Non-iterative Reconstruction Algorithm Research Articles

A fusion algorithm for mass flow rate measurement based on neural network and electrical capacitance tomography

The process tomography has received a noticeable attention in industry due to non-invasive and non-intrusive characterise. To asses the potential of electrical capacitance tomography for gravity-fallen mass flow rate measurement, a fusion algorithm based on neural network is designed and implemented. The hardware of instrument is composed of a pipe as circular phantom with 200 mm internal diameter and the front-end electronics. The specially programmed software, runs five well-known, non-iterative reconstruction algorithms (LBP, Tikhonov, SVD, ART and SIRT) and fusions the results in a MLP-NN. The sensor experimentally evaluated by wheat grains. Five implemented algorithms, and the fusion NN are compared using RMSE and concentration error parameters. According to evaluated results in whole of tests, the fusion algorithm reduces RMSE and concentration error by approximately 2–3 and 7–10 folds respectively. Since these five algorithms are completely independent, running the program in parallel by Multi-Thread mode, do not adds run-time.

Non-iterative reconstruction of interferenceless coded aperture correlation holography enabled high quality three-dimensional imaging

Interferenceless coded aperture correlation holography (I-COACH) is a rapidly developing indirect three-dimensional (3D) imaging technique. However the ideal point spread function of imaging system is not obtained in most cases, the object hologram is usually correlated with the system response of a limited-size pinhole during the reconstruction process. As a result, the quality of reconstructed images is contaminated by noise. In this paper, the system response of a limited-size pinhole is regarded as the convolution of the pinhole (as an object) intensity and the ideal point spread function of I-COACH, a mathematical analysis of the background noise is conducted and a general high-quality reconstruction mathematic model of I-COACH system is derived when a limited-size pinhole is used to record point spread hologram, in which the reconstructions and noise is separated. Then a non-iterative cross-correlation reconstruction algorithm has been developed here to achieve high-quality 3D reconstruction. The proposed method has been implemented on a regular I-COACH system in both transmission as well as reflection illumination modes to demonstrate the imaging ability of our method. The experimental results show that high quality reconstructions can be achieved by our proposal with a single-exposure object hologram.

Exploration of the pulse pileup effects in a clinical CdTe-based photon-counting computed tomography.

High tube current generates a high flux of x-rays to photon counting detectors (PCDs) that can potentially result in the piling up of pulses formed by concurrent photons, which can cause count loss and energy resolution degradation. To evaluate the performance of clinical photon-counting CT (PCCT) systems in high flux, potentially influenced by pulse pileup effects, in terms of task-generic image quality metrics. A clinical phantom was scanned on a commercial PCCT scanner (NAEOTOM Alpha, Siemens) at 120kV under fourteen different tube current levels (40-1000mA) with a rotation time of 0.25 s and a pitch of 1. The dose levels corresponded to CTDIvol (32cm phantom) of 0.79-19.8mGy. CT sinograms were reconstructed using QIR-off mode (noniterative reconstruction algorithm), Br44 kernel, and a voxel size of . imQuest, an open-source MATLAB-based software package was used to calculate noise power spectrum (NPS), task transfer function (TTF), contrast-to-noise ratio (CNR), and CT number according to AAPM Task Group 233 metrology. The 50% cut-off frequency of TTF (f50 ) remained mostly constant across all higher tube currents for all inserts, namely polyethylene, bone, air, and acrylic. Using the lowest two data points (40 and 80mA), the expected relationship between noise magnitude and tube current was determined to be noise mA-0.47 . The measured noise magnitude were up to 11.1% higher than the expected value at the highest tube current. The average frequency of NPS (fav ) decreased from 0.32 to 0.29mm-1 as tube current increased from 40 to 1000mA. No considerable effects were observed in CT number measurement of any insert; however, CT numbers for air and bone changed almost monotonically as tube current increased. Absolute CNR increased monotonically for all inserts; however, the difference between measured and expected CNRs were approximately -6% to 12% across all tube currents. Increasing tube currents did not affect the spatial resolution, but slightly affected the CT number and noise measurements of the clinical PCCT system. However, the effects were only considerable at clinically irrelevant tube currents used on a small 20-cm phantom. In general clinical practices, automatic exposure control techniques are used to decrease the variation of flux on the detector, which alleviates the chances of detector saturation due to high count rates. The observed effects could be due to pulse pileup, signal-dependent filtration of the system, or nonlinearities in the reconstruction algorithm. In conclusion, either the deadtime of the detector used in the photon-counting CT system is shorter such that count losses due to pulse pileup are negligible, or pulse pileup has inconsiderable effects on the image quality of clinical photon-counting CT systems in routine clinical practice due to possible corrections applied on the system.

