Biorthogonal Wavelet Research Articles

Implementing Fusion Technique Using Biorthogonal Dwt to Increase the Number of Minutiae in Fingerprint Images

Biometric devices identify persons based on the minutiae extracted from fingerprint images. Image quality is very important in this process. Usually, fingerprint images have low quality and in many cases they are obtained in various positions. The paper focuses on increasing minutiae detected number by fusing two fingerprint images obtained in various positions. Biorthogonal wavelets have advantages compared to orthogonal wavelets. Fusion is performed in wavelet domain by implementing biorthogonal wavelet. Terminations and bifurcations are extracted from the original and fused images using licensed software Papillon 9.02 and manually extraction by an expert. Biorthogonal Wavelet transform is implemented in the image fusion process, yielding in the increased number of the minutiae compared to the original one. Different biorthogonal wavelets are experimented and various results are obtained. Finding the appropriate wavelet is important in the fusion process since it has a direct impact in the number of minutiae extracted. Based on the number of minutiae and MSE results, the appropriate wavelet to be used in the fusion process is defined.

Performance comparison of wavelet families for noise reduction and intensity thresholding in Fourier Ptychographic microscopy

Microscopy is going through a digital renaissance and new schemes are developed where computer and algorithms constitute an integral part of the imaging process itself. Computational microscopy increases performance by offering better resolution, larger field of view, quantitative contrast and also reduced size, weight and economic cost. Fourier Ptychographic microscopy utilizes multiple images of a sample taken at lower resolution, each illuminated with a unique incidence angle coherent source, and synthesizes one high resolution complex valued image by iterative phase retrieval algorithms. The recorded images are often corrupted with background noise and pre-processing is needed to improve the quality of the FP recovered image. The pre-processing involves data denoising, thresholding and intensity balancing. We have investigated different wavelet families to test their performance in terms of having compact support and giving the desired level of decomposition for optimal intensity thresholding and denoising in Fourier Ptychography (FP). The wavelet families Daubechies, Biorthogonal, Reverse Biorthogonal, Coiflet, Fejer-Korovkin, Discrete Meyer and Symlet with different compact support have been studied. The obtained threshold was used with noisy synthetic and experimental images for a variety of objects to evaluate the performance of the described framework. In particular, Reverse Biorthogonal wavelets were found to preserve useful signal in corrupted images to a great extent (RMS error 0.39) with low computational cost. Consequently, quantitatively more correct amplitude and phase images with uniform and homogeneous background could be recovered.

Filtered-orthogonal wavelet division multiplexing (F-OWDM) technique for 5G and beyond communication systems.

Filtered-orthogonal frequency division multiplexing (F-OFDM) is one of the most protruding multicarrier modulation (MCM) techniques for fifth-generation and beyond wireless communication. However, it possesses a high peak-to-average power ratio (PAPR), which results in its poor performance. Thus, a novel wavelet based MCM technique, namely filtered orthogonal wavelet division multiplexing (F-OWDM), is proposed as an efficient alternative to conventional F-OFDM (C-F-OFDM) to reduce the PAPR. In this model, the traditional Fourier transforms (FT) as used in C-F-OFDM was replaced with Wavelet Transforms. The proposed F-OWDM system does not require a cyclic prefix because of the overlapping sub-carriers in the time and frequency domains. Thus, the F-OWDM system exhibits higher bandwidth efficiency. In this paper, the performance of the F-OWDM system with various wavelets from different wavelet families under an additive white Gaussian noise and flat fading channel is investigated. The PAPR and bit error rate (BER) of the F-OWDM system using Haar, discrete Meyer, bi-orthogonal, symlet, and Daubechies wavelets are analyzed. A comparative study between F-OWDM and C-F-OFDM is also presented. From the results, it is able to prove that F-OWDM has the advantage of lower PAPR and lower bit error rate than the C-F-OFDM system.

