarithm of the smoothing parameter As time series are usually noisy, the method uses Bayesian inference to establish the credibility of the components © The Authors Stat published by John Wiley & Sons Ltd

Multiresolution DCT decomposition for multifocus image fusion

Abstract: Image fusion is gaining momentum in the research community with the aim of combining all the important information from multiple images such that the fused image contains more accurate and comprehensive information than that contained in the individual images. In this paper, it is proposed to fuse multifocus images in the multiresolution DCT domain instead of the wavelet domain to reduce the computational complexity. The performance of the fused image in the proposed domain is compared with that of the wavelet domain with four recently-proposed fusion rules. The proposed method is applied on several pairs of multifocus images and the performance compared visually and quantitatively with that of wavelets. It is found that the performance of the proposed method is superior/similar to that of wavelets in terms of visual quality and quantitative parameters with extra benefits of computational efficiency and simplicity of implementation.

The Implementation and Performance Evaluation of $3\phi$ VS Wavelet Modulated AC - DC Converters

Abstract: This paper presents the implementation and performance testing of the wavelet modulation technique for operating three phase, voltage source (VS), six-pulse ac-dc converters. The wavelet modulation technique is realized by a nondyadic-type multiresolution analysis (MRA), which is constructed using sets of dilated and translated scale-based linearly combined wavelet basis functions. A dc reference signal is processed using this MRA, where three sets of groups of nonuniform recurrent samples are created by the analysis stage. The synthesis stage of the nondyadic MRA reconstructs the dc reference signal using three sets of dilated and translated scale-based linearly combined synthesis wavelet basis functions, which are used to activate the switching elements of the ac-dc converter. Simulation and experimental performances of the 3φ ac-dc converter, that is, operated by the wavelet modulation technique, are investigated for supplying static and dynamic load types. Performances of the 3φ wavelet modulated ac-dc converter are also investigated for unbalanced input 3φ voltages. Simulation and experimental results show that high magnitude of output dc components, and significant reductions of input and output harmonic components of the 3φ VS ac-dc converter can be accomplished using the wavelet modulation technique. These improvements in the performances of 3φ ac-dc converters are further demonstrated through comparisons with the pulse-width and space-vector modulation techniques under similar conditions of loading and 3φ input voltages.

Recognition of Tamil Handwritten Characters using Daubechies Wavelet Transforms and Feed-Forward Backpropagation Network

Abstract: This article suggests wavelet transform based feature extraction technique for extracting robust features from Tamil handwritten characters. The algorithm uses feed-forward back propagation neural network as the classifier. It presents the relevant features of Tamil script and describes various techniques used for character recognition. In common, all the pattern recognition tasks focus on extracting more differentiating features. This is the most important and complicated job. The proposed system concentrates on two dimensional discrete wavelet transformations for extraction of features. For multiresolution analysis of images, Wavelet Transform is used. This capability can be used to study the character image in different frequency bands. Localized basis functions of WT are used for extracting localized features of a character image. This enables us to obtain more distinct traits as features for each character. Feed forward back propagation neural network is one of the general neural network architectures and this architecture can be applied to many different tasks and is very popular.

Identification of Hysteretic Dynamic Systems by Using Hybrid Extended Kalman Filter and Wavelet Multiresolution Analysis with Limited Observation

Abstract: The availability of methods for the identification of nonlinear hysteretic systems is crucial for the assessment of the health and the repair of civil infrastructures during and after severe earthquakes. However, most methods used to identify hysteretic systems suffer from two problems: (1) the structural responses at all dynamic degrees of freedom (DOFs) must be measured, which is obviously impractical for real applications; and (2) the nonlinear model of a system is assumed to be known, and only the model parameters are to be identified, meaning that the nonlinear characteristics of the underlying structures may not be captured accurately. To overcome these two problems, this paper proposes a novel method that does not assume a nonlinear model and that does not require measurements at all DOFs. The new approach alternately uses the extended Kalman filter (EKF) and wavelet (W) multiresolution analysis. Within each time step, the identification can then be divided into two stages. In stage one, ba...