Evaluation of Image Enhancement Techniques for Electrical Capacitance Tomography Applications

The fast generation of images in Electrical Capacitance Tomography (ECT) systems is a desirable feature for many industrial applications. Non-iterative reconstruction algorithms which qualify for this requirement generate poor-quality images. The Linear Back Projection (LBP) is the fastest non-iterative reconstruction algorithm. The challenge is to find a technique to improve the quality of images from LBP at a low computational cost. Image enhancement techniques have been investigated for improving the quality of images reconstructed from the LBP algorithm. Simulated and measured static and dynamic flow data were used in the evaluation. The performance results were benchmarked with results from the Projected Land Weber (PLW) one of the accurate iterative reconstruction algorithms. The Gompertz enhancement algorithm was found to have 3.5 times more computation cost than the LBP reconstruction algorithm and the accuracy of the iterative PLW reconstruction algorithm. This is noteworthy since the algorithm does achieve a good balance between accuracy and speed. The fact that the accuracy gained satisfies the reservoir management standards in the multiphase hydrocarbon production sector is significant in this regard.
 Keywords: Electrical Capacitance tomography, Multiphase flow imaging, Maximum entropy thresholding, Gompertz distribution, Image enhancement

A multithreaded real-time solution for 2D EIT reconstruction with the D-bar algorithm

Electrical impedance tomography (EIT) is a non-ionizing real-time imaging tool for bedside pulmonary imaging. Dynamic cross-sectional images of ventilation and perfusion can be produced in real time with fast algorithms from measured voltage data arising from current applied on electrodes placed around the circumference of the patient’s chest. The D-bar method is a direct (non-iterative) reconstruction algorithm for EIT that uses equations of inverse scattering to independently reconstruct the conductivity at each point in the region of interest. However, this nonlinear reconstruction method has a computational complexity that makes real-time imaging a challenge. At the same time, it has the attributes that it does not require successive solutions of the forward problem, as is the case with iterative methods, and it is trivially parallelizable in the spatial variable. Here, we present a novel multithreaded implementation of the D-bar method with a front-end MATLAB/Octave program interfaced with C code that uses the pthreads library. The implementation is analyzed on several different platforms with concurrent threads ranging from 2 to 32 for spatial grids of several sizes. We demonstrate that on a CPU with many cores, very high frame rates (50 frames/s) with high resolution (6000 grid points) are achievable, and on a single AMD CPU real-time reconstructions (faster than 30 frames/s) are achieved with this implementation using 10 or more threads on a grid of 1969 points.

Reconstruction of pointwise sources in a time-fractional diffusion equation

This paper is concerned with an inverse pointwise source problem for the time-fractional diffusion equation in the two-dimensional case. The source term to be identified models the action of a finite number of small particles. Each particle is assumed to be no larger than a single point, characterized by its location and intensity. Both theoretical and numerical aspects are discussed. In the theoretical part, we analyse the well-posedness of the Dirac time-fractional diffusion problem. For the inverse problem, we establish that the unknown point sources can be uniquely identified from local measured data and we derive a local Lipschitz stability result. In the numerical part, we develop a fast and accurate reconstruction approach. The unknown pointwise sources are characterized as solution to an optimization problem minimizing a tracking-type functional. A noniterative reconstruction algorithm is devised, allowing us to determine the number, locations and intensities of the pointwise sources. The efficiency of the proposed approach is confirmed by some numerical examples.

Imaging of mass distributions from partial domain measurement

Abstract This paper deals with an inverse source problem governed by the Poisson equation. The aim is to reconstruct multiple anomalies from internal observation data within an arbitrary sub-region. The considered model problem is motivated by various applications such as the identification of geological anomalies underneath the Earth’s surface. To overcome the ill-posedness, the inverse problem is formulated as a self-regularized topology optimization one. A least-square functional measuring the misfit between the observed quantities and the values provided by the model problem is introduced. The misfit function involves a regularization term penalizing the relative perimeter of the unknown domain. Finally, it is minimized with respect to a finite number of circular-shaped anomalies. The existence and stability of the solution to the inverse problem are demonstrated. The reconstruction process is based on the topological derivative method. The variation of the shape functional with respect to a small geometric perturbation is studied, and the leading terms of a second-order topological asymptotic expansion are derived. A non-iterative reconstruction algorithm is developed via the minimization of the obtained asymptotic formula with respect to the location and size parameters of the unknown set of anomalies. The efficiency and accuracy of the proposed approach are justified by some numerical experiments.

