Wavelet Planes Research Articles

Image enhancement with wavelet-optimized whitening

Context. Due to its physical nature, the solar corona exhibits large spatial variations of intensity that make it difficult to simultaneously visualize the features present at all levels and scales. Many general-purpose and specialized filters have been proposed to enhance coronal images. However, most of them require the ad hoc tweaking of parameters to produce subjectively good results. Aims. Our aim was to develop a general purpose image enhancement technique that would produce equally good results, but based on an objective criterion. Methods. The underlying principle of the method is the equalization, or whitening, of power in the à trous wavelet spectrum of the input image at all scales and locations. An edge-avoiding modification of the à trous transform that uses bilateral weighting by the local variance in the wavelet planes is used to suppress the undesirable halos otherwise produced by discontinuities in the data. Results. Results are presented for a variety of extreme ultraviolet (EUV) and white light images of the solar corona. The proposed filter produces sharp and contrasted output, without requiring the manual adjustment of parameters. Furthermore, the built-in denoising scheme prevents the explosion of high-frequency noise typical of other enhancement methods, without smoothing statistically significant small-scale features. The standard version of the algorithm is about two times faster than the widely used multiscale Gaussian normalization (MGN). The bilateral version is slower, but provides significantly better results in the presence of spikes or edges. Comparisons with other methods suggest that the whitening principle may correspond to the subjective criterion of most users when adjusting free parameters.

Classifier for the functional state of the respiratory system via descriptors determined by using multimodal technology

Currently, intelligent systems built on a multimodal basis are used to study the functional state of living objects. Its essence lies in the fact that a decision is made through several independent information channels with the subsequent aggregation of these decisions. The method of forming descriptors for classifiers of the functional state of the respiratory system includes the study of the spectral range of the respiratory rhythm and the construction of the wavelet plane of the monitoring electrocardiosignal overlapping this range. Then, variations in the breathing rhythm are determined along the corresponding lines of the wavelet plane. Its analysis makes it possible to select slow waves corresponding to the breathing rhythm and systemic waves of the second order. Analysis of the spectral characteristics of these waves makes it possible to form a space of informative features for classifiers of the functional state of the respiratory system. To construct classifiers of the functional state of the respiratory system, hierarchical classifiers were used. As an example, we took a group of patients with pneumonia with a well-defined diagnosis (radiography, X-ray tomography, laboratory data) and a group of volunteers without pulmonary pathology. The diagnostic sensitivity of the obtained classifier was 76% specificity with a diagnostic specificity of 82%, which is comparable to the results of X-ray studies. It is shown that the corresponding lines of the wavelet planes are correlated with the respiratory system and, using their Fourier analysis, descriptors can be obtained for training neural network classifiers of the functional state of the respiratory system.

Simulation of a non‐linear, time‐variant circuit using the Haar wavelet transform

Wavelet theory has disentangled numerous complexities, including those pertinent to transient and steady-state responses of systems, when Laplace and Fourier transforms face insoluble obstacles. Reactive linear components (e.g. inductors and capacitors) are typically handled in the frequency plane. Non-linear (e.g. diodes) or time-variant components (e.g. switches) are conventionally simulated in the time plane (e.g. a diode via its I–V characteristic) and are considered open or short circuits in AC analyses (e.g. in circuit simulation software). Although translating circuits in an alternative plane, such as the Haar wavelet plane, significantly simplifies the process, a wide integration of wavelets into instruments and education is not yet realised; an underlying reason is the considerate complexity of applying wavelet theory to circuits and signals. The aim of this paper is to bridge this gap, providing a new user-friendly, Laplace-alike approach, utilising measurement-based models and the Haar wavelet. The Haar wavelet transform and a numerical method for the inverse Laplace transform which uses the Haar operational matrix are applied, to calculate the total current of a non-linear, time-variant system, that is the total current of a voltage source which powers a non-linear, time-variant load.

A multiscale wavelet algorithm for atom tracking in STM movies

High-speed scanning tunneling microscopy (STM) data have become available that provide movies of time-dependent surface processes. To track adsorbed atoms and molecules in such data automatic routines are required. We introduce a multiresolution wavelet particle detection algorithm for this purpose. To identify the particles, the images are decomposed by means of a discrete wavelet transform into wavelet planes of different resolutions. An ‘à trous’ low-pass filter is applied. The coefficients from the wavelet planes are filtered to remove noise. Wavelet planes with significant coefficients from the particles are multiplied, and the product is transformed into a binary particle mask. The precision of the method is tested with data sets of adsorbed CO molecules and O atoms on a Ru(0001) surface. The algorithm can safely detect and localize these particles with high precision, even in the presence of the enhanced noise characteristic for high-speed, constant-height STM data. By linking the particle positions, we obtain extended trajectories with a resolution of ∼0.5 Å or better allowing us to investigate the detailed motion of single atoms on a surface.

