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The minimization of the commutator of the Fock and density matrices as the error matrix in the direct inversion of the iterative subspace (CDIIS) developed by Pulay is a powerful self-consistent field (SCF) acceleration technique for the construction of optimum Fock matrix, if initiated with a fair initial guess. In this work, we present an alternative minimized error matrix to the commutator in the CDIIS, namely the residual or the gradient of the energy-functional for a Slater determinant subject to the orthonormality constraints among orbitals, representing the search for a newly improved Fock matrix in the direction of the residual in the direct inversion of the iterative subspace (RDIIS). Implemented in the computational chemistry package GAMESS, the RDIIS is compared with the standard CDIIS and the second order SCF orbital optimization (SOSCF) for tested molecules started with a crude guess. As a result, the RDIIS stably and efficiently performs the SCF convergence acceleration. Furthermore, the RDIIS is considerably independent on the subspace size with the concentrated linear coefficients accounting proportionally for the Fock matrices close to the current iteration.

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Objective. Dual spectral computed tomography (DSCT) is a very challenging problem in the field of imaging. Due to the nonlinearity of its mathematical model, the images reconstructed by the conventional CT usually suffer from the beam hardening artifacts. Additionally, several existing DSCT methods rely heavily on the information of the spectra, which is often not readily available in applications. To address this problem, in this study, we aim to develop a novel approach to improve the DSCT reconstruction performance.Approach. A model-based direct inversion network (MDIN) is proposed for DSCT, which can directly predict the basis material images from the collected polychromatic projections. The all operations are performed in the network, requiring neither the conventional algorithms nor the information of the spectra. It can be viewed as an approximation to the inverse procedure of DSCT imaging model. The MDIN is composed of projection pre-decomposition module (PD-module), domain transformation layer (DT-layer), and image post-decomposition module (ID-module). The PD-module first performs the pre-decomposition on the polychromatic projections that consists of a series of stacked one-dimensional convolution layers. The DT-layer is designed to obtain the preliminary decomposed results, which has the characteristics of sparsely connected and learnable parameters. And the ID-module uses a deep neural network to further decompose the reconstructed results of the DT-layer so as to achieve higher-quality basis material images.Main results. Numerical experiments demonstrate that the proposed MDIN has significant advantages in substance decomposition, artifact reduction and noise suppression compared to other methods in the DSCT reconstruction.Significance. The proposed method has a flexible applicability, which can be extended to other CT problems, such as multi-spectral CT and low dose CT.

Asunto(s)

Algoritmos , Redes Neurales de la Computación , Fantasmas de Imagen , Modelos Teóricos , Tomografía Computarizada por Rayos X/métodos , Artefactos , Procesamiento de Imagen Asistido por Computador/métodos

RESUMEN

PURPOSE: Magnetic resonance elastography (MRE) maps the viscoelastic properties of soft tissues for diagnostic purposes. However, different MRE inversion methods yield different results, which hinder comparison of values, standardization, and establishment of quantitative MRE markers. Here, we introduce an expandable, open-access, webserver-based platform that offers multiple inversion techniques for multifrequency, 3D MRE data. METHODS: The platform comprises a data repository and standard MRE inversion methods including local frequency estimation (LFE), direct-inversion based multifrequency dual elasto-visco (MDEV) inversion, and wavenumber-based (k-) MDEV. The use of the platform is demonstrated in phantom data and in vivo multifrequency MRE data of the kidneys and brains of healthy volunteers. RESULTS: Detailed maps of stiffness were generated by all inversion methods showing similar detail of anatomy. Specifically, the inner renal cortex had higher shear wave speed (SWS) than renal medulla and outer cortex without lateral differences. k-MDEV yielded higher SWS values than MDEV or LFE (full kidney/brain k-MDEV: 2.71 ± 0.19/1.45 ± 0.14 m/s, MDEV: 2.14 ± 0.16/0.99 ± 0.11 m/s, LFE: 2.12 ± 0.15/0.89 ± 0.06 m/s). CONCLUSION: The freely accessible platform supports the comparison of MRE results obtained with different inversion methods, filter thresholds, or excitation frequencies, promoting reproducibility in MRE across community-developed methods.

Asunto(s)

Diagnóstico por Imagen de Elasticidad , Encéfalo/anatomía & histología , Encéfalo/diagnóstico por imagen , Diagnóstico por Imagen de Elasticidad/métodos , Humanos , Riñón/diagnóstico por imagen , Imagen por Resonancia Magnética/métodos , Reproducibilidad de los Resultados

RESUMEN

Direct inversion (DI) derives tissue shear modulus by inverting the Helmholtz equation. However, conventional DI is sensitive to data quality due to the ill-posed nature of Helmholtz inversion and thus providing reliable stiffness estimation can be challenging. This becomes more problematic in the case of estimating shear stiffness of the lung in which the low tissue density and short T2* result in considerably low signal-to-noise ratio during lung MRE. In the present study, we propose to perform MRE inversion by compressive recovery (MICRo). Such a technique aims to improve the numerical stability and the robustness to data noise of Helmholtz inversion by using prior knowledge on data noise and transform sparsity of the stiffness map. The developed inversion strategy was first validated in simulated phantoms with known stiffness. Next, MICRo was compared to the standard clinical multi-modal DI (MMDI) method forin vivoliver MRE in healthy subjects and patients with different stages of liver fibrosis. After establishing the accuracy of MICRo, we demonstrated the robustness of the proposed technique against data noise in lung MRE with healthy subjects. In simulated phantoms with single-directional or multi-directional waves, MICRo outperformed DI with Romano filter or Savitsky and Golay filter, especially when the stiffness and/or noise level was high. In hepatic MRE application, agreement was observed between MICRo and MMDI. Measuringin vivolung stiffness, MICRo demonstrated its advantages over filtered DI by yielding stable stiffness estimation at both residual volume and total lung capacity. These preliminary results demonstrate the potential value of the proposed technique and also warrant further investigation in a larger clinical population.

