Exact Reconstruction Research Articles

Removing Cardiac Artifacts From Single-Channel Respiratory Electromyograms

Electromyographic (EMG) measurements of the respiratory muscles provide a convenient and noninvasive way to assess respiratory muscle function and detect patient activity during assisted mechanical ventilation. However, surface EMG measurements of the diaphragm and intercostal muscles are substantially contaminated by cardiac activity due to the vicinity of the cardiac muscles. Many algorithmic solutions to this problem have been proposed, yet a conclusive performance comparison of the most promising candidates currently is missing. The objective of this work is to provide a quantitative performance comparison of six previously proposed cardiac artifact removal algorithms operating on single-channel EMG measurements, and two newly proposed, improved versions of these algorithms. Algorithmic performance is evaluated quantitatively based on four different measures of separation success, using both synthetic validation signals and electromyographic measurements of the respiratory muscles in eight subjects. The compared algorithms are two versions of the empirical template subtraction algorithm, two model-based Bayesian filtering procedures, a wavelet denoising approach, an empirical mode decomposition (EMD) based approach, and classical high-pass filtering. Different algorithms perform well with respect to different performance measures. Template subtraction algorithms yield the best results if the characteristics of the raw signal are of interest, while filtering algorithms like simple high-pass filtering, wavelet denoising, and EMD-based denoising show superior performance for calculating a cleaned envelope signal. No algorithm completely removes the cardiac interference, but the characteristic errors introduced by the considered algorithms differ. Hence, the choice of the algorithm to use should be made depending on the target application. Finally, we also demonstrate that our empirical SNR measure, which can be calculated without knowledge of the true, undisturbed signals, correlates strongly with the exact reconstruction error. Thus, it represents a reliable indicator for algorithm performance on real measurement data.

Sketching and Stacking With Random Fork Based Exact Signal Recovery Under Sample Corruption

In this paper, we propose a new technique for exact recovery of missing data due to impulsive noise in time-domain sampled acoustic waves, named as sketching and stacking with random fork (SSRF). Existing methods recover the original signal from the corrupted sequence based on the correlation between each element of the signal or between the bases constituting the signal such as in the field of interpolation or compressive sensing. In addition, a partially corrupted signal is retrieved through statistical approaches using a large amount of pre-measured data in the machine learning domain. As a new approach, we hypothesize that if there is a novel method of re-sampling and processing, which can extract the intrinsic information of a corrupted signal, then the original signal can be recovered without information loss. The mathematical backgrounds in our study are twofold; first, a signal made up of overlapped k damped sinusoidal waves can be represented as the superposition of 2k number of geometric sequences according to Euler's formula; second, this superposed signal can be decomposed into individual geometric sequences by well-transformed 2k+1 informative matrices. The proposed method is to extract the parameters of 2k geometric sequences by transforming the non-corrupted samples into 2k+1 informative matrices, and retrieve the corrupted samples by extrapolating the obtained parameters. We reveal the condition where SSRF perfectly fulfills the exact reconstruction, and verify the quality of reconstruction by comparing the results with conventional schemes.

Minimally invasive treatment of tibial plateau depression fractures using balloon tibioplasty: Clinical outcome and absorption of bioabsorbable calcium phosphate cement.