Defining a no-reference image quality assessment by means of the self-affine analysis.

In this paper we propose a novel Blind Image Quality Assessment via Self-Affine Analysis (BIQSAA) method by considering the wavelet transform as a linear operation that decomposes a complex signal into elementary blocks at different scales or resolutions. BIQSAA decomposes a distorted image into a set of wavelet planes ωλ, ϕ of different spatial frequencies λ and spatial orientations ϕ, and it transforms these wavelet planes into one-dimension vector Ω using a Hilbert scanning. From the vector Ω there were obtained their wavelet coefficient fluctuations estimated by the inverse of the Hurst exponent in decibels, whose scaling-law or fractal behavior was obtained by applying Fractal Geometry or Self-Affine Analysis. The scaling exponents calculated for the coefficient fluctuation behavior of Image Lena at 24bpp, at 1.375bpp, and at 0.50bpp were H24bpp = 0.0395, H1.375bpp = 0.0551, and H0.50bpp = 0.0612, respectively. Our experiments show that BIQSAA algorithm improves in 14.36% the Human Visual System correlation, respect to the four state-of-the-art No-Reference Image Quality Assessments.

Wave Motion Analysis in Plane via Hermitian Cubic Spline Wavelet Finite Element Method

A plane Hermitian wavelet finite element method is presented in this paper. Wave motion can be used to analyze plane structures with small defects such as cracks and obtain results. By using the tensor product of modified Hermitian wavelet shape functions, the plane Hermitian wavelet shape functions are constructed. Scale functions of Hermitian wavelet shape functions can replace the polynomial shape functions to construct new wavelet plane elements. As the scale of the shape functions increases, the precision of the new wavelet plane element will be improved. The new Hermitian wavelet finite element method which can be used to simulate wave motion analysis can reveal the law of the wave motion in plane. By using the results of transmitted and reflected wave motion, the cracks can be easily identified in plane. The results show that the new Hermitian plane wavelet finite element method can use the fewer elements to simulate the plane structure effectively and accurately and detect the cracks in plane.

Rapid multi-scale analysis of near-surface geophysical anomaly maps: Application to an archaeo-geophysical data set

In near-surface geophysics, ground-based mapping surveys are routinely employed in a variety of applications including those from archaeology, civil engineering, hydrology, and soil science. The resulting geophysical anomaly maps of, for example, magnetic or electrical parameters are usually interpreted to laterally delineate subsurface structures such as those related to the remains of past human activities, subsurface utilities and other installations, hydrological properties, or different soil types. To ease the interpretation of such data sets, we propose a multi-scale processing, analysis, and visualization strategy. Our approach relies on a discrete redundant wavelet transform (RWT) implemented using cubic-spline filters and the à trous algorithm, which allows to efficiently compute a multi-scale decomposition of 2D data using a series of 1D convolutions. The basic idea of the approach is presented using a synthetic test image, while our archaeo-geophysical case study from North-East Germany demonstrates its potential to analyze and process rather typical geophysical anomaly maps including magnetic and topographic data. Our vertical-gradient magnetic data show amplitude variations over several orders of magnitude, complex anomaly patterns at various spatial scales, and typical noise patterns, while our topographic data show a distinct hill structure superimposed by a microtopographic stripe pattern and random noise. Our results demonstrate that the RWT approach is capable to successfully separate these components and that selected wavelet planes can be scaled and combined so that the reconstructed images allow for a detailed, multi-scale structural interpretation also using integrated visualizations of magnetic and topographic data. Because our analysis approach is straightforward to implement without laborious parameter testing and tuning, computationally efficient, and easily adaptable to other geophysical data sets, we believe that it can help to rapidly analyze and interpret different geophysical mapping data collected to address a variety of near-surface applications from engineering practice and research.

Evaluating the effectiveness of fusing remote sensing images with significantly different spatial resolutions for thematic map production

It is very challenging to fuse remote sensing images with significant spatial resolution difference. In this paper, such kind of images are fusing with one posteriori probability model for the purpose of creating thematic maps. The outlined solution consists of parsing the low spatial resolution multispectral images into intensity-hue-saturation triples with spatial and spectral properties separated; the contribution of the old intensity and the panchromatic image is factorized into posteriori probabilities using their wavelet planes under the aid of support vector machine; the wavelet planes are probabilistically weighted to foresee one new pan-sharpened intensity, from which the fused images are produced by inverse IHS. The outlined method along with two representative methods are evaluated with two sets of imagery covering contrasting heterogeneous landscapes for different purposes of road extraction and wheat area map.