Image Contrast Enhancement Method Based on Nonlinear Space and Space Constraints

Remote sensing, environmental monitoring, pattern recognition, and other fields all use this critical and indispensable basic technology. The article proposes an image contrast enhancement detection algorithm based on a linear model to address the problem that the current global contrast enhancement detection algorithm does not have high classification accuracy under the low-intensity JPEG compression quality factor. To decompose the original image, use the biorthogonal wavelet transform. The improved fuzzy set enhancement algorithm is used for the low-frequency subband coefficient. The results obtained after simulating this algorithm show that it is very effective in improving contrast, enhancing image details, and suppressing noise. It has the ability to greatly improve the image’s visual effect, as well as the advantages of parameter adaptation and high algorithm efficiency.

Wavelet adaptive proper orthogonal decomposition for large-scale flow data

The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by three-dimensional direct numerical simulations, is limited owing to its computational complexity. Here, we propose a wavelet-based adaptive version of the POD (the wPOD), in order to overcome this limitation. The amount of data to be analyzed is reduced by compressing them using biorthogonal wavelets, yielding a sparse representation while conveniently providing control of the compression error. Numerical analysis shows how the distinct error contributions of wavelet compression and POD truncation can be balanced under certain assumptions, allowing us to efficiently process high-resolution data from three-dimensional simulations of flow problems. Using a synthetic academic test case, we compare our algorithm with the randomized singular value decomposition. Furthermore, we demonstrate the ability of our method analyzing data of a two-dimensional wake flow and a three-dimensional flow generated by a flapping insect computed with direct numerical simulation.

An expert system for automated classification of phases in cyclic alternating patterns of sleep using optimal wavelet‐based entropy features

AbstractHumans spend a significant portion of their time in the state of sleep, and therefore one's’sleep health’ is an important indicator of the overall health of an individual. Non‐invasive methods such as electroencephalography (EEG) are used to evaluate the ’sleep health’ as well as associated disorders such as nocturnal front lobe epilepsy, insomnia, and narcolepsy. A long‐duration and repetitive activity, known as a cyclic alternating pattern (CAP), is observed in the EEG waveforms which reflect the cortical electrical activity during non‐rapid eye movement (NREM) sleep. The CAP sequences involve various, continuing periods of phasic activation (phase‐A) and deactivation (phase‐B). The manual analysis of these signals performed by clinicians are prone to errors, and may lead to the wrong diagnosis. Hence, automated systems that can classify the two phases (viz. Phase A and Phase B accurately can eliminate any human involvement in the diagnosis. The pivotal aim of this study is to evaluate the usefulness of stopband energy minimized biorthogonal wavelet filter bank (BOWFB) based entropy features in the identification of CAP phases. We have employed entropy features obtained from six wavelet subbands of EEG signals to develop a machine learning (ML) based model using various supervised ML algorithms. The proposed model by us yielded an average classification accuracy of 74.40% with 10% hold‐out validation with the balanced dataset, and maximum accuracy of 87.83% with the unbalanced dataset using ensemble bagged tree classifier. The developed expert system can assist the medical practitioners to assess the person's cerebral activity and quality of sleep accurately.

Three-Dimensional Quantitative Recognition of Filler Materials Ahead of a Tunnel Face via Time-Energy Density Analysis of Wavelet Transforms

Advanced geological prediction of tunnels has become an indispensable task to ensure the safety and effectiveness of tunnel construction before excavation in karst areas. Geological disasters caused by unfavorable geological conditions, such as karst caves, faults, and broken zones ahead of a tunnel face, are highly sudden and destructive. Determining how to predict the spatial location and geometric size of unfavorable geological bodies accurately is a challenging problem. In order to facilitate a three-dimensional quantitative analysis of the filler material ahead of the tunnel face, a biorthogonal wavelet with short support, linear phase, and highly matching waveform of ground penetrating radar (GPR) wavelet is constructed by lifting a simple and general initial filter on the basis of lifting wavelet theory. A method for a time-energy density analysis of wavelet transforms (TEDAWT) is proposed in accordance with the biorthogonal wavelet. Fifteen longitudinal and horizontal survey lines are used to detect void fillers of different heights. Then, static correction, DC bias, gain, band-pass filtering, and offset processing are performed in the original GPR profile to enhance reflected signals and converge diffraction signals. A slice map of GPR profile is generated in accordance with the relative position of longitudinal and horizontal survey lines in space. The wavelet transform analysis of a single-channel signal of each survey line is performed by adopting the TEDAWT method because of the similar rule of the single-channel signal of GPR on the waveform overlay and the ability of the constructed wavelet basis to highlight the time-frequency characteristics of GPR signals. The characteristic value points of the first and second interfaces of the void fillers can be clearly determined, and the three-dimensional spatial position and geometric sizes of different void fillers can be obtained. Therefore, the three-dimensional visualization of GPR data is realized. Results show that the TEDAWT method has a good practical application effect in the quantitative identification of void fillers, which provides a basis for the interpretation of advanced geological prediction data of tunnels and for the construction decision.

