Model In Wavelet Domain Research Articles

Wavelet Transform-Assisted Adaptive Generative Modeling for Colorization

Unsupervised deep learning has recently demonstrated the promise to produce high-quality samples. While it has tremendous potential to promote the image colorization task, the performance is limited owing to the high-dimension of data manifold and model capability. This study presents a novel scheme that exploiting the score-based generative model in wavelet domain to address the issue. By taking advantage of the multi-scale and multi-channel representation via wavelet transform, the proposed model learns the priors from stacked wavelet coefficient components, thus learns the image characteristics under coarse and detail frequency spectrums jointly and effectively. Moreover, such a highly flexible generative model without adversarial optimization can execute colorization tasks better under dual consistency terms in wavelet domain, namely data-consistency and structure-consistency. Specifically, in the training phase, a set of multi-channel tensors consisting of wavelet coefficients are used as the input to train the network by denoising score matching. In the test phase, samples are iteratively generated via annealed Langevin dynamics with data and structure consistencies. Experiments demonstrated remarkable improvements of the proposed model on colorization quality, particularly on colorization robustness and diversity.

A Robust Model Using SIFT and Gamma Mixture Model for Texture Images Classification: Perspectives for Medical Applications

The texture analysis of medical images is a powerful calculation tool for the discrimination between pathological and healthy tissue in different organs in medical images. Our paper proposes a novel approach named, GGD-GMM, based on statistical modeling in wavelet domain to describe texture images. Firstly, we propose a robust algorithm based on the combination of the wavelet transform and Scale Invariant Feature Transform (SIFT). Secondly, we implement the aforementioned algorithm and fit the result by using the finite Gamma Mixture Model (GMM). The results, obtained for two benchmark datasets, show that our proposed algorithm has a good relevance as it provides higher classification accuracy compared to some other well known models. Moreover, it displays others advantages relied to Noise-resistant and rotation invariant. Our algorithm could be useful for the analysis of several medical issues.

Adaptive Estimation of Parameters of a Gaussian Multifractal Model of Network Traffic in the Wavelet Domain

In this paper, an algorithm for adaptive estimation of the parameters of a multifractal model is proposed considering the Haar wavelet transform. The multifractal model is intended to describe real network traffic traces and it is based on a multiplicative cascade in the Wavelet domain, where it is assumed that the multipliers and other parameters of the model are Gaussian. Simulations are carried out to evaluate the performance of the Gaussian Wavelet Domain Model in capturing characteristics of real traffic traces with the application of the proposed parameter estimation algorithm in comparison to other models known in the literature.

Unsupervised change detection of VHR remote sensing images based on multi-resolution Markov Random Field in wavelet domain

ABSTRACT This paper proposes an unsupervised change detection method for very-high-resolution (VHR) remote sensing images based on multi-resolution Markov random field (MRF) model in wavelet domain. Firstly, the wavelet transform is performed on the difference image achieved by the change vector analysis (CVA) method, and the wavelet coefficients at each scale are obtained. Then, MRF model is constructed based on the wavelet coefficients. The wavelet high-frequency coefficients establish a feature field model that describes the feature attributes of each pixel location at each scale. The initial change map (changed and unchanged) at the coarse scale are generated through applying the k-means method to the wavelet low-frequency coefficients, and a label field model describing the region of the variation results is established. The label and feature field, at the same scale, got the optimized change map under the Bayesian criterion. Finally, the results of the low-resolution scale change map are directly projected as the adjacent higher-scale initial change map. The more accurate change map is obtained successively from the coarse scale to the original resolution scale, and the detection result of the original resolution is obtained at last. Experiments on Quick Bird, SPOT-5, and IKONOS optical images have demonstrated the effectiveness of the proposed method. The experimental results show that the method has better regional consistency and strong robustness.