Low Brightness Temperature in Microwaves at Periphery of Some Solar Active Regions

Abstract The microwave regions with low brightness temperature are found to overlap the regions of the depressed coronal emission and open field lines at the periphery of two solar active regions (ARs). The imaging microwave observations of the Sun with the Nobeyama Radio heliograph at 1.76 cm, the MRO-14 radio telescope of Metsähovi Radio Observatory at 0.8 cm, and the RT-32 of Ventspils International Radio Astronomy Centre in the range 3.2-4.7 cm are used. To reduce the noise in the intensity distribution of the RT-32 maps of the Sun, one wavelet plane of “à trous” wavelet space decomposition is subtracted from each map. To locate the open-field regions, the full-Sun coronal magnetic fields with the potential field source surface (PFSS) model for RSS = 1.8 Rʘ are simulated. We conclude that the revealed LTRs present narrow coronal hole-like regions near two ARs and imply an extra investigation on the plasma outflow.

Assessment of cardiac time intervals by wavelet transform of the impedance cardiogram.

Impedance cardiography (ICG) is an inexpensive, noninvasive technique for estimating hemodynamic parameters. ICG can be used to obtain the ejection fraction of the left atrium and to monitor systolic time intervals. Traditional ICG technique does not enable unambiguous detection of the left ventricle ejection time (LVET) and the time relationships between specific marker points. This work aims to approbate a new approach for ICG signal processing using wavelet transform (WT) and to investigate the possibilities of this approach for determination of the parameters which are related to the stroke volume (SV), in particular LVET. Thoracic tetrapolar polyrheocardiography method for simultaneous registration of ECG, ICG and phonocardiograms has been used. A control group consisted of eight healthy men aged 20-25 years. In addition, four patients with essential hypertension participated in the study. Wavelet representation of the ICG data produced local maxima in a two dimensional distribution of the wavelet coefficient. Each extremum point was characterized by the amplitude, scale and time, which determine SV. LVET was defined as the scale corresponding to the E-wave maximum related to the systolic phase of the cardiac cycle. Also, we defined the initial systolic time interval (ISTI) as the time interval between R peak in the ECG and E-wave maximum on the wavelet plane. During functional test LVET and ISTI values defined by WT demonstrated a proper hemodynamic response to loading for the control group and patients with essential hypertension. The proposed approach demonstrates the ability of ICG-WT technique for adequate assessment of SV parameters, including cardiac time intervals.

An Eigenpoint Based Multiscale Method for Validating Quantitative Remote Sensing Products

This letter first proposes the eigenpoint concept for quantitative remote sensing products (QRSPs) after discussing the eigenhomogeneity and eigenaccuracy for land surface variables. The eigenpoints are located according to the á trous wavelet planes of the QRSP. Based on these concepts, this letter proposes an eigenpoint based multiscale method for validating the QRSPs. The basic idea is that the QRSPs at coarse scales are validated by validating their eigenpoints using the QRSP at fine scale. The QRSP at fine scale is finally validated using observation data at the ground based eigenpoints at instrument scale. The ground based eigenpoints derived from the forecasted QRSP can be used as the observation positions when the satellites pass by the studied area. Experimental results demonstrate that the proposed method is manpower-and time-saving compared with the ideal scanning method and it is satisfying to perform simultaneous observation at these eigenpoints in terms of efficiency and accuracy.

Best tradeoff for remote sensing image fusion based on three-dimensional variation and à trous wavelet

For à trous wavelet-based remote sensing image fusion, it is significant to determine the number of decomposition levels (NDL) to derive the best tradeoff between the spatial and spectral qualities of the fused image. The tradeoff is modeled as a cost function from a novel three-dimensional variational point of view. By solving this cost function, a new fusion scheme is proposed that can be used to customize the tradeoff by weighting the wavelet planes with a factor. The optimal NDL is decided by the intersection of the characteristic curves of the spatial and spectral qualities. Three pairs of remote sensing images are used to test the analysis. The experimental results show that the proposed method provides the practitioner with a reference for selecting the fused image with different spatial and spectral qualities for different applications.