The exact reconstruction of the tibial plateau and articular surface is the main operative aim in the treatment of tibial plateau depression fractures. For selected cases, a novel technique with the use of balloon tibioplasty in combination of bioabsorbable calcium phosphate cement is available. In this study, the first objective was to answer the question whether the clinical outcome parameters after balloon tibioplasty are comparable to open reduction procedures described in the literature. Secondly, we asked whether the cement absorption is safe in relation to adverse effects like osteolysis and measured the absorption ability during the bone conversion process in the proximal tibia bone. Eight patients (mean age 54 years; 4 males and 4 females) received the abovementioned surgical procedure. Mean follow-up period was 27 months. This study evaluated clinical outcome and radiological measured cement absorption within the postoperative course. Cement absorption was measured on X-rays and calculated based on the greatest extend on anterior-posterior and lateral view radiographs just after the operation on the latest available follow-up. WOMAC score showed a mean of 93. Radiologic absorption was 1/5 at a mean of 18 months. No osteolysis reaction was seen surrounding the cement. This far, promising clinical and radiological results have been shown with WOMAC scores comparable to the results of noninjured knees. The indication for this relatively new technique is restricted to isolated depression fractures. It is a useful tool to facilitate the reduction of select depressed tibial fractures. The radiologic absorption effect seems to be quite fast in bone remodeling and safe without any osteolysis or osseous reaction.

CS-MRI reconstruction based on analysis dictionary learning and manifold structure regularization

Compressed sensing (CS) significantly accelerates magnetic resonance imaging (MRI) by allowing the exact reconstruction of image from highly undersampling k-space data. In this process, the high sparsity obtained by the learned dictionary and exploitation of correlation among patches are essential to the reconstructed image quality. In this paper, by a use of these two aspects, we propose a novel CS-MRI model based on analysis dictionary learning and manifold structure regularization (ADMS). Furthermore, a proper tight frame constraint is used to obtain an effective overcomplete analysis dictionary with a high sparsifying capacity. The constructed manifold structure regularization nonuniformly enforces the correlation of each group formed by similar patches, which is more consistent with the diverse nonlocal similarity in realistic images. The proposed model is efficiently solved by the alternating direction method of multipliers (ADMM), in which the fast algorithm for each sub-problem is separately developed. The experimental results demonstrate that main components in the proposed method contribute to the final reconstruction performance and the effectiveness of the proposed model.

Joint image reconstruction and segmentation: Comparison of two algorithms for few-view tomography

Two algorithms of few-view tomography are compared, specifically, the iterative Potts minimization algorithm (IPMA) and the algebraic reconstruction technique with TV-regularization and adaptive segmentation (ART-TVS). Both aim to reconstruct piecewise-constant structures, use the compressed sensing theory, and combine image reconstruction and segmentation procedures. Using a numerical experiment, it is shown that either algorithm can exactly reconstruct the Shepp-Logan phantom from as small as 7 views with noise characteristic of the medical applications of X-ray tomography. However, if an object has a complicated high-frequency structure (QR-code), the minimal number of views required for its exact reconstruction increases to 17–21 for ART-TVS and to 32–34 for IPMA. The ART-TVS algorithm developed by the authors is shown to outperform IPMA in reconstruction accuracy and speed and in resistance to abnormally high noise as well. ART-TVS holds good potential for further improvement.

A Four-Probe Method Using Different Probe Spacings for Measurement and Exact Reconstruction of Parallel Profiles

To realize the measurement and exact reconstruction of a pair of parallel profiles, a new scanning method using four displacement sensors as probes and different probe spacings has been invented with the advantage of preventing data processing error. The measuring device is placed between the measured objects and moved by a scanning stage to collect measurement data of both measured profiles. Considering many existing methods, the high lateral resolution of the reconstruction result and the rejection of the data processing error cannot always be achieved at the same time. When the measured profiles are in the short wavelength range, data processing errors are often on the same order of magnitude as the height difference of the measured profiles. The new method can eliminate both the straightness error of the measurement reference and the data processing error. The exact reconstruction retaining the high lateral resolution and without data processing error can be realized by rational position arrangement of sensors and corresponding processing method of the measurement data. The new method possesses the following advantages: (i) achievement of the exact reconstruction without data processing error; (ii) high lateral resolution not limited by probe spacing; (iii) concise operation without zero calibration of probes; and (iv) suitability for on-machine measurement. The feasibility and advantages of the new method were demonstrated by theoretical analyses, simulations, and experimental results.