Asunto(s)

Diagnóstico por Imagen de Elasticidad , Voluntarios Sanos , Humanos , Hígado/diagnóstico por imagen , Imagen por Resonancia Magnética , Fantasmas de Imagen

RESUMEN

PURPOSE: Magnetic resonance elastography (MRE) measures stiffness of soft tissues by analyzing their spatial harmonic response to externally induced shear vibrations. Many MRE methods use inversion-based reconstruction approaches, which invoke first- or second-order derivatives by finite difference operators (first- and second-FDOs) and thus give rise to a biased frequency dispersion of stiffness estimates. METHODS: We here demonstrate analytically, numerically, and experimentally that FDO-based stiffness estimates are affected by (1) noise-related underestimation of values in the range of high spatial wave support, that is, at lower vibration frequencies, and (2) overestimation of values due to wave discretization at low spatial support, that is, at higher vibration frequencies. RESULTS: Our results further demonstrate that second-FDOs are more susceptible to noise than first-FDOs and that FDO dispersion depends both on signal-to-noise ratio (SNR) and on a lumped parameter A, which is defined as wavelength over pixel size and over a number of pixels per stencil of the FDO. Analytical FDO dispersion functions are derived for optimizing A parameters at a given SNR. As a simple rule of thumb, we show that FDO artifacts are minimized when A/2 is in the range of the square root of 2SNR for the first-FDO or cubic root of 5SNR for the second-FDO. CONCLUSIONS: Taken together, the results of our study provide an analytical solution to a long-standing, well-recognized, yet unsolved problem in MRE postprocessing and might thus contribute to the ongoing quest for minimizing inversion artifacts in MRE.

Asunto(s)

Diagnóstico por Imagen de Elasticidad , Artefactos , Imagen por Resonancia Magnética , Relación Señal-Ruido , Vibración

RESUMEN

Electronic structure calculations representing the molecular orbitals (MOs) with contracted planewave basis functions (CPWBFs) have been reported recently. CPWBFs are Fourier-series representations of atom-centered basis functions. The mathematical features of CPWBFs permit the construction of matrix-vector products, FC o , involving the application of the Fock matrix, F, to the set of occupied MOs, C o , without the explicit evaluation of F. This approach offers a theoretical speed-up of M/n over F-based methods, where M and n are the number of basis functions and occupied MOs, respectively. The present study reports methodological advances that permit FC o -based optimization of wavefunction formed from CPWBFs. In particular, a technique is reported for optimizing wavefunctions by combining pseudodiagonalization techniques based on an exact representation of FC o , approximate information regarding the virtual orbital energies, and direct inversion of the iterative subspace optimization schemes to guide the wavefunction to a converged solution. This method is found to speed-up wavefunction optimizations by factors of up to ~6 - 8 over F-based optimization methods while providing identical results. Further, the computational cost of this technique is relatively insensitive to basis set size, thus providing further benefits in calculations using large CPWBF basis sets. The results of density functional theory calculations show that this method permits the use of hybrid exchange-correlation (XC) functionals with a small increase in effort over analogous calculations using generalized gradient approximation XC functionals. © 2019 Wiley Periodicals, Inc.

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Ways to reduce the computational cost of periodic electronic structure calculations by using basis functions corresponding to linear combinations of planewaves have been examined recently. These contracted planewave (CPW) basis functions correspond to Fourier series representations of atom-centered basis functions, and thus provide access to some beneficial properties of planewave (PW) and localized basis functions. This study reports the development and assessment of a direct inversion of the iterative subspace (DIIS) method that employs unique properties of CPW basis functions to efficiently converge electronic wavefunctions. This method relies on access to a PW-based representation of the electronic structure to provide a means of efficiently evaluating matrix-vector products involving the application of the Fock matrix to the occupied molecular orbitals. These matrix-vector products are transformed into a form permitting the use of direct diagonalization techniques and DIIS methods typically employed with atom-centered basis sets. The abilities of this method are assessed through periodic Hartree-Fock calculations of a range of molecules and solid-state systems. The results show that the method reported in this study is approximately five times faster than CPW-based calculations in which the entire Fock matrix is calculated. This method is also found to be weakly dependent upon the size of the basis set, thus permitting the use of larger CPW basis sets to increase variational flexibility with a minor impact on computational performance. © 2018 Wiley Periodicals, Inc.

RESUMEN

In this paper the authors have investigated spectroscopic data analysis according to a recent development, i.e. the Direct Inversion in the Spectral Subspace (DISS) procedure. DISS is a supervised curve resolution technique, consequently it can be used once the spectra of the potential pure components are known and the experimental spectrum of a chemical mixture is also presented; hence the task is to determine the composition of the unknown chemical mixture. In this paper, the original algorithm of DISS is re-examined and some further critical reasoning and essential developments are provided, including the detailed explanations of the constrained minimization task based on Lagrange multiplier regularization approach. The main conclusion is that the regularization used for DISS is needed because of the possible shifted spectra effect instead of collinearity; and this new property, i.e. treating the mild shifted spectra effect, of DISS can be considered as its main scientific advantage.