Bone Suppression of Chest Radiographs With Cascaded Convolutional Networks in Wavelet Domain

Bone suppression of chest radiographs (CXRs) is potentially useful for diagnosing lung diseases for radiologists and computer–aided diagnosis. This paper presents a cascaded convolutional network model in wavelet domain (Wavelet-CCN) for bone suppression in single conventional CXR. Wavelet coefficients are sparse and suitable as the output of convolutional network. The convolutional networks are trained to predict the wavelet coefficients of bone images from the wavelet coefficients of CXRs, using real two-exposure dual energy subtraction (DES) CXRs as training data. By combining the multi-level wavelet decomposition and a cascaded refinement framework, the Wavelet-CCN model can work automatically with a multi-scale approach and progressively refine the prediction in terms of accuracy and spatial resolution. Compared with previous work of CamsNet model which preforms bone prediction in gradient domain, the Wavelet-CCN model predicts the wavelet coefficients to reconstruct bone images and can avoid the inconsistent background intensity caused by 2D integration of gradients. The predicted bone image is subtracted from the original CXR to produce a soft-tissue image. The Wavelet-CCN model and its variants with different wavelet basis are evaluated on a dataset that consists of 504 cases of real two-exposure DES CXRs (404 cases for training and 100 cases for test). Experimental results show that among all the variants and different wavelet bases, the Wavelet-CCN model with Haar wavelet performs best. The average peak signal-to-noise ratio and structural similarity index of the soft-tissue images produced by the proposed Wavelet-CCN model are both higher than those of the previous CamsNet model in gradient domain, reaching values of 39.4 (±0.94) dB and 0.977 (±0.004), respectively. The results also demonstrate that the Wavelet-CCN model can process the CXRs acquired by four types of X-ray machines.

A new locally optimum watermark detection using vector-based hidden Markov model in wavelet domain

Watermark detection is a way of verifying the existence of a watermark in a watermarking scheme used for copyright protection of digital data. Statistical modeling of wavelet subband coefficients has been extensively used in watermark detection. The effectiveness of a watermarking scheme depends directly on how the wavelet coefficients are modeled. It is known that the vector-based hidden Markov model (HMM) is a very powerful statistical model for describing the distribution of the wavelet coefficients, since it is capable of capturing the subband marginal distribution as well as the inter-scale and cross orientation dependencies of the wavelet coefficients. In this paper, it is shown that modeling using the vector-based HMM gives a better fit for the empirical data in comparison to modeling with Cauchy, Bessel-K form (BKF) and generalized Gaussian (GG) distributions. In view of this, we propose a locally-optimum blind watermark detector using the vector-based HMM in the wavelet domain. In a Bayesian framework, closed-form expressions for the mean and variance of a test statistic are derived, experimentally validated and used in evaluating the performance of the proposed detector. Using a number of test images, the performance of the proposed detector is evaluated. It is shown that the proposed detector provides a detection rate higher than that provided by other detectors designed based on the Cauchy, Gaussian, BKF or GG distributions for the wavelet coefficients. The proposed detector is also shown to be highly robust against various kinds of attacks.

Evaluation of optical properties for real photonic crystal fiber based on total variation in wavelet domain

Abstract An evaluation method based on the total variation model (TV) in wavelet domain is proposed for modeling optical properties of real photonic crystal fibers (PCFs). The TV model in wavelet domain is set up to suppress the noise of the original image effectively and rebuild the cross section images of real PCFs with high accuracy. The optical properties of three PCFs are evaluated, including two kinds of PCFs that supplied from the Crystal Fiber A/S and a homemade side-leakage PCF, by using the combination of the proposed model and finite element method. Numerical results demonstrate that the proposed method can obtain high noise suppression ratio and effectively reduce the noise of cross section images of PCFs, which leads to an accurate evaluation of optical properties of real PCFs. To the best of our knowledge, it is the first time to denoise the cross section images of PCFs with the TV model in the wavelet domain.

