Multi-resolution Wavelet Domain Research Articles

Image Denoising Based on Implementing Threshold Techniques in Multi-Resolution Wavelet Domain and Spatial Domain Filters

Image Denoising Based on Implementing Threshold Techniques in Multi-Resolution Wavelet Domain and Spatial Domain Filters

Multiresolution Daubechies finite wavelet domain method for transient dynamic wave analysis in elastic solids

AbstractThe multiresolution capability provided by the family of Daubechies wavelets is exploited to develop a new computational approach, termed as multiresolution finite wavelet domain method for the fast and hierarchical prediction of transient dynamic problems with focus on wave propagation in one‐ and two‐dimensional structural configurations. In the developed method, both scaling and wavelet functions are employed as basis functions for the approximation of displacements in the governing dynamic equations. Because of the orthogonal and the multiresolution properties of Daubechies wavelets, a two‐scale system of mass uncoupled dynamic equations, representing the coarse and the fine spatial wave component solutions is derived. Numerical results concerning wave propagation in one‐ and two‐dimensional elastic structures demonstrate substantial computational gains of the method in comparison with other well‐established numerical methods. Moreover, additional benefits of the involved coarse and fine solutions enabling the analysis and characterization of the resultant wave response are revealed and discussed.

Digital Image Denoising Techniques Based on Multi-Resolution Wavelet Domain with Spatial Filters: A Review

Recently, with the explosion in the number of digital images captured every day in all life aspects, there is a growing demand for more detailed and visually attractive images. However, the images taken by current sensors are inevitably degraded by noise in various fields, such as medical, astrophysics, weather forecasting, etc., which contributes to impaired visual image quality. Therefore, work is needed to reduce noise by preserving the textural, information, and structural features of the image. So far, there are different techniques for reducing noise that various researchers have done. Each technique has its advantages and disadvantages. In this paper, a review of some significant work in the field of image denoising based on that the denoising methods is presented. These methods can be classified as wavelet domain, spatial domain, or both methods can combine to obtain the advantage them. After a brief discussion, the classification of image denoising techniques is explained. A comparative analysis of various image denoising methods is also performed to help researchers in the image denoising area. Besides, standard measurement parameters have been used to compute the results and to evaluate the performance of the used denoising techniques. This review paper aims to provide functional knowledge of image denoising methods in a nutshell for applications using images to provide ease for selecting the ideal strategy according to the necessity.

An asymmetric image encryption mechanism using QR decomposition in hybrid multi-resolution wavelet domain

In this paper, an asymmetric image encryption mechanism using QR decomposition technique in hybrid multi-resolution wavelet (HMW) domain is presented. QR decomposition technique utilized here makes the system asymmetric, as the obtained permutation matrix serves as ciphertext and the product of orthogonal and triangular matrices act as decryption keys. It also enables compression as the ciphertext obtained through QR decomposition is a sparse matrix which can be stored using CSR method. The HMW is obtained by utilizing existing orthogonal transforms: Walsh transform and fractional Fourier transform (frFT). Here the fractional orders of fractional Fourier transform (frFT) matrices are employed here to generate HMW, which function as supplementary keys. Therefore, they enhance the key space and strengthen the proposed system. The proposed encryption system exhibits non-linearity and enlarged key-space to dodge any brute-force attack. Computer-based simulations have been carried out on the grayscale images to verify and validate the proposed encryption mechanism. And the results obtained clearly demonstrate the robustness of the proposed mechanism against occlusion and noise attacks.

An asymmetric watermarking scheme based on random decomposition in hybrid multi-resolution wavelet domain using 3D Lorenz chaotic system

In this paper, an asymmetric watermarking mechanism based on the random decomposition in hybrid multi-resolution wavelet domain is proposed. To further enhance the security of the watermarking scheme, Lorenz’s chaotic system is employed for pixel swap over process. The hybrid multi-resolution wavelets are created by utilizing Walsh transform and the fractional Fourier transform of several orders. These fractional orders along with the Lorenz framework's parameters and initial conditions broadened the key-space. The proposed mechanism has non-linear characteristics and an enlarged key-space to oppose any brute-force attack. The proposed system is validated on gray-scale images. The principle behind the development of the proposed scheme has been elaborated by carrying out cryptanalysis on system based on the random decomposition. Personal computer based reproductions have been implemented to prove the validity and authenticity of the scheme. Results obtained authenticate that the proposed cryptosystem not only offers higher protection against brute force and noise attacks but is also unassailable to special attack.