Photoacoustic tomography with direction dependent data: an exact series reconstruction approach

Photoacoustic image reconstruction often assumes that the restriction of the acoustic pressure on the detection surface is given. However, commonly used detectors often have a certain directivity and frequency dependence, in which case the measured data are more accurately described as a linear combination of the acoustic pressure and its normal derivative on the detection surface. In this paper, we consider the inverse source problem for data that are a combination of the acoustic pressure and its normal derivative. For the special case of a spherical detection geometry we derive exact frequency domain reconstruction formulas. We present numerical results showing the robustness and validity of the derived formulas. Moreover, we compare several different combinations of the pressure and its normal derivative showing that used measurement model significantly affects the recovered initial pressure.

FBP-type CT reconstruction algorithms for triple-source circular trajectory with different scanning radii.

Multi-source computed tomography (CT) imaging has unique technical advantages not only for dynamic objects, but also for large-size objects by designing its imaging scan mode. Using the triple-source fan-beam imaging scan mode under three circular trajectories with two different radii, we in this study developed and analyzed theoretically several exact reconstruction algorithms in terms of full-scan and short-scan for three sets of truncated projection data. This triple-source scan configuration in different radii cases is easier to be simulated by a single-source scan configuration in an industrial CT system. The proposed algorithms are based on the idea of filtering-back-projection (FBP) algorithm, and can reconstruct the large-size objects under the same CT devices. The developed algorithms avoid data rebinning and can provide exact and fast image reconstruction. The results of the numerical simulation based data analysis verified that new algorithms were accurate and effective.

Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones

The main ideas of F-transform came from representing expert rules. It would be therefore reasonable to expect that the more accurately the membership functions describe human reasoning, the more successful will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions—however, somewhat surprisingly, many successful applications of F-transform use the simplest possible triangular membership functions. There exist some explanations for this phenomenon, which are based on local behavior of the signal. In this paper, we supplement these local explanations by a global one: namely, we prove that triangular membership functions are the only one that provide the exact reconstruction of the appropriate global characteristic of the signal.

High spatial resolution computed tomography of chemiluminescence with densely sampled parallel projections.

Computed tomography of chemiluminescence (CTC) is an effective tool for combustion diagnostics by using optical detectors to capture the projections of luminescence from multiple views and realizing the three-dimensional (3D) reconstruction by computed tomography (CT) theories. In the existing CTC, ordinary commodity lenses were employed in the system for imaging, the imaging effects complicate the projection model and the low sampling rate decreases the spatial resolution and reconstruction accuracy. In classical CT techniques, parallel projection based on 2D Radon transform is the simplest model, which has been widely used in CT applications. In this work, double telecentric lens is introduced in CTC to realize the acquisition of parallel projection with high sampling rate. Despite the parallel projection CT theories have been well studied, there are still a few theoretical and technological drawbacks need to be solved when utilizing double telecentric lens in CTC. Firstly, a simple method based on bilinear interpolation is studied to improve the calculation accuracy of the weight matrix. Secondly, the exact reconstruction condition for parallel projections is studied based on the discrete Radon transform theory. It establishes the theoretical relationship of the reconstruction quality and the sampling rate of the projections, the number of views, the range and the spatial resolution of the reconstructed region. In experiment, camera calibration technique for double telecentric lens is studied, and the results of which are used for projection correction. The tomographic reconstructions of an axisymmetric flame demonstrate the feasibility and accuracy of the studies.

Design of orthogonal graph filter bank with known eigenvalues of Laplacian matrix

In the conventional designs of orthogonal graph filter bank, both eigenvalues and eigenvectors of Laplacian matrix are assumed to be unknown such that graph filter bank can be efficiently implemented by using polynomial graph filters; that is, the output signal at each vertex is computed only from the signal at that vertex and its K -hop neighbourhoods. However, the disadvantage of these methods is that the designed orthogonal filter bank does not have the exact perfect reconstruction (PR). In this study, the authors first assume that the eigenvalues of Laplacian matrix are known but eigenvectors are still unknown. Then, the orthogonal graph filter bank is designed by solving the simultaneous equation or Lagrange multiplier method such that the PR condition at all eigenvalues can be achieved for a given graph structure. Although the proposed filter bank is a graph-structure-dependent design, it can be efficiently implemented by using polynomial graph filters. Finally, experimental results are shown to demonstrate the effectiveness of the proposed design method.