A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements

In this paper, a noniterative method for solving an inverse source problem governed by the two-dimensional time-fractional diffusion equation is proposed. The basic idea consists in reconstructing the geometrical support of the unknown source from partial boundary measurements of the associated potential. A Kohn–Vogelius type shape functional is considered together with a regularization term penalizing the relative perimeter of the unknown set of anomalies. Identifiability result is derived and uniqueness of a minimizer is ensured. The shape functional measuring the misfit between the solutions of two auxiliary problems containing information about the boundary measurements is minimized with respect to a finite number of ball-shaped trial anomalies by using the topological derivative method. In particular, the second-order topological gradient is exploited to devise an efficient and fast noniterative reconstruction algorithm. Finally, some numerical experiments are presented, showing different features of the proposed approach in reconstructing multiple anomalies of varying shapes and sizes by taking noisy data into account.

CSNet: A deep learning approach for ECG compressed sensing

Remote electrocardiogram (ECG) monitoring plays a very important role in the prevention and treatment of cardiovascular diseases. However, the current long-term ECG monitoring generates a large amount of data, which puts great pressure on the bandwidth and transmission systems. Compressed sensing (CS) has great attraction for resource-limited wearable devices used in remote ECG monitoring. Traditional CS reconstruction algorithms often require complex signal processing and prior knowledge, and the reconstruction process is time-consuming, which limits the application of CS in remote ECG monitoring systems. This paper proposes a non-iterative fast reconstruction algorithm based on CS and deep learning, which combines convolutional neural network (CNN) and long short-term memory (LSTM) to directly learn the mapping relationship between the rising dimension signal of the measurements and the original signal, and is validated in the MIT-BIH Arrhythmia Database (MITDB). The experimental results show that the reconstruction error of this method is lower than that of traditional algorithms including basis pursuit (BP), orthogonal matching pursuit (OMP), bound-optimization-based block sparse Bayesian learning (BSBL-BO) and rotate-singular value decomposition + basis pursuit (R-SVD+BP) at high compression ratios (CRs, when CR⩾50%). At the same time, for a 30-min ECG signal, only about 0.12 s is needed to complete the reconstruction, which is at least 45 times faster than the traditional algorithms, which is enough to support real-time applications. In addition, the proposed method is also validated in MIT-BIH Normal Sinus Rhythm Database (NSRDB), MIT-BIH Atrial Fibrillation Database (AFDB) and European ST-T Database (EDB), and the reconstructed signals of NSRDB and AFDB meet the clinical requirements at CR⩽70%, and the reconstructed signals of EDB meet the clinical requirements at CR⩽90%.

Imaging of small penetrable obstacles based on the topological derivative method

PurposeThe purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.Design/methodology/approachThe method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.FindingsIn this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.Originality/valueThe current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.

A stable non-iterative reconstruction algorithm for the acoustic inverse boundary value problem

<p style='text-indent:20px;'>We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that are stable. We prove the convergence of the algorithm and present its numerical implementation. The effectiveness of the algorithm is validated on both constant speed and variable speed, with full and partial boundary measurement as well as different levels of noise.</p>

Topological sensitivity method for reconstruction of the spatial component in the source term of a time-fractional diffusion equation

In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved. The topological sensitivity analysis method is presented. The considered problem is formulated as a topology optimization one. The proposed process leads to a non-iterative reconstruction algorithm can be applied for large class of cost functional. The unknown shape of the term source support is reconstructed using a level-set curve of the topological gradient. Several numerical simulations are presented to show the efficiency and the accuracy of the algorithm.

Iterative versus non-iterative image reconstruction methods for sparse magnetic resonance imaging.

Magnetic resonance imaging (MRI) using under-sampled k-space data is a common method to shorten the imaging time. Iterative Bayesian algorithms are usually used for its image reconstruction. This paper compares an iterative Bayesian image reconstruction method that uses both spatial and temporal constraints and a non-iterative reconstruction algorithm that does not use temporal constraints. Three patient studies are performed. It is interesting to notice that the images reconstructed by the iterative Bayesian algorithm may introduce more bias than the non-iterative algorithm, even though the images provided by the iterative Bayesian algorithm look less noisy. The bias can be reduced by decreasing the influence of the temporal constraints.

Identifying an unknown source term in a heat equation with time-dependent coefficients

ABSTRACT An inverse source problem for an n-dimensional heat equation with a time-varying coefficient is investigated. The spatially dependent component of a source function is determined from a measurement at the final time. The inverse problem is regularized by a mollification method. Hölder-type stability estimates are proved. Error estimates of Hölder type are also proved for regularized solutions for both a priori and a posteriori mollification parameter choice rules. A non-iterative reconstruction algorithm is proposed. Numerical examples in one and two dimensions are shown to illustrate the performance of the proposed method.