An iris biometric protection scheme using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain

In this paper, a hybrid iris biometric protection scheme using 4D hyperchaotic system by means of coherent superposition and modified equal modulus decomposition in hybrid multi-resolution wavelet domain is proposed. The 4D hyperchaotic framework is employed for producing the permutation keystream for pixel swap-over mechanism. The hybrid multi-resolution is produced by means of Kronecker product of Walsh transform and fractional Fourier transform of different orders. Fractional orders of the hybrid multiresolution wavelet along with the parameters and initial conditions of the 4D hyperchaotic framework, later fill in as additional keys, thus enhancing the key space of the proposed mechanism. The proposed scheme has nonlinear characteristics and has high robustness against brute-force attack attributable to its enormous key-space. Numerical simulations have been carried out on grayscale images to prove the authenticity and efficacy of the proposed cryptosystem. The functioning of the proposed cryptosystem is investigated against various attacks including special attack. Outcomes display that the proposed iris template protection scheme not only has higher robustness against noise attack but is also unassailable to the iterative transform-based attacks.

An asymmetric hybrid cryptosystem using hyperchaotic system and random decomposition in hybrid multi resolution wavelet domain

In this paper, an asymmetric hybrid cryptosystem utilizing four-dimensional (4D) hyperchaotic framework by means of coherent superposition and random decomposition in hybrid multi-resolution wavelet domain is put forward. The 4D hyperchaotic framework is utilized for creating permutation keystream for a pixel swapping procedure. The hybrid multi-resolution wavelet is formed by combining Walsh transform and fractional Fourier transform of various orders. The 4D hyperchaotic framework’s parameters and preliminary conditions alongside the fractional orders extend the key-space and consequently give additional strength to the proposed cryptosystem. The proposed cryptosystem has an extended key-space to avoid any brute-force attack and is nonlinear in nature. The scheme is validated on greyscale images. Computer-based simulations have been executed to validate the robustness of the proposed scheme against different types of attacks. Results demonstrate that the proposed cryptosystem along with offering higher protection against noise and occlusion attacks is also unassailable to special attack.

Asymmetric hybrid encryption scheme based on modified equal modulus decomposition in hybrid multi-resolution wavelet domain

ABSTRACTIn this paper, an asymmetric hybrid encryption scheme, using coherent superposition and modified equal modulus decomposition in a hybrid multi-resolution wavelet, is proposed. The hybrid multi-resolution wavelet is generated using fractional Fourier transform of multiple orders and Walsh transform. The fractional orders of the fractional Fourier transform increase the key space and hence provide additional strength to the cryptosystem. The designed scheme has a large key space to avoid brute-force attack and is non-linear in nature. The scheme is validated on grey-scale images. Computer-based simulations have been performed to verify the validity and performance of the proposed scheme against various attacks. Scheme's robustness to the special attack is also checked. Results show that single equal modulus decomposition with fractional Fourier transform and hybrid transform are vulnerable to the special attack, whereas the proposed scheme endures the special attack.

Optical asymmetric watermarking using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain

In this paper, an asymmetric optical watermarking scheme using 4D hyperchaotic system with coherent superposition and modified equal modulus decomposition in hybrid multi-resolution wavelet domain is proposed. The 4D hyperchaotic system is used for generating permutation keystream for a pixel-swapping mechanism. The hybrid multi-resolution is generated using both the fractional Fourier transform of multiple orders and Walsh transform. The 4D hyperchaotic system’s parameters and initial conditions along with the multiple fractional orders of the fractional Fourier transform increase the key-space and hence provide additional strength to the watermarking mechanism. The designed watermarking scheme is non-linear in nature and resists brute-force attack due to its large key-space. Computer-based simulations have been performed on grayscale images to verify the validity and performance of the scheme against various attacks including special attack. Results show that the proposed watermarking scheme not only offers high resistance to occlusion and noise attacks but is also invulnerable to the special attack.

Adaptive video watermarking integrating a fuzzy wavelet-based human visual system perceptual model

An adaptive Fuzzy Inference Perceptual model has been proposed for watermarking of video streams. The model is designed to be adaptive to the human visual characteristics to attest the owner identification and discourage the unauthorized copying. The proposed model integrates the human visual characteristics of video motion sub-regions, in the frequency multi-resolution wavelet domain, with multi-dimensional fuzzy inference perceptual model. The designed fuzzy multi-variable input system inherits luminance, texture and gradient to generate an adaptive watermark embedding strength factor. Interacting motion estimation is applied for the selection of the candidate frames and sub-blocks. A fuzzy-based scheme has been proposed to generate a perceptual membership degree for strength watermark embedding factor for the selected candidate motion blocks. Experiments have been carried out with different benchmark test videos of different sizes, visual characteristics and sampling rates. Various sizes of watermark signatures have been applied on the model. Several experimental attacks have been applied such as frame dropping, frame averaging, JPEG compression, Gaussian noises. It manifests considerable robustness against various geometric and signal processing attacks. Several attacks have been applied to the proposed scheme and the experiments revealed promising results in terms of visual quality and extracted watermark distortion. In addition, the model has been compared with different other watermarking schemes in literature. The proposed model showed superior performance in terms of fidelity, robustness to attacks and high level of imperceptibility.