Image Contrast Enhancement using Atrous Wavelet Transforn and Singular Value Decomposition(SVD)

this paper, a new satellite image contrast enhancement technique based on s Atrous wavelet transform and singular value decomposition (SVD) has been proposed. To obtain shift invariant discrete wavelet transform decomposition for images, we introduced the discrete wavelet transform known a A trous algorithm to decompose the image into wavelet planes which is computed as the difference between two consecutive approximations and calculate the singular value matrix of the residual image. The enhanced image is obtained by applying inverse transforms. These techniques are compared with conventional image equalization techniques such as general histogram equalization and discrete wavelet transform. Quality metrics were used to evaluate the superiority of the proposed method.

A System Characteristic Parameters Identification Method by Wavelet Transform Image Ridge

Dynamic characteristic of a system have to be obtained so as to offer the reliable data for the system dynamic modification and dynamic optimum design. The system modal parameters identification can be changed into the global optimization problem in wavelet plane because the wavelet ridges can carry much information of system characteristic parameters. Firstly, the paper will introduce the so-called PSO (Particle Swarm Optimization) technique into the modal analysis and propose the PSO wavelet ridge extraction algorithm. Furthermore, the formulas identifying modal parameters from a wavelet ridge are derived and computation steps were given. The simulation experiments are implemented in order to evaluate precision of this method and the robustness of noise. Finally, the proposed method applies to the modal parameters identification of a watermelon to explore the effectiveness. The experiment results prove the method is precision and insensitive to noise.

A hybrid wavelet and time plane based method for QT interval measurement in ECG signals

Here we present a method of QT interval meas-urement for Physionet's online QT Challenge ECG database using the combination of wavelet and time plane feature extraction mechanisms. For this we mainly combined two previous works one done using the Daubechies 6 wavelet and one time plane based with modifications in their algorithms and inclusion of two more wavelets (Daubechies 8 and Symlet 6). But found that out of these three wavelets Daube-chies 6 and 8 gives the best output and when averaged with the interval of time plane feature extraction method it gives least percentage of error with respect to the median reference QT interval as specified by Physionet. Our modified time plane feature extraction scheme along with the wavelet method together produces best re-sults for automated QT wave measurement as its regular verification is important for analyzing cardiac health. For the V2 chest lead particularly whose QT wave is of tremendous significance we have tested on 530 recordings of Physionet. This is because delay in cardiac repolarization causes ventricular tachyarrhythmias as well as Torsade de pointes (TdP). A feature of TdP is pronounced prolongation of the QT interval in the supraventricular beat preceding the ar-rhythmia. TdP can degenerate into ventricular fibrillation, leading to sudden death.

Tissue segmentation in ultrasound images by using genetic algorithms

This paper presents a genetic based incremental neural network (GINeN) for the segmentation of tissues in ultrasound images. Performances of the GINeN and the Kohonen network are investigated for tissue segmentation in ultrasound images. Feature extraction is carried out by using continuous wavelet transform. Pixel intensities at the same spatial location on 12 wavelet planes and on the original image are considered as features, leading to 13-dimensional feature vectors. The same training set is used for the training of the Kohonen network and the GINeN. This paper proposes the use of wavelet transform and genetic based incremental neural network together in order to increase the segmentation performance. It is observed that genetic based incremental neural network gives satisfactory segmentation performance for ultrasound images.

A208 ウェーブレット解析を用いた建築用外装タイルの定量的剥離診断

This paper describes a detection method of two types of exfoliations for outward tile wall. One of the tile exfoliations is an outer exfoliation separated the tile surface from mortar concrete, the other is an inner exfoliation deteriorated space between the substrate and mortar concrete. In order to research these exfoliations, we focused attention on the wavelet analysis that enable to analyze the frequency element of a waveform on time phase continuously. An impulse sound by a small hammer was measured using a mockup wall that reproduced two types of exfoliations, and then these sound data were inspected by wavelet analysis. As a result, the characteristics of two exfoliations were semi-empirically recognized visualizing the wavelet plane and the quantitative parameters judged the two exfoliations were obtained processing the wavelet data statistically.

Multiresolution image reconstruction using wavelets

To overcome the problem of noise amplification during the image reconstruction process, we present a new method based on wavelet decomposition. After decomposing the raw image to be reconstructed into several wavelet planes and a residual image, we reconstruct each one independently using an iterative Maximum Likelihood algorithm. To control the processs, we stop the reconstruction of each one of the wavelet planes and the residual image at a different number of iterations. The inverse problem is then transformed into a multi-channel reconstruction problem. The method has been applied to a real image of the planet Saturn obtained by the non-refurbished Hubble Space Telescope.