Texture retrieval using mixtures of generalized Gaussian distribution and Cauchy–Schwarz divergence in wavelet domain

This paper presents a novel similarity measure in a texture retrieval framework based on statistical modeling in wavelet domain. In this context, we use the recently proposed finite mixture of generalized Gaussian distribution (MoGG) thanks to its ability to model accurately a wide range of wavelet sub-bands histograms. This model has already been relied on the approximation of Kullback–Leibler divergence (KLD) which hinders significantly the retrieval process. To overcome this drawback, we introduce the Cauchy–Schwarz divergence (CSD) between two MoGG distributions as a similarity measure. Hence, an analytic closed-form expression of this measure is developed in the case of fixed shape parameter. Otherwise, when the shape parameter is variable, two approximations are derived using the well-known stochastic integration with Monte-Carlo simulations and numerical integration with Simpson׳s rule. Experiments conducted on a well known dataset show good performance of the CSD in terms of retrieval rates and the computational time improvement compared to the KLD.

An image segmentation algorithm based on improved multiscale random field model in wavelet domain

Image segmentation is the key step in image analysis and image manipulating. Image segmentation based on multiscale random field model in wavelet domain (WMSRF) is a useful implementation tool. It can capture image structure information in different resolution and reduce the reliance on initial segmentation. However, WMSRF has boundary block effect and its operating efficiency is low. In this paper we propose an improved segmentation algorithm based on WMSRF (improved WMSRF). The improved WMSRF algorithm consists of two fields: the image characteristic field and the labeling field. The former is built on a series of boundary that is extracted by wavelet transform, and modeled by Gauss-MRF. The latter is also built on the boundary in corresponding scale, and modeled by multiscale random field (MSRF). Both fields constrain each other at the joint probability. This integrates interactions in inter-scale and inner-scale, and helps to describe image’s non-stationary property. Then the parameters in the models are estimated by using expectation–maximization. Consequently the segmentation result of initial image is achieved by using Bayesian and sequential maximum a posteriori estimation. In this paper, the medical images are utilized as experiment images. The simulations are compared with the WMSRF algorithm and the results show the improved algorithm can not only distinguish different regions effectively, but also improve the efficiency.

Wavelet-based classification and influence matrix analysis method for the fast discrimination of Chinese herbal medicines according to the geographical origins with near infrared spectroscopy

A discriminant analysis technique using wavelet transformation (WT) and influence matrix analysis (CAIMAN) method is proposed for the near infrared (NIR) spectroscopy classification. In the proposed methodology, NIR spectra are decomposed by WT for data compression and a forward feature selection is further employed to extract the relevant information from the wavelet coefficients, reducing both classification errors and model complexity. A discriminant-CAIMAN (D-CAIMAN) method is utilized to build the classification model in wavelet domain on the basis of reduced wavelet coefficients of spectral variables. NIR spectra data set of 265 salviae miltiorrhizae radix samples from 9 different geographical origins is used as an example to test the classification performance of the algorithm. For a comparison, k-nearest neighbor (KNN), linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA) methods are also employed. D-CAIMAN with wavelet-based feature selection (WD-CAIMAN) method shows the best performance, achieving the total classification rate of 100% in both cross-validation set and prediction set. It is worth noting that the WD-CAIMAN classifier also shows improved sensitivity, selectivity and model interpretability in the classifications.

Tree-Based Backtracking Orthogonal Matching Pursuit for Sparse Signal Reconstruction

Compressed sensing (CS) is a theory which exploits the sparsity characteristic of the original signal in signal sampling and coding. By solving an optimization problem, the original sparse signal can be reconstructed accurately. In this paper, a new Tree-based Backtracking Orthogonal Matching Pursuit (TBOMP) algorithm is presented with the idea of the tree model in wavelet domain. The algorithm can convert the wavelet tree structure to the corresponding relations of candidate atoms without any prior information of signal sparsity. Thus, the atom selection process will be more structural and the search space can be narrowed. Moreover, according to the backtracking process, the previous chosen atoms’ reliability can be detected and the unreliable atoms can be deleted at each iteration, which leads to an accurate reconstruction of the signal ultimately. Compared with other compressed sensing algorithms, simulation results show the proposed algorithm’s superior performance to that of several other OMP-type algorithms.

