Three-layer Decomposition Research Articles

A three-layer decomposition method based on structural texture perception for fusion of CT and MRI images

The fusion of computed tomography (CT) images and magnetic resonance imaging (MRI) images has made essential contribution to clinical diagnosis because of its ability of complementary visual information enhancement and redundancy elimination. However, some methods that involve upsampling and downsampling operations may lose information during image processing, which affects the fusion results. In this paper, a medical image fusion algorithm based on structural texture perception is proposed. The proposed method demonstrates enhanced performance in preserving both detailed texture information and energy information of source images. First, the source image is decomposed into a signal strength layer, a base layer, and a texture layer based on the proposed three-layer decomposition framework. Then, the signal strength layers are fused using a saliency detection method based on iterative least squares. The texture layer is fused using the principle of spatial frequency maximization. For the fusion of the base layer, a non-linear function is designed to calculate the fusion weights. Finally, the final fusion result is obtained through image reconstruction. The proposed algorithm is compared with nine state-of-the-art fusion algorithms to verify its superiority. Experimental results show that the proposed method can effectively preserve the intensity information of CT images and the detailed texture of MRI images.

Functional and Anatomical Image Fusion Based on Gradient Enhanced Decomposition Model

Medical image fusion technology can synthesize complementary information from multimodal medical images while saving storage costs. Targeting the problems of reduced contrast, blurred details, color distortion, and excessive processing time requirement in fusion algorithms, we propose a new functional and anatomical image fusion algorithm based on a gradient enhanced decomposition model. First, a new gradient-enhanced decomposition (GED) model is proposed. Subsequently, the proposed GED model is expanded into a three-layer decomposition, wherein the input image is decomposed into a basic, local mean energy, and texture layers using alternating direction method of multipliers. Compared with other classic decomposition method, the proposed three-layer decomposition has the advantages of no additional noise and requiring less time while enhanced gradient. Second, we propose targeted fusion rules for each layer. After the basic layer is weighted averaged, the gamma function is used to adjust its brightness. The product of the local l2 norm and largest singular value constitutes the fusion weights of the local mean energy layers. The fusion weights of the texture layers are determined by the product of the local l1 norm and largest singular value. Finally, the fused image is reconstructed. We perform numerous experiments to prove that the proposed fusion algorithm providing clearer edge details and superior colors in a short processing time, and there was a statistically significant difference compare with other classical algorithms.

Predicting China’s energy consumption: Combining machine learning with three-layer decomposition approach

Accurately predicting energy consumption (EC) is a difficult task, owing to its inherent complexity and nonlinearity features. To decrease the complexity of EC predictions, applying a novel three-layer decomposition approach to decompose a complex series into a trend sub-series and several simpler non-trend sub-series. Since the trend sub-series describes the developing tendency that is determined by the primarily influencing factors on EC, it is predicted by multivariate linear regression (MLR). In view of its learning ability of nonlinear mappings and excellent performance in dealing with long term dependency, long short-term memory neural network (LSTM) is applied to predict non-trend sub-series. Then, the final EC prediction is solved by calculating the sum of all these sub-series prediction values. A novel EC forecasting model based on machine learning with three-layer decomposition-ensemble approach is proposed in this study. Compared with traditional decomposition approaches (trend decomposition (TD), wavelet decomposition (WD), empirical mode decomposition (EMD), TD-EMD and TD-WD), the proposed three-layer decomposition approach can improve the prediction performance by combining the advantages of TD, EMD and WD. The proposed forecasting model is validated by empirical studies using the EC data of China and U.S. Finally, this study gives the China’s EC prediction in 2020–2024.

Research on Multi-focal Image Fusion Based on Wavelet Transform

In recent years, wavelet transform theory has been paid more and more attention in image fusion. With the development of wavelet transform image fusion, wavelet transform is introduced, and the basic principles and types of wavelet transform are introduced. Then, aiming at two images with different focal lengths, the discrete wavelet transform method of three-layer decomposition is used, the low-frequency and high-frequency components are fused by different fusion rules, and the differences of different fusion strategies in wavelet transform image fusion are compared and analyzed. Experimental results show that wavelet transform has the characteristics of convenient application, rapid fusion and real image, and has a good application prospect.

