Cross-Correlated Subspace-Based Optimization Method for Solving Electromagnetic Inverse Scattering Problems

Contrast source inversion method (CSIM) is a well-known and effective microwave imaging method. CSIM has been modified to improve the accuracy and convergence of the method: multiplicative regularized CSIM (MR-CSIM), where the total variation is used for regularization, and cross-correlated CSIM (CC-CSIM), where the cost functional is updated to include the cross correlation of the state and data errors. In this work, CSIM, MR-CSIM, and CC-CSIM are examined and compared in terms of efficiency and accuracy for noiseless and noisy measurement data by applying them to two dimensional inverse scattering problems. It is shown that MR-CSIM performs better on noiseless data and CC-CSIM is more immune to noise than MR-CSIM and CSIM.

In this letter, an incident field optimization (IO) method integrated with contrast source inversion (CSI) method and multiplicative regularized CSI (MR-CSI) method is proposed to deal with the electromagnetic inverse problems. For the conventional iterative inversion methods, the incident field is a prior knowledge and is usually obtained by the calibration process. Through the synthetic data experiments, it can be found that a small distortion of the incident field has little impact on the inversion results, but a high distortion will lead to fault inversion results or no convergence. In this letter, the incident field optimal factor, being updated during the iterative process, is introduced into the CSI and MR-CSI method, named as IO-CSI and MR–IO–CSI. The new methods have good inversion performance even with high incident field distortion. The proposed methods are applied to the Fresnel experiment data directly without the calibration procedure. Both the single-frequency and multifrequency inversion experiments demonstrate that the IO-CSI and MR–IO–CSI method can achieve good inversion results, indicating the method’s practical applicability.

The properties of singular value decomposition (SVD) are used to implement an SVD spatial domain pseudoinverse restoration filter. This type of filter is attractive for poor imaging conditions (low spatial resolution, high image noise) and is thus appealing for nuclear medicine images. The method might offer some advantages over more traditional frequency domain filter techniques since the restoration is performed on a local rather than global basis. High-contrast thyroid phantom images collected at different count densities and low-contrast liver phantom images were processed with the SVD filter. Restored images yielded improved spatial resolution, lesion contrast, and signal-to-noise ratio. The SVD pseudoinverse restoration filter implemented as an interactive process permits the operator to terminate filtering at a stage where the visually "best" image is obtained compared to the original data. Processed images suggest that the technique may have potential for improving lesion detection in nuclear medicine.

In this paper, two new properties of singular value decomposition (SVD) on images are proved. The first property demonstrates the quantitative relationship between singular values and power spectrum. The second one proves that under the condition of losing equal power spectrum, the square-error of the reconstructed image is much smaller when we reduce all singular values proportionally instead of neglect the smaller ones. Based on the two properties, a new data-hiding scheme is proposed. It performs well as for robustness, for it satisfies power-spectrum condition (PSC), and PSC-compliant watermarks are proven to be most robust. Besides, the proposed scheme has a good performance as for capacity and adaptability.

Block-wise reversible data hiding in encrypted domain using SVD

Author profiling is a challenging task that consists of identifying a person’s relevant attributes based on the content he/she generates. In this article, we validate a classification method based on the reconstructive classification to identify two demographic attributes, age and gender, for users of social networks based on the text content they publish. For the problem, we consider balanced and unbalanced data, where a gender or age group has a larger presence than the others. The proposed method is based on using the reconstructive property of singular value decomposition (SVD), and its suitability to work with sparse data, to find a matrix with the main latent components to represent the information of specific gender or age classes. Afterward, we use such a matrix to project and reconstruct new users’ information to identify their demographic variables. We test our method with a set of datasets in several languages collected from Twitter and Pinterest users, and we use different evaluation metrics to compare their performance with the ones of several popular classifiers based on traditional machine learning, and on deep learning, and with some relevant works in the literature. The results show that the proposed classifier performs generally well in identifying the age and gender of users in social networks.

The security of information exchange is very important on the network. Authentication and information hiding have also become important issues. Information hiding techniques are acquiring an increasing importance due to the widespread diffusion of multimedia contents. The aim of this chapter is to focus on the Singular Value Decomposition (SVD) transform, with the aim of providing an exhaustive overview on those steganography, image cryptography and watermarking techniques leveraging on the important properties of such a transform. Despite the attention it has received in the last years, SVD in image processing and security is still in its infancy. Many SVD characteristics are still unutilized in image processing. In this chapter the author tries to highlight the basic properties of SVD and some of their applications in the field of security to encourage researchers to discover more about SVD properties which are not yet utilized.

We propose a technique for video shot segmentation and classification based on singular value decomposition (SVD). For the input video sequence, we create a feature-frame matrix A, and perform the SVD on it. From this SVD, we are able to not only derive the refined feature space to better segment the video sequence along the time axis, but also define metrics to enable classifications of the detected video shots. Using these SVD properties, we achieve the two goals of accurate video shot segmentation, and visual content-based shot classification at the same time.

The Debye empirical formulas are often used for the description of the dispersion characteristics of common media, such as biological tissues, water, and soil. In order to reconstruct their frequency‐related electrical properties, a multi‐frequency contrast source inversion (CSI) method is modified from the direct estimation of the contrast between Debye scatterers and background medium, into the reconstruction of three kinds of Debye model parameters, namely, the optical relative permittivity, relative permittivity difference, and static conductivity. Through three two‐dimensional (2D) benchmark numerical experiments, detailed comparisons between the results by the improved CSI method, and those by the frequency hopping (FH) technique, single frequency subspace‐based optimization method (SOM) with deep learning (DL), multi frequency (MF) dispersive SOM, and time‐domain inverse scattering (TDIS) approach, show preliminarily that the modified CSI (M‐CSI) method is feasible and robust, and that it exhibits acceptable compromise performance by the comprehensive consideration of convergence characteristics, positioning accuracy, reconstruction errors, and computational efficiency. Also, the M‐CSI method has been successfully applied to quantitatively reconstruct the internal breast composition in a 2D cancerous phantom extracted from a realistic numerical breast, dielectrically and anatomically.

