Iterative Regularization Algorithm Research Articles

Accelerate Bregman MRI Image Reconstruction Algorithm

CS used in MRI image reconstruction is a research hotspot recent year. For the problem that reconstruction rate slow in MRI image reconstruction based on CS .Type acceleration Bregman iterative regularization algorithm to solve the MRI imaging sparse model ,and use the accelerate gradient method and the Restring in processing . The simulation data express this algorithm effective enhance the reconstruction rate, It’s have positive meaning in MRI image reconstruction that have strict in time requirement.

Two soft-thresholding based iterative algorithms for image deblurring

Iterative regularization algorithms, such as the conjugate gradient algorithm for least squares problems (CGLS) and the modified residual norm steepest descent (MRNSD) algorithm, are popular tools for solving large-scale linear systems arising from image deblurring problems. These algorithms, however, are hindered by a semi-convergence behavior, in that the quality of the computed solution first increases and then decreases. In this paper, in order to overcome the semi-convergence behavior, we propose two iterative algorithms based on soft-thresholding for image deblurring problems. One of them combines CGLS with a denoising technique like soft-thresholding at each iteration and another combines MRNSD with soft-thresholding in a similar way. We prove the convergence of MRNSD and soft-thresholding based algorithm. Numerical results show that the proposed algorithms overcome the semi-convergence behavior and the restoration results are slightly better than those of CGLS and MRNSD with their optimal stopping iterations.

On the filtering effect of iterative regularization algorithms for discrete inverse problems

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge number of studies has been carried out in the optimization field to provide the fastest methods for the reconstruction of the solution, involving choices of adaptive parameters and scaling matrices. However, in the presence of an ill-conditioned model and real data, the need for a regularized solution instead of the least-squares one changed the point of view in favour of iterative algorithms able to combine fast execution with stable behaviour with respect to the restoration error. In this paper we analyse some classical and recent gradient approaches for the linear least-squares problem by looking at their way of filtering the singular values, showing in particular the effects of scaling matrices and non-negative constraints in recovering the correct filters of the solution. An original analysis of the filtering effect for the image deblurring problem with Gaussian noise on the data is also provided.

Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

A new parameter estimation algorithm based on ensemble Kalman filter (EnKF) is developed. The developed algorithm combined with the proposed problem parametrization offers an efficient parameter estimation method that converges using very small ensembles. The inverse problem is formulated as a sequential data integration problem. Gaussian process regression is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen–Loeve expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative regularized EnKF algorithm. The filter is converted to an optimization algorithm by using a pseudo time-stepping technique such that the model output matches the time dependent data. The EnKF Kalman gain matrix is regularized using truncated SVD to filter out noisy correlations. Numerical results show that the proposed algorithm is a promising approach for parameter estimation of subsurface flow models.

Landweber iterative algorithm based on regularization in electromagnetic tomography for multiphase flow measurement

For multiphase flow that contains conductive or magnetic permeable material, it is possible to use an electromagnetic tomography technique to measure its flow rate and phase density. The main challenge of this kind of measurement is how to improve the image reconstruction quality. In this paper the comparison of linear back project, Landweber iterative and Tikhonov regularization algorithms are studied for an electromagnetic tomography system. Then an improved method of the Landweber iterative is introduced which uses a Tikhonov regularization reconstruction image as the initial iterative value for the iterative. Compared with the original Landweber iterative using a linear back project result as the initial value, this method can improve the quality of the reconstructed image. Moreover, the convergence speed of the iterative can be improved by using this method. The effectiveness of this method is verified by simulation reconstruction.

Estimation of fusion front in 2D axisymmetric welding using inverse method

This paper deals with heat transfer analysis in a static welding process. A method is developed to estimate the evolution of a 2D axisymmetric shape of a fusion front. The estimation is performed from theoretical temperature measurements taken in the solid part from a multiphysics problem which is validated with an experiment. The estimation procedure is based on the conjugate gradient method coupled with the iterative regularization algorithm. The gradient is computed using adjoint equations. The goal of this work is to apply an ALE (Arbitrary Lagrangian Eulerian) moving mesh method suitable for solving two-dimensional and axisymmetric moving-boundary problems. Owing to the calculation of the fluid flow inside the melt pool, the definition and the resolution of the multiphysics problem are very difficult (unknown phenomena and computation time). Thus a simplified problem, without the liquid zone, is developed. This means that at each time increment, the domain is modeled considering the fusion of the material and the shape is estimated by an inverse method.

Seismic Input Motion Determined from a Surface-Downhole Pair of Sensors: A Constrained Deconvolution Approach

Abstract We apply a deconvolution approach to the problem of determining the input motion at the base of an instrumented borehole using only a pair of recordings, one at the borehole surface and the other at its bottom. To stabilize the bottom-to-surface spectral ratio, we apply an iterative regularization algorithm that allows us to constrain the solution to be positively defined and to have a finite time duration. Through the analysis of synthetic data, we show that the method is capable of retrieving reliable input motion, suppressing the effect of the negative interference generated by the downgoing waves. Results obtained by applying the methodology to weak earthquakes recorded at the Atakoy (Istanbul) vertical array are also presented and show that removing the effect of the downgoing waves is remarkable, even considering the recording at a depth of 140 m.