Wavelet transform approach for denoising and decomposition of satellite-derived ocean color time-series: Selection of optimal mother wavelet

Wavelet Transform (WT) has remarkable advantages for feature extraction and denoising of satellite-derived ocean color time series datasets. The selection of mother wavelet (MWT) is the main challenging issue in the wavelet transform analysis of ocean color time series, since different MWT applied to the same dataset may produce different results. In this study, 57 MWTs were investigated to find the optimal wavelet functions for WT analysis of ocean color time series datasets with particular emphasis on the quantitative approaches. The daily, weekly, and monthly averaged of MODIS Level-3 Chlorophyll-a (Chl-a) series were denoised and decomposed by Discrete Wavelet Transform (DWT) using different MWTs. The seasonal trends of all datasets were extracted using the Seasonal Trend decomposition procedure based on LOcally wEighted Scatterplot Smoothing (LOESS) (STL) and Census X-11 methods, used as references. The statistical Cross Correlation Function (CCF), Signal to Noise Ratio (SNR), and Mean Standard Error (MSE), indexes, plus a Magnitude-Shape quantitative model were used to calculate the correlation and similarity between original and corresponding decomposed and denoised reference Chl-a signals. The similarity indexes were analyzed to evaluate the similarity and correlation between reconstructed denoised signals with original Chl-a series, and between DWT seasonal components with the reference seasonal trends. For a more assessment, two different weekly averaged Chl-a series of SeaWiFS satellite sensor over Bermuda-Atlantic region (open ocean waters) and Chesapeake Bay (coastal waters) were evaluated using SeaBASS in situ measurements, and seasonal trends in comparison with corresponding DWT components. The results revealed that the “db10” and “db5” from Daubechies wavelet family were respectively the best options for denoising and decomposition of Chl-a series using WT methods. Also MWTs from Biorthogonal and Reverse biorthogonal wavelet families gave a poor performance, and therefore these functions are not recommended to use in DWT denoising and decomposition of Chl-a signals.

Design of Biorthogonal Wavelets based on Spline and Spline-like Functions for Image Compression

Wavelet theory inspired from Fourier analysis is based on the basis function and its properties. Different wavelets use different basis functions which may better suit to some applications. The properties of basis functions along with their shape and magnification effects the performance of an application. The standard biorthogonal wavelets utilize spline functions for their construction. In this paper first the design procedure of biorthogonal wavelets is presented. Then a modified spline function is proposed. Based on the proposed spline function, three biorthogonal wavelets are designed with different length. The performance of proposed wavelets is analyzed by applying them on to images for SPIHT compression. The simulation results shown that the proposed wavelets have performed well compared to that of standard spline based biorthogonal wavelets.

Wavelet Multi Resolution Analysis based Data Hiding with Scanned Secrete Images

Wavelet Multi Resolution Analysis (MRA) based data hiding with scanned secrete images is proposed for improvement of invisibility of the secrete images. Daubechies (biorthogonal basis was adopted as the wavelet, but it was demonstrated that the key image (or secret image data) information can be restored with the biorthogonal wavelet. Also, the information of what to adopt as the biorthogonal wavelet is hidden. Key image information can also be protected by doing so, that the horizontal biorthogonal wavelet of the image does not have to be the same as the vertical biorthogonal wavelet, and the insertion position of the secret image data can be freely selected. It is also possible to divide the bit string of the secret image data and insert it into an arbitrary high frequency component, that the information hiding capability changes depending on the number of bit strings (information amount) of the secret image data, and the secret image in the public image data. Random scanning is effective for improving the visibility of data, selection of scanning method type, random number initial value It was shown that sharing only among parties is useful for improving confidentiality, resistance to noise, resistance to data compression, and resistance to tampering with data.