Pollution Sources Reconstruction Based on the Topological Derivative Method

The topological derivative method is used to solve a pollution sources reconstruction problem governed by a steady-state convection-diffusion equation. To be more precise, we are dealing with a shape optimization problem which consists of reconstruction of a set of pollution sources in a fluid medium by measuring the concentration of the pollutants within some subregion of the reference domain. The shape functional measuring the misfit between the known data and solution of the state equation is minimized with respect to a set of ball-shaped geometrical subdomains representing the pollution sources. The necessary conditions for optimality are derived with the help of the topological derivative method which consists in expanding the shape functional asymptotically and then truncate it up to the second order term. The resulting expression is trivially minimized with respect to the parameters under consideration which leads to a noniterative second-order reconstruction algorithm. Two different cases are considered. Firstly, when the velocity of the leakages is given and we reconstruct the support of the unknown sources, including their locations and sizes. In the second case, we consider the size of the pollution sources to be known and find out the mean velocity of the leakages and their locations. Numerical examples are presented showing the capability of the proposed algorithm in reconstructing multiple pollution sources in both cases.

A non-iterative reconstruction method for bioluminescence tomography

In this paper, we study an inverse source problem of the bioluminescence tomography in three dimensional case. Our aim is to reconstruct a bioluminescent source distribution within a body from the knowledge of the boundary measurements. The inverse source problem is reformulated as a topology optimization one minimizing an energy like type functional. It measures the difference between the solutions of two auxiliary boundary value problems. An asymptotic expansion of the considered functional with respect to a set of ball-shaped anomalies is computed using the topological sensitivity analysis method. The obtained theoretical result leads to build a non-iterative reconstruction algorithm. Finally, some numerical examples in 3D are presented in order to show the effectiveness of the devised reconstruction algorithm.

Topological Sensitivity Analysis and Kohn-Vogelius Formulation for Detecting a Rigid Inclusion in an Elastic Body

Our main interest in this work is to detect a rigid inclusion immersed in an isotropic elastic body $\Omega$ from a single pair of Cauchy data on $\partial \Omega$ in two dimensions. We want to completely characterize the unknown rigid inclusion, namely, the shape and the location of inclusion. The idea is to rewrite the inverse problem as an optimization problem, where an energy like functional is minimized with respect to the presence of a small inclusion. A topological sensitivity analysis is derived for an energy like functional. We proposed a non-iterative reconstruction algorithm based on the topological gradient concept. The unknown rigid inclusion is defined by a level curve of a scalar function. The proposed numerical approach is very robust with respect to noisy data. Finally, in order to show the efficiency and accuracy of the proposed algorithm, we present some numerical results.

A concept for single-shot volumetric fluorescence imaging via orthogonally polarized excitation lattices

The deconvolution of widefield fluorescence images provides only guesses of spatial frequency information along the optical axis due to the so called missing cone in the optical transfer function. Retaining the single-shot imaging speed of deconvolution microscopy while gaining access to missing cone information is thus highly desirable for microscopy of volumetric samples. Here, we present a concept that superimposes two orthogonally polarized excitation lattices with a phase-shift of p between them. In conjunction with a non-iterative image reconstruction algorithm this permits the restoration of missing cone information. We show how fluorescence anisotropy could be used as a method to encode and decode the patterns simultaneously and develop a rigorous theoretical framework for the method. Through in-silico experiments and imaging of fixed biological cells on a structured illumination microscope that emulates the proposed setup we validate the feasibility of the method.

Gridrec-MS: an algorithm for multi-slice tomography.

Advances in imaging systems and modeling allow for depth information to be retrieved from projections via virtual sectioning of the imaged object. Here we introduce a regridding method that explicitly and directly incorporates this information into a general and non-iterative tomographic reconstruction algorithm. The method is applicable to any imaging scheme that provides depth-resolved projections. Additionally, we show, via numerical simulations, that with this method the required number of projections for adequate angular sampling can be reduced.

Noniterative Hyperspectral Image Reconstruction From Compressive Fused Measurements

Compressive spectral imaging (CSI) enables the acquisition of spectral and spatial information of a scene using fewer projected measurements than traditional scanning approaches. Recently, research efforts have focused on obtaining high-resolution spectral images via expensive detectors and sophisticated CSI devices. Alternatively, high-resolution spectral images can be obtained using side information or fusion of compressed measurements, without significantly increasing acquisition costs. Indeed, these approaches retrieve improved resolution images applying iterative and computationally expensive algorithms. This paper proposes the fusion of compressed measurements obtained from two state-of-the-art CSI systems, the single-pixel camera (SPC) and the three-dimensional coded aperture snapshot imaging system (3D-CASSI), such that high-resolution images can be obtained by exploiting detailed spectra provided by the SPC and high spatial resolution of the 3D-CASSI. Specifically, a noniterative reconstruction algorithm is proposed, based on the fact that the spatial-spectral data lie in a low-dimensional subspace. In contrast to related works, the proposed approach relies on implementable CSI systems. Simulations and experimental results show the effectiveness of the proposed method compared to similar approaches, both in reconstruction quality and complexity. Specifically, the proposed method is up to 5.6 times faster than its counterparts and provides comparable quality of attained reconstructions.