Multiscale methods in signal processing for adaptive optics

Abstract: In this thesis, we introduce a new approach to wavefront phase reconstruction in Adaptive Optics (AO) from the low-resolution gradient measurements provided by a wavefront sensor, using a non-linear approach derived from the Microcanonical Multiscale Formalism (MMF). MMF comes from established concepts in statistical physics, it is naturally suited to the study of multiscale properties of complex natural signals, mainly due to the precise numerical estimate of geometrically localized critical exponents, called the singularity exponents. These exponents quantify the degree of predictability, locally, at each point of the signal domain, and they provide information on the dynamics of the associated system. We show that multiresolution analysis carried out on the singularity exponents of a high-resolution turbulent phase (obtained by model or from data) allows a propagation along the scales of the gradients in low-resolution (obtained from the wavefront sensor), to a higher resolution. We compare our results with those obtained by linear approaches, which allows us to offer an innovative approach to wavefront phase reconstruction in Adaptive Optics.

Clustering datasets by complex networks analysis

Abstract: This paper proposes a method based on complex networks analysis, devised to perform clustering on multidimensional datasets. In particular, the method maps the elements of the dataset in hand to a weighted network according to the similarity that holds among data. Network weights are computed by transforming the Euclidean distances measured between data according to a Gaussian model. Notably, this model depends on a parameter that controls the shape of the actual functions. Running the Gaussian transformation with different values of the parameter allows to perform multiresolution analysis, which gives important information about the number of clusters expected to be optimal or suboptimal. Solutions obtained running the proposed method on simple synthetic datasets allowed to identify a recurrent pattern, which has been found in more complex, synthetic and real, datasets.

Coset Sum: An Alternative to the Tensor Product in Wavelet Construction

Abstract: A multivariate biorthogonal wavelet system can be obtained from a pair of multivariate biorthogonal refinement masks in multiresolution analysis setup. Some multivariate refinement masks may be decomposed into lower dimensional refinement masks. Tensor product is a popular way to construct a decomposable multivariate refinement mask from lower dimensional refinement masks. We present an alternative method, which we call coset sum, for constructing multivariate refinement masks from univariate refinement masks. The coset sum shares many essential features of the tensor product that make it attractive in practice: 1) it preserves the biorthogonality of univariate refinement masks, 2) it preserves the accuracy number of the univariate refinement mask, and 3) the wavelet system associated with it has fast algorithms for computing and inverting the wavelet coefficients. The coset sum can even provide a wavelet system with faster algorithms in certain cases than the tensor product. These features of the coset sum suggest that it is worthwhile to develop and practice alternative methods to the tensor product for constructing multivariate wavelet systems. Some experimental results using 2-D images are presented to illustrate our findings.

Inferring Information Across Scales in Acquired Complex Signals

Abstract: Transmission of information across the scales of a complex signal has some interesting potential, notably in the derivation of sub-pixel information, cross-scale inference and data fusion. It follows the structure of complex signals themselves, when they are considered as acquisitions of complex systems. In this work we contemplate the problem of cross-scale information inference through the determination of appropriate multiscale decomposition. Our goal is to derive a generic methodology that can be applied to propagate information across the scales in a wide variety of complex signals. Consequently, we first focus on the determination of appropriate multiscale characteristics, and we show that singularity exponents computed in microcanonical formulations are much better candidates for the characterization of transitions in complex signals: they outperform the classical "linear filtering" approach of the state-of-the-art edge detectors (for the case of 2D signals). This is a fundamental topic as edges are usually considered as important multiscale features in an image. The comparison is done within the formalism of reconstructible systems. Critical exponents, naturally associated to phase transitions and used in complex systems methods in the framework of criticality are key notions in Statistical Physics that can lead to the complete determination of the geometrical cascade properties in complex signals. We study optimal multiresolution analysis associated to critical exponents through the concept of "optimal wavelet". We demonstrate the usefulness of multiresolution analysis associated to critical exponents in two decisive examples: the reconstruction of perturbated optical phase in Adaptive Optics (AO) and the generation of high resolution ocean dynamics from low resolution altimetry data.