Search Results (8)

We consider the problem of computed tomography (CT). This ill-posed inverse problem arises when one wishes to investigate the internal structure of an object with a non-invasive and non-destructive technique. This problem is severely ill-conditioned, meaning it has infinite solutions and is extremely sensitive to perturbations in the collected data. This sensitivity produces the well-known semi-convergence phenomenon if iterative methods are used to solve it. In this work, we propose a multigrid approach to mitigate this instability and produce fast, accurate, and stable algorithms starting from unstable ones. We consider, in particular, symmetric Krylov methods, like lsqr, as smoother, and a symmetric projection of the coarse grid operator. However, our approach can be extended to any iterative method. Several numerical examples show the performance of our proposal. Full article

In the present paper, the problems of longitudinal and flexural vibrations of an inhomogeneous rod are considered. The Young’s modulus and density are variable in longitudinal coordinate. Vibrations are caused by a load applied at the right end. The proposed method allows us to consider a wider class of inhomogeneity laws in comparison with other numerical solutions. Sensitivity analysis is carried out. A new inverse problem related to the simultaneous identification of the variation laws of Young’s modulus and density from amplitude–frequency data, which are measured in given frequency ranges, is considered. Its solution is based on an iterative process: at each step, a system of two Fredholm integral equations of the first kind with smooth kernels is solved numerically. The analysis of the kernels is carried out for different frequency values. To find the initial approximation, several approaches are proposed: a genetic algorithm, minimization of the residual functional on a compact set, and additional information about the values of the sought-for functions at the ends of the rod. The Tikhonov regularization and the LSQR method are proposed. Examples of reconstruction of monotonic and non-monotonic functions are presented. Full article

Rapid perception of the location of the fire point is crucial to building fire emergency response in the process of building fire emergency response, which can help firefighters direct fire-fighting operations, effectively control fire sources, and provide strong evidence for the analysis and investigation of fire causes. This paper uses acoustic CT temperature measurement technology to determine the fire source location of a building fire and verifies its validity and applicability as follows: we construct various fire point numerical models based on the fire dynamics simulator (FDS) and obtain temperature data at different times; neural network means were used to obtain the time-of-flight (TOF) of an acoustic wave traveling; the large ill-conditioned matrix equation of acoustic flight under different meshing schemes was constructed and solved based on the simultaneous algebraic reconstruction technique (SART) and least squares QR-decomposition (LSQR), and then reconstruction temperature data under each scheme were obtained. Through the error analysis, the reconstruction effect of each reconstruction scheme is evaluated, and then the applicability of the location coordinate determination of the fire point is analyzed. The results show that the determination of the fire location under the conditions of various fire points in the building space can be realized by acoustic CT temperature measurement technology. Full article

The power law particle size distribution (PSD) slope parameter is commonly used to characterize sediment fluxes, resuspension, aggregates, and settling rates in coastal and estuarine waters. However, particle size distribution metrics are also very useful for understanding sediment source and dynamic processes. In this study, a method was proposed to employ the particle size parameters commonly used in sedimentary geology (average particle size (ø), sorting, skewness, and kurtosis) as indicators of changes in sediment dynamic processes, and MODIS images were used to estimate these parameters. The particle size parameters were estimated using a Mie scattering model, Quasi-Analytical Algorithm (QAA) analysis algorithm, and least squares QR decomposition (LSQR) solution method based on the relationship between the power law distribution of the suspended particles and their optical scattering properties. The estimates were verified by field measurements in the Yellow Sea and Bohai Sea regions of China. This method provided good estimates of the average particle size (ø), sorting, and kurtosis. A greater number of wavebands (39) was associated with more accurate particle size distribution curves. Furthermore, the method was used to monitor changes in suspended particulate matter in the vicinity of the Heini Bay of China before and after the passage of a strong storm in August 2011. The particle size parameters represented the influence of a strong typhoon on the distribution of the near-shore sediment and, together with the PSD slope, comprehensively reflected the changes in the near-shore suspended particulate matter. This method not only established the relationship between remote sensing monitoring and the historical sediment record, it also extends the power law model to the application of sediment source and dynamic processes in coastal waters. Full article

