Inverse Update Research Articles

On the Implementation of Iterative Methods Without Inverse Updating for Solving Equations in Banach Spaces

The implementation of iterative methods using inverses to solve equations is a computationally expensive or impossible task in general. This is the case, since the analytical form of the inverse is difficult to find in practice. That is why, we replace the inverse by a sum of linear operators which is well defined. The convergence of the resulting hybrid methods is studied based on majorizing sequences under generalized continuity assumptions on the operators involved and in the setting of a Banach space. It is demonstrated by numerical experimentations that the convergence order as well as the number of iterations required to obtain a predetermined error tolerance when comparing the original to the hybrid method is essentially the same.

The impact of acquisition geometry on full-waveform inversion updates

Full-waveform inversion (FWI) is a high-resolution model-building technique that uses the entire recorded seismic data content to build the earth model. Conventional FWI usually utilizes diving and refracted waves to update the low-wavenumber components of the velocity model. However, updates are often depth limited due to the limited offset range of the acquisition design. To extend conventional FWI beyond the limits imposed by using only transmitted energy, we must utilize the full acquired wavefield. Analyzing FWI kernels for a given geology and acquisition geometry can provide information on how to optimize the acquisition so that FWI is able to update the velocity model for targets as deep as basement level. Recent long-offset ocean-bottom node acquisition helped FWI succeed, but we would also like to be able to utilize the shorter-offset data from wide-azimuth data acquisitions to improve imaging of these data sets by developing the velocity field with FWI. FWI models are heading toward higher and higher wavenumbers, which allows us to extract pseudoreflectivity directly from the developed velocity model built with the acoustic full wavefield. This is an extremely early start to obtaining a depth image that one would usually produce in much later processing stages.

Accelerating implant RF safety assessment using a low-rank inverse update method.

PurposePatients who have medical metallic implants, e.g. orthopaedic implants and pacemakers, often cannot undergo an MRI exam. One of the largest risks is tissue heating due to the radio frequency (RF) fields. The RF safety assessment of implants is computationally demanding. This is due to the large dimensions of the transmit coil compared to the very detailed geometry of an implant.MethodsIn this work, we explore a faster computational method for the RF safety assessment of implants that exploits the small geometry. The method requires the RF field without an implant as a basis and calculates the perturbation that the implant induces. The inputs for this method are the incident fields and a library matrix that contains the RF field response of every edge an implant can occupy. Through a low‐rank inverse update, using the Sherman–Woodbury–Morrison matrix identity, the EM response of arbitrary implants can be computed within seconds. We compare the solution from full‐wave simulations with the results from the presented method, for two implant geometries.ResultsFrom the comparison, we found that the resulting electric and magnetic fields are numerically equivalent (maximum error of 1.35%). However, the computation was between 171 to 2478 times faster than the corresponding GPU accelerated full‐wave simulation.ConclusionsThe presented method enables for rapid and efficient evaluation of the RF fields near implants and might enable situation‐specific scanning conditions.

Parameter crosstalk and modeling errors in viscoacoustic seismic full-waveform inversion

Simultaneous use of data within relatively broad frequency bands is essential to discriminating between velocity and [Formula: see text] errors in the construction of viscoacoustic full-waveform inversion (QFWI) updates. Individual frequencies or narrow bands in isolation cannot provide sufficient information to resolve parameter crosstalk issues in a surface seismic acquisition geometry. At the same time, too broad a frequency band introduces significant problems in the presence of modeling errors. The risk of modeling errors arising in QFWI is high because of the range of very different geologic contributors to attenuation and dispersion and the variety of available mathematical descriptions. We perform numerical tests that suggest that by relaxing the typical requirement that the frequency dependence of the assumed intrinsic attenuation model be self-consistent across the full spectrum, significant improvement in the fidelity of the inversion results can be obtained in cases where the attenuation model assumed in the inversion differs substantially from the true subsurface behavior. We find that the size of the frequency bands used in this inversion approach is a useful hyperparameter controlling trade-off between crosstalk reduction and flexibility in coping with uncertain physics.

Inverse analysis of the tool life in laser-assisted milling

In current study, an inverse analysis is conducted on tool life based on five process parameters, by predicting tool life based on guessed process parameters, which is defined as the forward problem, and applying iterative gradient search to find process parameters for next iteration, which is defined as the inverse problem. For forward problem, the effect of laser beam is included by treating it as a heat source on top surface. Next, the milling configuration is simplified as orthogonal cutting followed by angular-dependent coordinate transformation at each rotation angle. The effective force due to flank wear is predicted by integrating the stress components along the chip cross section and wear land, and the average stress on tool-workpiece interface is then derived based on the effective force and contact area. The average temperature along the interface is derived by considering secondary and rubbing heat sources. The stress and temperature affects the abrasion, adhesion, and diffusion which determine the flank wear rate. The tool life is then decided as the cutting time when the flank wear limit of the tool is reached. The iterative gradient search or variance-based recursive method is applied to solve inverse problem and update process parameters to match the tool life. Three cutting parameters including depth of cut, feed per tooth, and cutting speed, and two laser parameters including laser-tool distance and laser power are updated in each iteration. The proposed model is validated through experimental measurements on the laser-assisted milling of K24 nickel-based superalloy. The proposed predictive model is able to match the measured tool life with high computation efficiency less than 540 s and high accuracy of less than 7% difference.