Design and Implementation of New Biorthogonal Wavelets and its Application to Image Processing

Wavelet transformation has been an interesting field since its exposure with wavelet-based compression standard embedded zerotree wavelet. Though, the origin of wavelets back to many decades, the presence of research at the very beginning of wavelet bases is also being carried out in the research community. This is because of the wide presence of its applicability as well as its structure of adapting to the type of problem at hand. In this paper, an approach of designing biorthogonal wavelets is presented. This approach may be extended to design variety of wavelets. This paper mainly focus on the design steps and corresponding coding in MATLAB. By varying the length, type of the bases and other parameters, different wavelets may be devised.

Cuckoo Search Algorithm based on Levy flight for the Biorthogonal Wavelet Filters on Compressed Sensing

Cuckoo Search Algorithm based on Levy flight for the Biorthogonal Wavelet Filters on Compressed Sensing

Experimental Research on Evaluation of Soil Water Content Using Ground Penetrating Radar and Wavelet Packet-Based Energy Analysis

Soil water content is one of the most important factors affecting the safety and stability of buildings or structures, especially in roadbeds, slopes, earth dams and foundations. Accurate assessments of soil water content can ensure the quality of construction, reduce construction costs and prevent accidents, among other benefits. In this study, ground penetrating radar (GPR) was used to detect and evaluate changes in soil water content. The GPR signal is usually nonstationary and nonlinear; however, traditional Fourier theory is typically suitable for periodic stationary signals, and cannot reflect the law of the frequency and energy of the GPR signal changing with time. Wavelet transform has good time-frequency localization characteristics, and therefore represents a new method for analyzing and processing GPR signals. According to the time-frequency characteristics of GPR signals, in this paper, a new biorthogonal wavelet basis which was highly matched with the GPR waveform was constructed using the lifting framework of wavelet theory. Subsequently, an evaluation method, namely, the wavelet packet-based energy analysis (WPEA) method, was proposed. The method was utilized to calculate the wavelet packet-based energy indexes (WPEI) of the GPR single-channel signals for clay samples with water contents ranging from 10% to 24%. The research results showed that there was a highly correlated linear relationship between the WPEI and the soil water contents, and the relationship between the two was fitted with a linear fitting function. The feasibility of the method was verified by comparing our results with those obtained using classical wavelet bases to perform the wavelet packet transform. The large-area, continuous scanning measurement method of GPR was shown to be suitable for evaluations of soil water contents in roadbeds, slopes, earth dams, and foundations.

Calculation of the permittivity of inhomogeneous media based on the TEDAWT method

In the field of nondestructive inspection, ground-penetrating radar (GPR) is a widely used investigation tool, usually to evaluate quality and safety in structural engineering. However, its development has been limited due to differences in the dielectric constant in inhomogeneous media. In this study, a time-energy density analysis of wavelet transform (TEDAWT) method for GPR signal singularity recognition was proposed. In addition, a biorthogonal wavelet basis with high similarity to GPR signal waveform was innovatively constructed and added into the wavelet toolbox. A model experiment was conducted to validate the feasibility of inverse calculation of the permittivity of wet clay by the TEDAWT method. Results showed that this method offered the advantages of signal denoising, resolution improvement, singularity recognition in GPR signal processing. Subsequently, a basic flow chart was established, which could be used to inversely calculate the permittivity of inhomogeneous media, and be applied to the quantitative identification of the thickness of the reinforcement protective layer in an expressway tunnel. The calculation results showed that the inverse calculation value of reinforcement protection layer thickness was 3.74% lower than the average relative theoretical error value. That improved detection accuracy provided a new method to quantitatively identify inhomogeneous media by GPR.