SAR Image Multiclass Segmentation Using a Multiscale TMF Model in Wavelet Domain

The triplet Markov field (TMF) model recently proposed is suitable for dealing with nonstationary synthetic aperture radar (SAR) image segmentation. In this letter, we propose a multiscale TMF model in wavelet domain, named as the wavelet-domain TMF (WTMF) model. In the WTMF model, a multiscale causal WTMF energy function is constructed to capture the intra- and interscale dependences in random fields <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(X, U)$</tex> </formula> . Moreover, multiscale likelihoods of the WTMF model are derived based on a wavelet hidden Markov tree to capture the statistical properties of wavelet coefficients. The proposed model can integrate the global and local information in terms of spatial configuration and image features in a more complete manner. The coarser scale information is utilized to guide the finer scale segmentation, and the coarse-to-fine causal interactions are considered using a Markov chain. Experimental results prove that the proposed model can segment SAR images better than several models previously proposed.

A multi-scale pseudo-force model in wavelet domain for identification of damage in structural components

Damage identification using wavelet-transform (WT)-processed vibration signals has been practiced over the years. In most studies, WT was used as an effective signal analysis tool to filter out noise and bring damage-incurred singularities into prominence. In spite of its proven effectiveness, such a processing is often carried out without theoretical footstones sustained by solid mechanics models, which are able to link characteristics of WT with features of damage. In the present work, a multi-scale pseudo-force model over wavelet domain was developed for vibration-based damage identification. By canvassing damage-caused local perturbance to dynamic equilibrium characteristics of a structural component, the underlying hypostasis of the model has explicit physical implication, addressing features of damage (e.g., a slot or a fine crack) and enabling a sophisticated solution to multi-scale modeling and identification of damage. In the model, WT was used as a multi-scale differential operator to acquire higher-order derivatives of equation of motion for characterizing damage of tiny dimension. The multi-scale nature brings additional benefits to enhance robustness of the detection under noisy measurement conditions. Without loss of generality, an Euler–Bernoulli beam component (EBC) was considered to facilitate understanding of the principle of the model. As proof-of-concept validation, a fine crack in an EBC was quantified using the model through numerical simulation and experiment. Satisfactory results have demonstrated the effectiveness of the model in evaluating fine damage and enhancing tolerance of the detection to measurement noise.

Nonsubsampled contourlet transform-based algorithm for no-reference image quality assessment

No-reference image quality assessment (NRIQA) is to be used when a reference image may not be available. The existing well-known NRIQA algorithms are those that use natural scene statistics (NSS), such as NSS model in wavelet domain (WNSS) and NSS model in contourlet domain (CNSS). WNSS is only applicable to evaluate JPEG2000 compressed images, while CNSS can be used to evaluate five different distortion types of image sets such as JPEG, JPEG2000, white noise, Gaussian blur, and fast fading. However, due to the downsamplers and upsamplers, the contourlet transform is not shift-invariant and may cause pseudo-Gibbs phenomena. In this paper, we propose an improved NRIQA based on the nonsubsampled contourlet transform (NSCT) which has shift-invariant characteristics, multiscale, and multidirection expansion. The basic observation of the proposed algorithm is that in the nonsubsampled contourlet domain natural images exhibit certain common joint statistical characteristics which can be represented by a mathematical model and disturbed by a wide variety of distortions. Performance evaluation tests show that the predicted quality scores obtained by the proposed algorithm are more effective and consistent with visual quality than those by WNSS or CNSS-based NRIQA on four distortion types of image sets in the LIVE image database except for JPEG2000 compressed images.

A comparison of robust Bayesian and LVQ neural network for visual uniformity recognition of nonwovens

The visual uniformity recognition of nonwoven materials using image analysis and neural network is a typical application of pattern recognition in textile industry. In this paper, we try to find a solution to this problem by combining the generalized Gaussian density (GGD) model in wavelet domain and two types of neural networks, robust Bayesian and learning vector quantization (LVQ) neural network. The proposed model is constituted with two stages, i.e., texture representation and pattern recognition. For texture representation, each image is decomposed into four levels using the 9-7 bi-orthogonal wavelet base. The wavelet coefficients in each subband are independently modelled by the GGD model. Moreover, taken as textural features, the corresponding scale and shape parameters estimated from the wavelet coefficients distribution with the maximum likelihood (ML) estimation are extracted in order to train and test the neural network for visual uniformity classification. During the pattern recognition part, robust Bayesian neural network and LVQ neural network are used as classifier. Especially, the experiments based on robust Bayesian neural network are taken as the key point. Experimental results indicate that the robust Bayesian neural network perform superiorly.