Modular Bayesian damage detection for complex civil infrastructure

We address the problem of damage identification in complex civil infrastructure with an integrative modular Bayesian framework. The proposed approach uses multiple response Gaussian processes to build an informative yet computationally affordable probabilistic model, which detects damage through inverse updating. Performance of structural components associated with parameters of the developed model was quantified with a damage metric. Particular emphasis is given to environmental and operational effects, parametric uncertainty and model discrepancy. Additional difficulties due to usage of costly physics-based models and noisy observations are also taken into account. The framework has been used to identify a reduction of a simulated cantilever beam elastic modulus, and anomalous features in main/stay cables and bearings of the Tamar bridge. In the latter case study, displacements, natural frequencies, temperature and traffic monitored throughout one year were used to form a reference baseline, which was compared against a current state, based on one month worth of data. Results suggest that the proposed approach can identify damage with a small error margin, even under the presence of model discrepancy. However, if parameters are sensitive to environmental/operational effects, as observed for the Tamar bridge stay cables, false alarms might occur. Validation with monitored data is also highlighted and supports the feasibility of the proposed approach.

High‐throughput signal detection based on fast matrix inversion updates for uplink massive multiuser multiple‐input multi‐output systems

In this study, zero-forcing matrix decomposition polynomial expansion update (ZF-MDPE-update) and zero-forcing successive over relaxation update (ZF-SOR-update) algorithms are proposed to update a zero-forcing detector quickly without requiring complicated matrix inversion recomputations when massive multiple-input multi-output systems channel estimates contain a small perturbation. To further accelerate the convergence rate and to maximise date throughput, a new method of calculating the optimal coefficients for the matrix polynomial that can significantly improve the accuracy of the initial input inverse matrix approximation is considered by the ZF-MDPE-update algorithm. On the other hand, the ZF-SOR-update algorithm with an optimal iterative initial solution and an optimal relaxation parameter is devised, which achieves excellent detection performance. Results demonstrate that when the ratio of base station (BS) antennas to user terminal (UT) antennas, , is small, the proposed update detection algorithms, with only a few operations, achieve a significant improvement in the average achievable rate of the UTs compared to the recently proposed update algorithm. Therefore, more UTs can be served in a cell with a fixed number of BS antennas. At the same time, the authors' algorithms are shown to facilitate easy memory transfer and are low cost.

Optimal Regularized Inverse Matrices for Inverse Problems

In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem, where the key novelties are that we allow for updates to existing approximations and we allow for incorporation of additional probabilistic information. Since computing optimal regularized inverse matrices under rank constraints can be challenging, especially for problems where matrices are large and sparse or are only accessable via function call, we propose an efficient rank-update approach that decomposes the problem into a sequence of smaller rank problems. Using examples from image deblurring, we demonstrate that more accurate solutions to inverse problems can be achieved by using rank updates to existing regularized inverse approximations. Furthermore, we show the potential benefits of using optimal regularized inverse matrix updates for solving perturbed tomographic reconstruction problems.

Fast Matrix Inversion Updates for Massive MIMO Detection and Precoding

In this letter, methods and corresponding complexities for fast matrix inversion updates in the context of massive multiple-input multiple-output (MIMO) are studied. In particular, we propose an on-the-fly method to recompute the zero forcing (ZF) filter when a user is added or removed from the system. Additionally, we evaluate the recalculation of the inverse matrix after a new channel estimation is obtained for a given user. Results are evaluated numerically in terms of bit error rate (BER) using the Neumann series approximation as the initial inverse matrix. It is concluded that, with fewer operations, the performance after an update remains close to the initial one.