Three-Dimensional Reconstruction for Fluorescence Tomography Using Cylinder Phantoms

Based on the finite element analysis, this study applies three iterative regularization algorithms to the 3D reconstruction of fluorescent yield, including conjugate gradient least square (CGLS), least square QR decomposition (LSQR), and 2-order pre-iteration method. By using a non-contact, multi-angle transmission imaging system, the experiments of single fluorescent target and double targets with the common-used cylinder phantom are conducted. Experimental results show that the above three methods could estimate the position of fluorescence targets accurately, while the time cost of each method is only about 2% of that of algebraic reconstruction technology (ART).

Iterative regularization algorithms for constrained image deblurring on graphics processors

The ability of the modern graphics processors to operate on large matrices in parallel can be exploited for solving constrained image deblurring problems in a short time. In particular, in this paper we propose the parallel implementation of two iterative regularization methods: the well known expectation maximization algorithm and a recent scaled gradient projection method. The main differences between the considered approaches and their impact on the parallel implementations are discussed. The effectiveness of the parallel schemes and the speedups over standard CPU implementations are evaluated on test problems arising from astronomical images.

Electrical impedance tomography with an optimized calculable square sensor

Electrical impedance tomography is a technique that reconstructs the medium distribution in a region of interest through electrical measurements on its boundary. In this paper, an optimized square sensor was designed for electrical impedance tomography in order to obtain maximum information over the cross section of interest, e.g., circulating fluidized beds, in the sense of Shannon information entropy. An analytical model of the sensor was obtained using the conformal transformation. The model indicates that the square sensor possesses calculable property, which allows the calculation of standard values of the sensor directly from a single dimensional measurement that can be made traceable to the SI unit of length. Based on the model, the sensitivity maps and electrical field lines can be calculated in less than a second. Two model based algorithms for image reconstruction, i.e., back projection algorithm based on electrical field lines and iterative Lavrentiev regularization algorithm based on the sensitivity map, were introduced. Simulated results and experimental results validate the feasibility of the algorithms.

Structured Multiblock Body-Fitted Grids Solution of Transient Inverse Heat Conduction Problems in an Arbitrary Geometry

The aim of this study is to develop iterative regularization algorithms based on parameter and function estimation techniques to solve two-dimensional/axisymmetric transient inverse heat conduction problems in curvilinear coordinate system. The multiblock method is used for geometric decomposition of the physical domain into regions with patched-overlapped interface grids. The central finite-difference version of the alternating-direction implicit technique together with structured body-fitted grids is implemented for numerical solution of the direct problem and other partial differential equations derived by inverse analysis. The approach of estimating unknown parameters and functions is iterative inverse analysis algorithms based on the Levenberg-Marquardt method and conjugate gradient methods. The temperature histories are delivered by noisy/non-noisy sensors located on the lower boundary of the domain. Three cases are considered, (1) a time-space-varying upper boundary condition, (2) two time-varying heat sources, and (3) a time-varying heat source and a time-space-varying boundary condition, within a two-dimensional/axisymmetric solid body of arbitrary geometry. The simultaneous estimation of two unknown functions is performed to assess the performance of inverse analysis methods to solve complicated inverse heat conduction problems. The results of the present study are compared to those of exact heat sources and boundary condition, and good agreement is achieved. However, the results show that the accuracy of the upper boundary condition identification is dependent on the uncertainty of the measured temperature data, the number of grid points, and the curvature of the geometric configuration as well.

Estimation of the surface normal velocity of high frequency ultrasound transducers

This paper is concerned with the characterization of the true locally resolved surface normal velocity of an assumed piston-type ultrasonic transducer. Instead of involving a very complicated direct pointwise measurement of the velocity distribution, an inverse problem is solved which yields a spatially discretized weighting vector for the surface normal velocity of the transducer. The study deals with a spherically focused high frequency transducer, which is driven in pulse-echo mode. As a means of posing the inverse problem, the active transducer surface is divided into annuli of equal surface so that for each annulus the spatial impulse response can be calculated. An acrylic glass plate acts as a simple structured target. The resulting ill-posed nonlinear inverse problem is solved with an iterative regularized Gauss-Newton algorithm. The solution of the inverse problem yields an estimated weight for the surface normal velocity for each annulus. Experimental results for a thin copper wire target are compared to simulation results for both uniform and estimated surface normal velocities.

Improvement of Space-Invariant Image Deblurring by Preconditioned Landweber Iterations

The Landweber method is a simple and flexible iterative regularization algorithm, whose projected variant provides nonnegative image reconstructions. Since the method is usually very slow, we apply circulant preconditioners, exploiting the shift invariance of many deblurring problems, in order to accelerate the convergence. This way reasonable reconstructions can be obtained within a few iterations; the method becomes competitive and more robust than other approaches that, although faster, sometimes lead to lower accuracy. Some theoretical analysis of convergence is given, together with numerical validations.