Bayesian Image Denoising Using an Anisotropic Markov Random Field Model

This paper presents a Bayesian denoising method based on an anisotropic Markov Random Field (MRF) model in wavelet domain in order to improve the image denoising performance and reduce the computational complexity. The classical single-resolution image restoration method using MRFs and the maximum a posteriori (MAP) estimation is extended to the wavelet domain. To obtain the accurate MAP estimation, a novel anisotropic MRF model is proposed under this framework. As compared to the simple isotropic MRF model, this new model can capture the intrascale dependencies of wavelet coefficients significantly better. Simulation results demonstrate our proposed method has a good denoising performance while reducing the computational complexity.

Steganography for 3D Model Based on Frame Transform and HMM Model in Wavelet Domain

Steganography for 3D Model Based on Frame Transform and HMM Model in Wavelet Domain

Supervised Image Segmentation Based on Tree-Structured MRF Model in Wavelet Domain

In the tree-structured Markov random field (TS-MRF) model, a sequence of MRFs was hierarchically defined on the single spatial resolution in the format of a tree structure which might suffer from the deficiency of modeling the nonstationary property of a given image. In order to overcome such a problem and motivated by nonredundant directional selectivity and highly discriminative nature of the wavelet representation, we attempt to introduce the TS-MRF model into the wavelet domain and propose a new image modeling method-WTS-MRF, in which each MRF is defined over a multiresolution subset of the lattice sites corresponding to the wavelet decomposition. Based on WTS-MRF, a supervised image segmentation algorithm is carried out, and experiment on a remotely sensed image proves the better performance than the supervised segmentation algorithm based on the TS-MRF model.

Denosing Algorithm Based on Local Laplace Model in Wavelet Domain and Its Application in Mechanical Fault Diagnosis

A denoising algorithm based on local Laplace model in wavelet domain is proposed,and it is successfully applied in mechanical fault diagnosis.Magnitude-phase compounding information of complex wavelet transform is used to position singular points of signal on each level for its good sensitivity to singular points of signal.And then the coefficients of real wavelet transform are separated into two sorts by the certain neighborhood width and the positions of singular points on each level,the two sorts include effective coefficients and ineffective coefficients.And ineffective coefficients out of neighborhoods of singular points are directly set zero,while local statistical distribution of efficient coefficients in neighborhood is assumed to Laplace model.And on the basis of prior distribution,maximum a posteriori(MAP) estimator is used to restore the wavelet coefficients to signal from the noisy observations.New wavelet coefficients are used for the reconstruction to the denoising signal.This algorithm is analyzed and certificated by simulation and automotive main reducer gear fault diagnosis example respectively.Analysis results show that this algorithm has good noise reduction effect,and can efficiently reduce the noise of gear fault signal in main reducer.

Writer identification of Chinese handwriting documents using hidden Markov tree model

Handwriting-based writer identification, a branch of biometrics, is an active research topic in pattern recognition. Since most existing methods and models aim to on-line and/or text-dependent writer identification, it is necessary to propose new methods for off-line, text-independent writer identification. At present, two-dimensional Gabor model is widely acknowledged as an effective and classic method for off-line, text-independent handwriting identification, while it still suffers from some inherent shortcomings, such as the excessive calculational cost. In this paper, we present a novel method based on hidden Markov tree (HMT) model in wavelet domain for off-line, text-independent writer identification of Chinese handwriting documents. Our experiments show this HMT method, compared with two-dimensional Gabor model, not only achieves better identification results but also greatly reduces the elapsed time on computation.