Accelerating 2D orthogonal matching pursuit algorithm on GPU

Two-dimensional orthogonal matching pursuit (2D-OMP) algorithm is an extension of the one-dimensional OMP (1D-OMP), whose complexity and memory usage are lower than the 1D-OMP when they are applied to 2D sparse signal recovery. However, the major shortcoming of the 2D-OMP still resides in long computing time. To overcome this disadvantage, we develop a novel parallel design strategy of the 2D-OMP algorithm on a graphics processing unit (GPU) in this paper. We first analyze the complexity of the 2D-OMP and point out that the bottlenecks lie in matrix inverse and projection. After adopting the strategy of matrix inverse update whose performance is superior to traditional methods to reduce the complexity of original matrix inverse, projection becomes the most time-consuming module. Hence, a parallel matrix---matrix multiplication leveraging tiling algorithm strategy is launched to accelerate projection computation on GPU. Moreover, a fast matrix---vector multiplication, a parallel reduction algorithm, and some other parallel skills are also exploited to boost the performance of the 2D-OMP further on GPU. In the case of the sensing matrix of size 128 $$\times $$ × 256 (176 $$\times $$ × 256, resp.) for a 256 $$\times $$ × 256 scale image, experimental results show that the parallel 2D-OMP achieves 17 $$\times $$ × to 41 $$\times $$ × (24 $$\times $$ × to 62 $$\times $$ × , resp.) speedup over the original C code compiled with the O $$_2$$ 2 optimization option. Higher speedup would be further obtained with larger-size image recovery.

Generation of classes of symmetric rank-2 secant updates and the maximality of the Davidon class

We first catalogue several classes of secant updates including the Dennis class, the Davidon class, and the class of all symmetric rank-2 updates. Reflection on the parametric form of this class leads to a maximality property of the Davidon class and to a natural derivation of the Broyden–Fletcher–Goldfarb–Shanno update, analogous to that presented by Fletcher for the Davidon–Fletcher–Powell inverse update. Next, we propose a symmetric rank-1 extension process for classes of updates that allows us to introduce a degree of commonness to the material presented. An application of the symmetric rank-1 extension process to the class of rank-1 secant updates produces the Dennis class, an application to the Dennis class produces the Davidon class, and an application to the Davidon class leaves the Davidon class fixed implying that it is a maximal class. The maximality of the Davidon class, the definition of the symmetric rank-1 extension process, and the demonstration that this extension process can be used to unify an important part of the literature on update classes are the contributions of the paper.

실시간 영상 지오레퍼런싱을 위한 온라인 항공삼각측량 알고리즘의 비교 및 성능 검증

Real-time image georeferencing is required to generate spatial information rapidly from the image sequences acquired by multi-sensor systems. To complement the performance of position/attitude sensors and process in real-time, we should employ on-line aerial triangulation based on a sequential estimation algorithm. In this study, we thus attempt to derive an efficient on-line aerial triangulation algorithm for real-time georeferencing of image sequences. We implemented on-line aerial triangulation using the existing Given transformation update algorithm, and a new inverse normal matrix update algorithm based on observation classification, respectively. To compare the performance of two algorithms in terms of the accuracy and processing time, we applied these algorithms to simulated airborne multi-sensory data. The experimental results indicate that the inverse normal matrix update algorithm shows 40 % higher accuracy in the estimated ground point coordinates and eight times faster processing speed comparing to the Given transformation update algorithm. Therefore, the inverse normal matrix update algorithm is more appropriate for the real-time image georeferencing.

Groupwise Geometric and Photometric Direct Image Registration

Image registration consists in estimating geometric and photometric transformations that align two images as best as possible. The direct approach consists in minimizing the discrepancy in the intensity or color of the pixels. The inverse compositional algorithm has been recently proposed by Baker et al. for the direct estimation of groupwise geometric transformations. It is efficient in that it performs several computationally expensive calculations at a pre-computation phase. Photometric transformations act on the value of the pixels. They account for effects such as lighting change. Jointly estimating geometric and photometric transformations is thus important for many tasks such as image mosaicing. We propose an algorithm to jointly estimate groupwise geometric and photometric transformations while preserving the efficient pre-computation based design of the original inverse compositional algorithm. It is called the dual inverse compositional algorithm. It uses different approximations than the simultaneous inverse compositional algorithm and handles groupwise geometric and global photometric transformations. Its name stems from the fact that it uses an inverse compositional update rule for both the geometric and the photometric transformations. We demonstrate the proposed algorithm and compare it to previous ones on simulated and real data. This shows clear improvements in computational efficiency and in terms of convergence.

An Algorithm for the Fast Simulation of Multicomponent Object Deformation

In this paper, a fast algorithm for the simulation of deformable objects composed of multiple components made of different materials is introduced. By using the boundary element method and considering individual components and their interfaces separately, a relationship between the unknown and known displacements is established. Based on this expression, a component-based condensation method can be applied. This reduces the size of the matrix to be inverted to depend only on the number of unknown displacements of the components with changing boundary condition. To speed up the construction of the required matrices, a maximal matrix method is proposed. By categorizing the changes in boundary conditions, three fast update strategies on matrix inverse are introduced. Based on the maximal matrix method and the matrix inverse update strategy, we define eight easily formed characteristic matrices, which enhance the computation speed further. The efficiency of the proposed method is demonstrated by a set of experimental results.