Joint image fusion and denoising via three-layer decomposition and sparse representation

Image fusion has been received much attentions in recent years. However, solving both noise-free image fusion and noise-perturbed image fusion problems remains a big challenge. To solve the weak performance and low computational efficiency for current image fusion methods when dealing with the case of noisy source images, an image fusion method based on three-layer decomposition and sparse representation is proposed in this paper. In view of the high-pass characteristics of noise, the source image is first decomposed into the high-frequency and low-frequency components, and the sparse reconstruct error parameter is adaptively designed according with the noise level, so as to realize the fusion and denoising for high-frequency components simultaneously. To make full use of the details and energy in the low-frequency component, the structure–texture​ decomposition model is carried out and two fusion rules are carefully designed to fuse them. The fused image can be reconstructed by the perfused high-frequency, low-frequency structure and low-frequency texture layers. Experimental results demonstrate that the proposed method can effectively address the clean and noisy image fusion problems, and yield better performance than some state-of-the-art methods in terms of subjective visual and quantitative evaluations.

Medical image fusion based on hybrid three-layer decomposition model and nuclear norm

The aim of medical image fusion technology is to synthesize multiple-image information to assist doctors in making scientific decisions. Existing studies have focused on preserving image details while avoiding halo artifacts and color distortions. This paper proposes a novel medical image fusion algorithm based on this research objective. First, the input image is decomposed into structure, texture, and local mean brightness layers using a hybrid three-layer decomposition model that can fully extract the features of the original images without the introduction of artifacts. Secondly, the nuclear norm of the patches, which are obtained using a sliding window, are calculated to construct the weight maps of the structure and texture layers. The weight map of the local mean brightness layer is constructed by calculating the local energy. Finally, remapping functions are applied to enhance each fusion layer, which reconstructs the final fusion image with the inverse operation of decomposition. Subjective and objective experiments confirm that the proposed algorithm has a distinct advantage compared with other state-of-the-art algorithms.

Hyperspectral Inversion of Petroleum Hydrocarbon Contents in Soil Based on Continuum Removal and Wavelet Packet Decomposition

Hyperspectral remote sensing is widely used to detect petroleum hydrocarbon pollution in soil monitoring. Different spectral pretreatment methods seriously affect the prediction and analysis of petroleum hydrocarbon contents (PHCs). This study adopted a combined spectral data preprocessing technique that improves the prediction accuracy of petroleum hydrocarbons in soil. We combined continuum removal and wavelet packet decomposition (CR–Daubechies 3 (db3)) to process the hyperspectral reflectance data of 26 soil samples in the oil production work area in China and judged the correlation between spectral reflectance and petroleum hydrocarbons in soil. Partial least squares regression was used to construct an optimal model for the inversion of PHCs in soil and the leave-one-out cross-validation was used to select the best factor number. The best model of soil petroleum hydrocarbon inversion was determined by comprehensively comparing the initial spectrum, db3 to high-frequency spectrum, db3 to low-frequency spectrum, after-continuum removal spectrum, CR-db3 to high-frequency spectrum, and CR-db3 to low-frequency spectrum comprehensively. The main contributions of this study are as follows: (1) three-layer decomposition with CR-db3 can improve the correlation between spectral reflectance and PHCs and effectively improve the sensitivity of the spectrum to PHCs; (2) the prediction accuracy of the high-frequency spectrum of wavelet packet decomposition for PHCs in soil is higher than that of low-frequency information; (3) the proposed petroleum hydrocarbon prediction model based on CR-db3 processed spectra to obtain high-frequency information is optimal (coefficient of determination = 0.977, root mean square error of calibration = 3.078, root mean square error of cross-validation = 4.727, root mean square error of prediction = 4.498, ratio of performance to deviation = 6.12).

On the Symmetry Reduction of Information Inequalities

Information inequalities can be used to derive the fundamental limits of information systems. Many information inequalities and problem-specific constraints are linear equalities or inequalities of joint entropies, and thus, outer bounding the fundamental limits can be viewed as and in principle computed through linear programming. However, for many practical engineering problems, the resultant linear program (LP) is very large, rendering such a computational approach almost completely inapplicable in practice. It was shown recently that symmetry can be used to effectively reduce the scale of the LP; however, the precise amount of reduction was not well understood. In this paper, we provide a method to pinpoint this reduction by counting the number of orbits induced by the symmetry on the set of the LP variables and the LP constraints, respectively. The Polya counting theorem is a powerful tool for such counting task, which requires identifying the cycle index function. We propose a generic three-layer decomposition of the group structures for the quantities in typical information systems to facilitate such a calculation. Three problems are studied using this approach: extremal pairwise cyclically symmetric entropy inequalities, the regenerating code problem, and the caching problem, for which explicit formulas are provided for the cycle indices of the induced permutations.

Pansharpening with a Guided Filter Based on Three-Layer Decomposition.