State estimators and observers for continuous and discrete linear systems. Part 2. Integral observers for exact state reconstruction

In the paper, the exact state observers will be presented. The state estimators and observers can be used in technical processes for many purposes like the fault detection and diagnosis, the implementation of the state controllers, and soft reconstruction of inaccessible for measurements variables of the system. As the standard, for continuous systems the differential estimators of Kalman filter or Luenberger type observer are commonly used. However, if the initial conditions of the real state are unknown, both estimators guarantee only an asymptotic quality of the real state tracking. The paper presents another type of the state observers, which for continuous system have the structure given by two integral operators. Based on measurements of the system input and output signals on some predefined finite time interval T, they can reconstruct the initial state exactly. In on-line version, the exact state reconstruction is performed continuously for every t, based on special procedure executed within two moving windows of width T, on sliding time interval [t-T, t].

Microlocal analysis for spherical Radon transform: two nonstandard problems

Assume that is a connected convex closed hyper-surface in . Let be the spherical Radon transform that sends a function f to its integrals on the set of spheres centered on . In this article, we consider a general family of filtered-backprojection reconstruction formulas for , in two non-standard cases: (i) f is supported outside of and (ii) f is supported inside and is non-smooth. For the first case, we show that the resulting operator is a pseudo-differential operator with a singular symbol. It is associated with two cleanly intersecting Lagrangians; one is the diagonal and one is a fold canonical relation obtained by reflection. For the second case, we restrict our attention to the two dimensional space and being a square. We show that generates artifacts along circles centered at the vertices of . This fact, in particular, implies that there are no exact filtered-backprojection reconstruction formulas in this case.

Phase retrieval exact solution based on structured window modulation without direct reference waves

Arising in coherent diffraction imaging (CDI), the phase retrieval problem is to reconstruct a complex object by measuring only diffraction intensity patterns. Existing approaches, such as iterative Fourier algorithm (IFA), transport intensity equation (TIE) methods and matrix optimisation, result in near-optimal solutions rather than exact solutions. This paper proposes an analytic method to get the exact phase retrieval solution without relying on direct reference waves. Based on structured template windows, the object far-field phase is solved analytically from the recorded Fourier intensities, from which the exact object reconstruction can be achieved. Sufficient conditions for obtaining exact phase retrieval solution are analysed rigorously and verified by numerical simulations, which also show the robustness of the method through simulations under noises, dynamic range, nonlinear response and bad alignment. A simple experimental result is provided to demonstrate the practical feasibility of the method. It achieves analytic phase retrieval for arbitrary complex-valued objects and may be applicable to quick phase imaging.

Two relay control robustification by continuous switched integral sliding modes

Robust generation of self-oscillation for mechanical systems in the presence of matched uncertainties/perturbations based on a two-relay controller, which naturally has a switched structure, is presented. Two scenarios are considered: the case when all the system states are available and the case when only output information is measured. In both scenarios, a continuous switched integral sliding modes controller is implemented to guarantee theoretically exact compensation of matched uncertainties/perturbations before the first switching. The chattering attenuation in the presence of fast parasitic dynamics can be realised by a switched gain strategy of the super-twisting algorithm. In the output-based scenario, the observer and the controller are initiated sequentially. A super twisting-based observer is used, guaranteeing theoretically exact reconstruction of the states before the controller is activated. The observer gains are also switched to diminish the chattering. Once the observer has converged, the reconstructed state is used in the controller to achieve the control objective. The observer and controller are designed to attain convergence before the first switching.