A New Approach for Secure Data Transfer based on Wavelet Transform.

In today's world, there are a number of cryptographic and steganographic techniques used in order to have secured data transfer between a sender and a receiver. In this paper we present a new hybrid approach that integrates the merits of cryptography and Image steganography based on multi resolution wavelet domain. First, the original message is encrypted using modified blowfish algorithm and the resultant cipher text is embedded into a cover image. After that the Steg image is decomposed into approximation and detailed image using discrete wavelet transform. The resultant reduced image is transmitted to the receiver and the reverse process is done in order to get back the original plain text. Our experimental results show that our system is unique in its design as well as it is suspicion less.

A Novel Multiresolution Spatiotemporal Saliency Detection Model and Its Applications in Image and Video Compression

Salient areas in natural scenes are generally regarded as areas which the human eye will typically focus on, and finding these areas is the key step in object detection. In computer vision, many models have been proposed to simulate the behavior of eyes such as SaliencyToolBox (STB), Neuromorphic Vision Toolkit (NVT), and others, but they demand high computational cost and computing useful results mostly relies on their choice of parameters. Although some region-based approaches were proposed to reduce the computational complexity of feature maps, these approaches still were not able to work in real time. Recently, a simple and fast approach called spectral residual (SR) was proposed, which uses the SR of the amplitude spectrum to calculate the image's saliency map. However, in our previous work, we pointed out that it is the phase spectrum, not the amplitude spectrum, of an image's Fourier transform that is key to calculating the location of salient areas, and proposed the phase spectrum of Fourier transform (PFT) model. In this paper, we present a quaternion representation of an image which is composed of intensity, color, and motion features. Based on the principle of PFT, a novel multiresolution spatiotemporal saliency detection model called phase spectrum of quaternion Fourier transform (PQFT) is proposed in this paper to calculate the spatiotemporal saliency map of an image by its quaternion representation. Distinct from other models, the added motion dimension allows the phase spectrum to represent spatiotemporal saliency in order to perform attention selection not only for images but also for videos. In addition, the PQFT model can compute the saliency map of an image under various resolutions from coarse to fine. Therefore, the hierarchical selectivity (HS) framework based on the PQFT model is introduced here to construct the tree structure representation of an image. With the help of HS, a model called multiresolution wavelet domain foveation (MWDF) is proposed in this paper to improve coding efficiency in image and video compression. Extensive tests of videos, natural images, and psychological patterns show that the proposed PQFT model is more effective in saliency detection and can predict eye fixations better than other state-of-the-art models in previous literature. Moreover, our model requires low computational cost and, therefore, can work in real time. Additional experiments on image and video compression show that the HS-MWDF model can achieve higher compression rate than the traditional model.

Content-Based Image Retrieval Using Multiresolution Color and Texture Features

In this paper, we propose a content-based image retrieval method based on an efficient combination of multiresolution color and texture features. As its color features, color autocorrelo- grams of the hue and saturation component images in HSV color space are used. As its texture features, BDIP and BVLC moments of the value component image are adopted. The color and texture features are extracted in multiresolution wavelet domain and combined. The dimension of the combined feature vector is determined at a point where the retrieval accuracy becomes saturated. Experimental results show that the proposed method yields higher retrieval accuracy than some conventional methods even though its feature vector dimension is not higher than those of the latter for six test DBs. Especially, it demonstrates more excellent retrieval accuracy for queries and target images of various resolutions. In addition, the proposed method almost always shows performance gain in precision versus recall and in ANMRR over the other methods.