The Contrast Source Inversion (CSI) method has been successfully applied to inverse problems in electromagnetics for a number of applications. Forward solvers supporting inhomogeneous backgrounds provide a means to incorporate prior information into the inversion process, and are a continued focus of research for improving imaging results. To expand the capabilities of CSI for exploiting physical and/or numerical backgrounds, we present a CSI formulation that supports multiple simultaneous inhomogeneous backgrounds.

This research work will examine singular value decomposition (SVD), Fast Fourier Transform (FFT) and least square technique for the estimation of harmonics in power system. Harmonics in power system disturbs the quality of energy supplied to load, increased energy losses and reduce the reliability of the power system. In some cases, the large power converter systems produce not only typical harmonics but also a significant amount of inter harmonics which can significantly deteriorate the quality of power supply voltage. Inter harmonics are those components of current or voltage waveform which are not integer multiple of fundamental frequency component. Since poor power quality cause losses in power system that's why researchers are working to find techniques to estimate and control the harmonics in power system. Singular value decomposition approach is an ideal technique to estimate harmonics in power system located far away. Since in most of the cases, power system produce over determine equations which can easily be solved using SVD for optimal solution. Singular vector decomposition, SVD is really a mathematical method to lessen a dataset containing an extensive number of qualities to a dataset containing fundamentally less values, yet which still contains a huge portion of the variability introduce in the first information. SVD investigation brings about a more reduced representation of correlations, particularly with multivariate datasets and can give knowledge into spatial and temporal variations exhibited in the fields of data being analysed under different circumstance. Similarly traditional least square method is also one of the most prominent method to estimate the line of best fit. This research work will show the analysis of said techniques to find the optimal approximation of noisy and distorted wave form. To investigate effectiveness of said techniques; simulations will be carried out in MATLAB with same parameters.

Regularization technology is an efficient and robust method to implement forward-looking imaging of scanning radar, and the selection of regularization parameter is quite important for the imaging performance. When the imaging scene contains sparse strong targets as well as a weak background, different regularization parameters should be adopted. A dual-channel fast iterative shrinkage-thresholding (D-FIST) regularization algorithm is proposed. First, by setting a threshold with mean segmentation method, the strong targets are extracted from the echo to formulate the data of channel I, and the entire data are included in channel II. The L-curve method is adopted to determine the regularization parameter for two channels data, respectively. Then, the data are processed by the FIST algorithm with corresponding parameters. At last, the imaging result is obtained by combining the results of two channels. Simulation experiments show that the imaging results of D-FIST are better than that of direct method, especially in a low SNR situation.

To develop a novel regularization method for GRAPPA by which the regularization parameters can be optimally and adaptively chosen. In the fit procedures in GRAPPA, the discrepancy principle, which chooses the regularization parameter based on a priori information about the noise level in the autocalibrating signals (ACS), is used with the truncated singular value decomposition (TSVD) regularization and the Tikhonov regularization, and its performance is compared with the singular value (SV) threshold method and the L-curve method, respectively by axial and sagittal head imaging experiments. In both axial and sagittal reconstructions, normal GRAPPA reconstruction results exhibit a relatively high level of noise. With discrepancy-based choices of parameters, regularization can improve the signal-to-noise ratio (SNR) with only a very modest increase in aliasing artifacts. The L-curve method in all of the reconstructions leads to overregularization, which causes severe residual aliasing artifacts. The 10% SV threshold method yields good overall image quality in the axial case, but in the sagittal case it also leads to an obvious increase in aliasing artifacts. Neither a fixed SV threshold nor the L-curve are robust means of choosing the appropriate parameters in GRAPPA reconstruction. However, with the discrepancy-based parameter-choice strategy, adaptively regularized GRAPPA can be used to automatically choose nearly optimal parameters for reconstruction and achieve an excellent compromise between SNR and artifacts.

A combination of a multiresolution (MR) preconditioner and matrix decomposition algorithm – singular value decomposition (MDA-SVD) algorithm is proposed for the analysis of densely discretised electromagnetic (EM) scatterers. In realistic EM scattering problems, the discretisation may be very dense to accurately describe the geometric shape of targets. However, dense discretisations will generate two major drawbacks: (i) the badly conditioned method of moments (MoM) matrix which makes iterative solvers difficult to converge; (ii) the dense near-field MoM matrix for which the computational cost is large, even multilevel fast multipole algorithm (MLFMA) is applied. To remedy the first shortcoming of dense discretisations, an MR preconditioner can be applied to improve the condition of MoM matrices. To reduce the computational cost in solving the MoM matrix equation, an MDA-SVD algorithm can be applied to accelerate the matrix−vector multiplication. Compared with the traditional MLFMA, the MDA-SVD algorithm has no limit on the size of octree boxes which makes the MDA-SVD algorithm suitable for the analysis of dense discretisations. Therefore an MR preconditioner is combined with the MDA-SVD algorithm for fast analysis of dense discretisations. Numerical results indicate that the combination of the MR preconditioner and the MDA-SVD algorithm is efficient.

Characterization of the Tikhonov regularization for numerical analysis of inverse boundary value problems by using the singular value decomposition