A derivative-free nonmonotone line-search technique for unconstrained optimization

A tolerant derivative–free nonmonotone line-search technique is proposed and analyzed. Several consecutive increases in the objective function and also nondescent directions are admitted for unconstrained minimization. To exemplify the power of this new line search we describe a direct search algorithm in which the directions are chosen randomly. The convergence properties of this random method rely exclusively on the line-search technique. We present numerical experiments, to illustrate the advantages of using a derivative-free nonmonotone globalization strategy, with approximated-gradient type methods and also with the inverse SR1 update that could produce nondescent directions. In all cases we use a local variation finite differences approximation to the gradient.

On the Coding Efficiency of MCTF Update Steps for Scalable Video Coding

It has been widely believed that motion-compensated update steps performed in the motion-compensated temporal filtering (MCTF) framework improve coding efficiency in comparison to conventional hybrid coding. However, the coding efficiency of MCTF update steps for scalable video coding has not been examined sufficiently in the past. In this paper, we investigate the efficiency of the decoder side update steps by analyzing the effect of performing the inverse update steps at the decoder side. We demonstrate, by theoretical approach, that the MCTF update step at the decoder side does not contribute significantly to the coding efficiency, except at high spatial-temporal resolutions with high bit rates. The results in our study provide a theoretical justification for not including MCTF update steps in the decoding process for scalable video coding

RLS-based initialization for per-tone equalizers in DMT receivers

Per-tone equalization has recently been proposed as an alternative receiver structure for discrete multitone-based systems improving upon the well-known structure based on time-domain equalization. Fast initialization of all the equalizer coefficients has been identified as an open problem. In this letter, a recursive initialization scheme based on recursive least squares with inverse updating is presented for the per-tone equalizers. Simulation results show convergence with an acceptably small number of training symbols. Complexity calculations are made for per-tone equalization and for the case where tones are grouped. It is demonstrated with an example that in the latter case, initialization complexity becomes sufficiently low and comparable to complexity during data transmission.

Error probability analysis for CDMA systems with closed-loop power control

Fast closed-loop-power-control (CLPC) plays a key role in direct-sequence (DS) code division multiple access (CDMA) systems, aiming at achieving acceptable carrier-to-interference (C/I) ratios in all active links. Assuming a terrestrial mobile access, where the round-trip delay may be smaller than the channel time-coherence, fast CLPC can compensate for fading and reduce the error burstiness, as well. This paper provides analytical expressions for the bit error probability given: the CLPC algorithm specified in terms of loop delay and updating rate, the propagation power delay-profile and the terminal speed. A binary PSK DS spread spectrum radio interface, with RAKE processing of multipath or diversity, is considered. Our link-level analysis, being conditioned to a specified average value of C/I, is focused on the inverse update algorithm, which is aimed at keeping the received power at a constant level. Applications of the derived method, aimed at getting insight about CLPC performance in 3rd generation radio interfaces, is also provided and discussed.

Efficient bifurcation analysis of periodically-forced distributed parameter systems

Changes in the qualitative features of the bifurcation diagrams or the dynamic features of forced periodic systems occur at singular points, which satisfy certain defining conditions. The loci of these singular points may be constructed by a continuation procedure and used to bound parameter regions with qualitatively different features. When the model of a forced periodic system is a set of partial differential equations, construction of these loci may require extensive computational time, making this task often impractical. We present here a novel, very efficient numerical method for construction of these loci. The procedure uses Fréchet differentiation to simplify the determination of the defining conditions and the Broyden inverse update method to accelerate the iterative steps involved in the shooting method. The procedure is illustrated first by construction of a map of parameter regions with qualitatively different bifurcation diagrams for an adiabatic reverse-flow reactor (RFR), the direction of feed to which is changed periodically. We then construct a map of parameter regions in which a cooled RFR has qualitatively different dynamic features. Both maps reveal surprising features.

Motion control of non-fixed base robotic manipulators

Robotic manipulators mounted on spacecraft experience a number of kinematic, dynamic, and control problems because the motion of the spacecraft is affected by the robot motion. In this paper, the general three dimensional equations of motion are derived for an n link manipulator mounted on a non-fixed base object. Instead of performing a single inverse kinematic calculation at the beginning of a movement to determine the required joint setpoints, multiple inverse kinematic updates are done throughout a movement. The updating sequence is determined by an optimal inverse kinematic updating algorithm. This motion control algorithm is based on experimental simulation results performed in Matlab and a set of performance indices that are used as guidelines. Simple PD joint controllers and a special joint trajectory generator are used for servoing the manipulator joints for a planar robot application. The derived motion control techniques incorporate the base motion without base motion control.