To reduce the maintenance cost and safeguard machinery operation, remaining useful life (RUL) prediction is very important for long term health monitoring. In this paper, we introduce a novel hybrid method to deal with the RUL prediction for health management. Firstly, the sparse reconstruction algorithm of the optimized Lasso and the Least Square QR-factorization (Lasso-LSQR) is applied to compressed sensing (CS), which can realize the sparse optimization for long term health monitoring data. After the sparse signal is reconstructed, the minimum entropy de-convolution (MED) is used to identify the fault characteristics and to obtain significant fault information from the machinery operation. Health indicators with Skip-over, sample entropy and approximate entropy are then performed to track the degradation of the machinery process. The performance analysis of the Skip-over is superior to other indicators. Finally, Fractal Autoregressive Integrated Moving Average model (FARIMA) is employed to predict the Skip-over using the R/S method. The analysis results evidence that the novel hybrid method yields a good performance, and such method can achieve highly accurate RUL prediction and safeguard machinery operation for long term monitoring. Full article

We propose an alternative processing method for quantitative susceptibility mapping of the prostate that reduces artifacts and enables better visibility and quantification of calcifications and other lesions. Three-dimensional gradient-echo magnetic resonance data were obtained from 26 patients at 3 T who previously received a planning computed tomography of the prostate. Phase images were unwrapped using Laplacian-based phase unwrapping. The background field was removed with the V-SHARP method using tissue masks for the entire abdomen (Method 1) and masks that excluded bone and the rectum (Method 2). Susceptibility maps were calculated with the iLSQR method. The quality of susceptibility maps was assessed by one radiologist and two physicists who rated the data for visibility of lesions and data quality on a scale from 1 (poor) to 4 (good). The readers rated susceptibility maps computed with Method 2 to be, on average, better for visibility of lesions with a score of 2.9 ± 1.1 and image quality with a score of 2.8 ± 0.8 compared with maps computed with Method 1 (2.4 ± 1.2/2.3 ± 1.0). Regarding strong artifacts, these could be removed using adapted masks, and the susceptibility values seemed less biased by the artifacts. Thus, using an adapted mask for background field removal when calculating susceptibility maps of the prostate from phase data reduces artifacts and improves visibility of lesions. Full article

The precise knowledge of the point spread function is central for any imaging system characterization. In fluorescence microscopy, point spread function (PSF) determination has become a common and obligatory task for each new experimental device, mainly due to its strong dependence on acquisition conditions. During the last decade, algorithms have been developed for the precise calculation of the PSF, which fit model parameters that describe image formation on the microscope to experimental data. In order to contribute to this subject, a comparative study of three parameter estimation methods is reported, namely: I-divergence minimization (MIDIV), maximum likelihood (ML) and non-linear least square (LSQR). They were applied to the estimation of the point source position on the optical axis, using a physical model. Methods’ performance was evaluated under different conditions and noise levels using synthetic images and considering success percentage, iteration number, computation time, accuracy and precision. The main results showed that the axial position estimation requires a high SNR to achieve an acceptable success level and higher still to be close to the estimation error lower bound. ML achieved a higher success percentage at lower SNR compared to MIDIV and LSQR with an intrinsic noise source. Only the ML and MIDIV methods achieved the error lower bound, but only with data belonging to the optical axis and high SNR. Extrinsic noise sources worsened the success percentage, but no difference was found between noise sources for the same method for all methods studied. Full article

In this paper, we propose a new iterative algorithm to solve the matrix equation AXB + CX^T D = E. The algorithm can obtain the minimal Frobenius norm solution or the least-squares solution with minimal Frobenius norm. Our algorithm is better than Algorithm II of the paper [M. Wang, etc., Iterative algorithms for solving the matrix equation AXB + CX^T D = E, Appl. Math. Comput. 187, 622-629, 2007] Full article