State-of-the-art pansharpening methods generally inject the spatial structures of a high spatial resolution (HR) panchromatic (PAN) image into the corresponding low spatial resolution (LR) multispectral (MS) image by an injection model. In this paper, a novel pansharpening method with an edge-preserving guided filter based on three-layer decomposition is proposed. In the proposed method, the PAN image is decomposed into three layers: A strong edge layer, a detail layer, and a low-frequency layer. The edge layer and detail layer are then injected into the MS image by a proportional injection model. In addition, two new quantitative evaluation indices, including the modified correlation coefficient (MCC) and the modified universal image quality index (MUIQI) are developed. The proposed method was tested and verified by IKONOS, QuickBird, and Gaofen (GF)-1 satellite images, and it was compared with several of state-of-the-art pansharpening methods from both qualitative and quantitative aspects. The experimental results confirm the superiority of the proposed method.

The Rock–Water–Ice Topographic Gravity Field Model RWI_TOPO_2015 and Its Comparison to a Conventional Rock-Equivalent Version

RWI_TOPO_2015 is a new high-resolution spherical harmonic representation of the Earth’s topographic gravitational potential that is based on a refined Rock–Water–Ice (RWI) approach. This method is characterized by a three-layer decomposition of the Earth’s topography with respect to its rock, water, and ice masses. To allow a rigorous separate modeling of these masses with variable density values, gravity forward modeling is performed in the space domain using tesseroid mass bodies arranged on an ellipsoidal reference surface. While the predecessor model RWI_TOPO_2012 was based on the \(5'\times 5'\) global topographic database DTM2006.0 (Digital Topographic Model 2006.0), the new RWI model uses updated height information of the \(1'\times 1'\) Earth2014 topography suite. Moreover, in the case of RWI_TOPO_2015, the representation in spherical harmonics is extended to degree and order 2190 (formerly 1800). Beside a presentation of the used formalism, the processing for RWI_TOPO_2015 is described in detail, and the characteristics of the resulting spherical harmonic coefficients are analyzed in the space and frequency domain. Furthermore, this paper focuses on a comparison of the RWI approach to the conventionally used rock-equivalent method. For this purpose, a consistent rock-equivalent version REQ_TOPO_2015 is generated, in which the heights of water and ice masses are condensed to the constant rock density. When evaluated on the surface of the GRS80 ellipsoid (Geodetic Reference System 1980), the differences of RWI_TOPO_2015 and REQ_TOPO_2015 reach maximum amplitudes of about 1 m, 50 mGal, and 20 mE in terms of height anomaly, gravity disturbance, and the radial–radial gravity gradient, respectively. Although these differences are attenuated with increasing height above the ellipsoid, significant magnitudes can even be detected in the case of the satellite altitudes of current gravity field missions. In order to assess their performance, RWI_TOPO_2015, REQ_TOPO_2015, and RWI_TOPO_2012 are validated against independent gravity information of current global geopotential models, clearly demonstrating the attained improvements in the case of the new RWI model.

Cognitive approach to the construction of three-language terminological thesaurus

Cognitive approach to the construction of three-language terminological thesaurusThe paper is devoted to developing a lexicographic database of a three-language terminological dictionary. The detailed analysis of a relations scheme between tables and structures of tables with the help of three-layer decomposition predicate method is carried out, which has allowed to define ways of solving direct and reversible three-language electronic dictionaries creation problem.

A Wavelet-Based Assessment of Topographic-Isostatic Reductions for GOCE Gravity Gradients

Gravity gradient measurements from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE) contain significant high- and mid-frequency signal components, which are primarily caused by the attraction of the Earth’s topographic and isostatic masses. In order to mitigate the resulting numerical instability of a harmonic downward continuation, the observed gradients can be smoothed with respect to topographic-isostatic effects using a remove–compute–restore technique. For this reason, topographic-isostatic reductions are calculated by forward modeling that employs the advanced Rock–Water–Ice methodology. The basis of this approach is a three-layer decomposition of the topography with variable density values and a modified Airy–Heiskanen isostatic concept incorporating a depth model of the Mohorovicic discontinuity. Moreover, tesseroid bodies are utilized for mass discretization and arranged on an ellipsoidal reference surface. To evaluate the degree of smoothing via topographic-isostatic reduction of GOCE gravity gradients, a wavelet-based assessment is presented in this paper and compared with statistical inferences in the space domain. Using the Morlet wavelet, continuous wavelet transforms are applied to measured GOCE gravity gradients before and after reducing topographic-isostatic signals. By analyzing a representative data set in the Himalayan region, an employment of the reductions leads to significantly smoothed gradients. In addition, smoothing effects that are invisible in the space domain can be detected in wavelet scalograms, making a wavelet-based spectral analysis a powerful tool.