Biorthogonal Wavelet Packets in $$H^s(\mathbb {K})$$

Biorthogonal Wavelet Packets in $$H^s(\mathbb {K})$$

Nonuniform biorthogonal wavelets on positive half line via Walsh Fourier transform

In this article, we introduce the notion of nonuniform biorthogonal wavelets on positive half line. We first establish the characterizations for the translates of a single function to form the Riesz bases for their closed linear span. We provide the complete characterization for the biorthogonality of the translates of scaling functions of two nonuniform multiresolution analysis and the associated biorthogonal wavelet families in L^2({mathbb {R}}^+). Furthermore, under the mild assumptions on the scaling functions and the corresponding wavelets associated with nonuniform multiresolution analysis, we show that the wavelets can generate Reisz bases.

A Fusion-Based Hybrid-Feature Approach for Recognition of Unconstrained Offline Handwritten Hindi Characters

Hindi is the official language of India and used by a large population for several public services like postal, bank, judiciary, and public surveys. Efficient management of these services needs language-based automation. The proposed model addresses the problem of handwritten Hindi character recognition using a machine learning approach. The pre-trained DCNN models namely; InceptionV3-Net, VGG19-Net, and ResNet50 were used for the extraction of salient features from the characters’ images. A novel approach of fusion is adopted in the proposed work; the DCNN-based features are fused with the handcrafted features received from Bi-orthogonal discrete wavelet transform. The feature size was reduced by the Principal Component Analysis method. The hybrid features were examined with popular classifiers namely; Multi-Layer Perceptron (MLP) and Support Vector Machine (SVM). The recognition cost was reduced by 84.37%. The model achieved significant scores of precision, recall, and F1-measure—98.78%, 98.67%, and 98.69%—with overall recognition accuracy of 98.73%.

Multiple Sclerosis Recognition by Biorthogonal Wavelet Features and Fitness-Scaled Adaptive Genetic Algorithm.

Aim: Multiple sclerosis (MS) is a disease, which can affect the brain and/or spinal cord, leading to a wide range of potential symptoms. This method aims to propose a novel MS recognition method.Methods: First, the bior4.4 wavelet is used to extract multiscale coefficients. Second, three types of biorthogonal wavelet features are proposed and calculated. Third, fitness-scaled adaptive genetic algorithm (FAGA)—a combination of standard genetic algorithm, adaptive mechanism, and power-rank fitness scaling—is harnessed as the optimization algorithm. Fourth, multiple-way data augmentation is utilized on the training set under the setting of 10 runs of 10-fold cross-validation. Our method is abbreviated as BWF-FAGA.Results: Our method achieves a sensitivity of 98.00 ± 0.95%, a specificity of 97.78 ± 0.95%, and an accuracy of 97.89 ± 0.94%. The area under the curve of our method is 0.9876.Conclusion: The results show that the proposed BWF-FAGA method is better than 10 state-of-the-art MS recognition methods, including eight artificial intelligence-based methods, and two deep learning-based methods.

Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and application to free-slip divergence-free wavelets

This paper presents a new construction of a homogeneous Dirichlet wavelet basis on the unit interval, linked by a diagonal differentiation-integration relation to a standard biorthogonal wavelet basis. This allows to compute the solution of Poisson equation by renormalizing the wavelet coefficients - as in Fourier domain but using locally supported basis functions with boundary conditions-, which yields a linear complexity O(N) for this problem. Another application concerns the construction of free-slip divergence-free wavelet bases of the hypercube, in general dimension, with an associated decomposition algorithm as simple as in the periodic case.

Segmentation Based Biomedical Image Retrieval with Low-Level Feature Extraction

Content based image retrieval (CBIR) is an imperative and testing errand in numerous fields, for example, military, common, restorative and even in web applications. Here, we implemented medical image retrieval focused on novel material with decimated bi-orthogonal spline wavelet filter banks. Proposed algorithm is an extension for the existing low-level feature extraction method done by using spline wavelet filters, also utilized iterative partitioning (IP) for extracting the similar patterns of Pictures of query & database. In terms of consistency & memory, simulation results indicate that the approach suggested was better than the current scheme.