Modified LDA classifier in multi resolution wavelet domain for multi-pose face recognition

Abstract:This paper presents multipose faces recognition. The proposed scheme is based onholistic information of face image and small modification of classical LDA (modifiedLDA) classifier. The holistic information called as facial features is obtained by multiresolutionwavelet analysis. The modified LDA (MLDA) classifier that works based onmultivariate analysis classifies the facial features to a person’s class. The objectives ofthe proposed method are to create a compact and meaningful facial features withoutremoving significant face image information, to build a simple classification techniquewhich can well classify face images to a person’s class, to make the M-LDA-basedtraining system to solve the retraining problem of the PCA and LDA based recognitionsystem, to reduce the high memory space requirement of classical LDA and PCA, andto compare the effectiveness of proposed method to established LDA based recognitionsystems such as RLDA, DLDA, and SLDA. The result shows that the proposed methodgives good enough performance i.e. high enough success rate, short time processing,and small enough EER compare to establish LDA. In addition, the wavelet transforms isan efficient way for reducing the dimensional size of original image.

A fast wavelet-based moment method for solving thin-wire EFIE

Solving the thin-wire electric field integral equation (EFIE) by the multiresolution wavelet expansion method involves a time-consuming double numerical integration for each nonzero element of the moment matrix which in turn can outweigh the advantages of achieving a sparse matrix. To speed up the matrix fill process in wavelet-based moment method codes, first, the triangular scaling functions of a nonorthogonal piecewise liner wavelet at the finest spatial resolution are appropriately replaced by sinusoidal dipoles for which mutual impedances are available in closed-form analytical expressions. The fast wavelet bases transform is then exploited to effectively transfer the resultant matrix equation to multiresolution wavelet domain. Numerical results obtained by the compactly supported semi-orthogonal linear B-spline wavelet demonstrate dramatic reduction of the overall solution time without any degradation in the accuracy of the final solution

Application of multi-resolution analysis of wavelets to nondestructive damage evaluation: I. Theory

A wavelet application to the vibration-based damage evaluation technique is introduced. Using a few of the lower mode shapes before and after a small damage event, the proposed method is able to provide the unique damage indices in order to detect, locate, and size damage on beam-like and plate-like structures. Based on a small damage assumption, a damage index equation is revealedn the context of elasticity. It turns out that the resulting damage index equation inherently suffers from singularities near inflection nodes. The transformation of the problem into the multi-resolution wavelet domain provides a set of coupled linear equations. With the aid of the singular value decomposition technique, the solution to the damage index equation is achieved in the Haar wavelet space. Next, the physical desired solution to the damage index equation is reconstructed from the one in the wavelet space.

Nondestructive damage evaluation of plates using the multi-resolution analysis of two-dimensional Haar wavelet

A wavelet application to the vibration-based damage evaluation technique is introduced. The proposed method requires only a few of the lower mode shapes before and after a small damage event in order to detect, locate, and size damage on plate-like structures. The proposed method takes account for uncertainty in mass density, surrounding forces, foundation stiffness, etc. Based on a small damage assumption of a thin plate, the two-dimensional damage index (DI) equation is revealed within the context of elasticity. The singularity problem, which occurs in the resulting DI equation, is solved in the two-dimensional multi-resolution wavelet domain with the aid of the singular value decomposition technique. Finally, the desired damage measures are reconstructed from the one in the wavelet space by inverse wavelet transformation. The performance of the proposed method is compared with an existing damage detection method. Finally, an uncertainty analysis of the proposed method is provided.

Damage estimation on beam-like structures using the multi-resolution analysis

This work proposes a vibration-based damage evaluation method that can detect, locate, and size damage utilizing only a few of the lower mode shapes. The proposed method is particularly advantageous for beam-like structures with uncertain applied axial load, mass density, and foundation stiffness. Based on a small damage assumption, a linear relationship between damaged and undamaged curvatures is revealed in the context of elasticity. It turns out that the resulting damage index equation inherently suffers from singularities near inflection nodes. The transformation of the problem into the multi-resolution wavelet domain provides a set of coupled linear equations. With the aid of the singular value decomposition technique, the solution to the damage index equation is achieved in the wavelet space. Next, the desired physical solution to the damage index equation is reconstructed from the one in the wavelet space. The performance of the proposed method is compared with two existing damage detection methods using a set of numerical simulations. The proposed method attempts to resolve the mode selection problem, the singularity problem, the axial force problem, and the absolute severity estimation problem, all of which remained unsolved by earlier attempts.

Exact and fast algorithm for two-dimensional image wavelet moments via the projection transform

Wavelet moments are perfect representations of moments in multiresolution wavelet domain, which integrates the theory of moment invariants into wavelet analysis. However, the calculations of moments are very complicated in terms of computational complexity, so it is difficult to implement them in real time. An exact and fast projection-based algorithm for two-dimensional wavelet moments is presented in this paper. In our approach, the computation of a two-dimensional wavelet moment of order of r is performed in ( r + 1 ) different one-dimensional spaces. Since only additions are required to perform the projection transform, the total computational complexity can be greatly reduced.