An iterative regularization method for the 2-constrained pseudoinversion of an operator equation

An iterative regularization algorithm is proposed for solving a special optimization problem, the so-called 2-constrained operator pseudoinversion. The convergence of the algorithm is examined in the case of perturbed input data. An error estimate is derived, and an a priori choice of the regularization parameters is described. The algorithm is applied to an optimal control problem with minimal costs.

Measurement of particle-size distribution and concentration in heterogeneous turbid media with multispectral diffuse optical tomography

We present a method that is capable of extracting particle-size distribution (PSD) and concentration in heterogeneous turbid media by use of multispectral diffuse optical tomography (MSDOT). After the spectroscopic scattering images of the heterogeneous turbid media are obtained with MSDOT, the morphologic information of particles in the heterogeneities is recovered with an iterative regularized reconstruction algorithm based on Mie scattering theory when a particular form of PSD is assumed (Gaussian distribution is used in this study). The method described is tested and evaluated with both simulated and experimental data. The simulations are intended to test the sensitivity of the overall approach to noise effect. A series of phantom experiments are conducted with our newly developed ten-wavelength MSDOT system. Polystyrene microsphere suspensions contain particles of varying size from 2 to 6 microm as targets are embedded in a scattering background medium in these experiments. To achieve optimized results from experimental data, we developed a data preprocessing method for MSDOT as well as a scheme for calibrating scattering spectra. The results from both simulations and experiments show that the particle mean size and concentration can be reconstructed with acceptable accuracy, whereas the recovery of the standard deviation is sensitive to noise effect and can be as large as 86% from the experimental data.

MSE-based regularization approach to direction estimation of coherent narrowband signals using linear prediction

This paper addresses the problem of directions of arrival (DOAs) estimation of coherent narrowband signals impinging on a uniform linear array (ULA) when the number of signals is unknown. By using an overdetermined linear prediction (LP) model with a subarray scheme, the DOAs of coherent signals can be estimated from the zeros of the corresponding prediction polynomial. Although the corrected least squares (CLS) technique can be used to improve the accuracy of the LP parameters estimated from the noisy array data, the inversion of the resulting matrix in the CLS estimation is ill-conditioned, and then, the CLS estimation becomes unstable. To combat this numerical instability, we introduce multiple regularization parameters into the CLS estimation and show that determining the number of coherent signals is closely related to the truncation of the eigenvalues. An analytical expression of the mean square error (MSE) of the estimated LP parameters is derived, and it is clarified that the number of signals can be determined by comparing the optimal regularization parameters with the corresponding eigenvalues. An iterative regularization algorithm is developed for estimating directions without any a priori knowledge, where the number of coherent signals and the noise variance are estimated from the noise-corrupted received data simultaneously.

Error concealment algorithms for compressed video

In this paper we propose an error concealment algorithm for compressed video sequences. For packetization and transmission, a two layer ATM is utilized so that the location of information loss is easily detected. The coded image can be degraded due to channel error, network congestion, and switching system problems. Seriously degraded images may therefore result due to information loss represented by DCT coefficients and motion vectors, and due to the inter-dependency of information in predictive coding. In order to solve the error concealment problem of intra frames, two spatially adaptive algorithms are introduced; an iterative and a recursive one. We analyze the necessity of an oriented high pass operator we introduce, and the requirement of changing the initial condition in iterative regularized recovery algorithm. Also, the convergence of iteration is analyzed. In recursive interpolation algorithm, the edge direction of the missing areas is estimated from the neighbors, and estimated edge direction is utilized for steering the direction of interpolation. For recovery of the lost motion vectors, an overlapped region matching algorithm is introduced. Several experimental results are presented.

An iterative method for maximum entropy regularization reconstruction in MRI

Many problems in physics involve imaging objects with high spatial frequency content in a limited amount of time. The limitation of available experimental data leads to the infamous problem of diffraction limited data, which manifests itself by causing ringing in the image. This ringing is due to interference phenomena in optics and is known as the Gibbs phenomenon in engineering. In this paper, an iterative maximum entropy regularization (IMER) algorithm for magnetic resonance imaging (MRI) is developed, which produces a super-resolution and optimal signal-to-noise solution to the problem of reconstructing a source from partial Fourier transform data. This method is capable, in principle, of unlimited resolution and is robust with respect to Gaussian white noise perturbation. Comparisons of the IMER method with the conventional Fourier transform method are carried out with the real magnetic resonance data to illustrate the performance of the proposed method. © 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 427–431, 1999

An iterative regularization for approximating the penalties method in Hilbert space

Agreements are found for the controlling parameters for iterative regularization algorithms in imposing a penalty on the boundaries and approximation of convex problems in Hilbert space. Cases of an integral penalty and non-smooth penalty of maximum type from the boundaries are considered. Ways of weakening the traditional assumptions (on the smoothness and existence of a saddle point of the Legendre function) are discussed. Theorems on convergence are proved including one for an iterative combination using the gradient projections method (stochastic quasigradients) in the approximating space, and an algorithm is presented.