Improved rotor position determination for a sensorless star‐connected PMSM drive using Direct Flux Control

A technique for driving a star-connected PMSM without a position or speed sensor, which is known in the literature as Direct Flux Control (DFC), is described here. This technique is based on voltage measurements at the machine star point and can work even at very low speeds including standstill. The underlying principle of this technique is outlined and an improved position estimation algorithm allowing the exact reconstruction of the direction of maximum inductance is presented. The DFC technique is implemented on a microcontroller board and experimental validation is conducted on a PMSM both for quasi-static characterisation and for open-loop driving.

Decomposition of Turbulent Fluxes from Filtered Data and Application to Turbulent Premixed Combustion Modelling

The exact reconstruction of statistical quantities from filtered data is a fundamental question in turbulence research. Filtered data can be either data from a Large Eddy Simulation (LES) or it can be experimental data with insufficient resolution to capture the finest scales. Usually it is assumed that averages of filtered and unfiltered quantities are the same and as a consequence the Reynolds stress or turbulent scalar flux is traditionally split in a resolved part and a mean subfilter part. However, this decomposition holds only true for homogeneous flows without mean gradients as demonstrated recently (Klein and Germano [1]). In this work an exact relation between filtered, respectively Favre filtered, and unfiltered turbulent fluxes will be derived and tested in the context of turbulent premixed combustion, where heat release gives locally rise to strong gradients and consequently the failure of the standard assumption is expected. For demonstration of the problem, filtered data will be considered from a purely mathematical point of view by applying a convolution operation to data representing solutions to the Navier-Stokes Equations. Results will be discussed for the subfilter stress, the turbulent scalar flux and the subfilter scalar variance.

Efficient solving algorithm for determining the exact sampling condition of limited-angle computed tomography reconstruction.

Total variation (TV) regularization-based iterative reconstruction algorithms have an impressive potential to solve limited-angle computed tomography with insufficient sampling projections. The analysis of exact reconstruction sampling conditions for a TV-minimization reconstruction model can determine the minimum number of scanning angle and minimize the scanning range. However, the large-scale matrix operations caused by increased testing phantom size are the computation bottleneck in determining the exact reconstruction sampling conditions in practice. When the size of the testing phantom increases to a certain scale, it is very difficult to analyze quantitatively the exact reconstruction sampling condition using existing methods. In this paper, we propose a fast and efficient algorithm to determine the exact reconstruction sampling condition for large phantoms. Specifically, the sampling condition of a TV minimization model is modeled as a convex optimization problem, which is derived from the sufficient and necessary condition of solution uniqueness for the L1 minimization model. An effective alternating direction minimization algorithm is developed to optimize the objective function by alternatively solving two sub-problems split from the convex problem. The Cholesky decomposition method is used in solving the first sub-problem to reduce computational complexity. Experimental results show that the proposed method can efficiently solve the verification problem of the accurate reconstruction sampling condition. Furthermore, we obtain the lower bounds of scanning angle range for the exact reconstruction of a specific phantom with the larger size.

Noise-robust Mojette reconstruction using sparse-view CT projections.

Sparse-view Computed Tomography (CT) has important significance in industrial inspection and medical diagnosis. Mojette transform is a kind of discrete Radon transform that can yield exact reconstructions instead of an approximate solution due to finite Radon sampling. However, the image is iteratively reconstructed pixel by pixel from corner to center, and the image error is proportional to the number of iterations. In this paper, we propose that there exist different sets of projection combinations to recover the original image within the close-to-minimal iterations. And a scheme is given to obtain multiple projection sets, each of which has the same number of minimum iterations and can recover a CT image with a similar level of small noise but different distributions. These images can be used further to restore the final CT image by counteracting noise with each other. The accuracy and validity of the proposed algorithm are verified by comparison with both other Mojette inversion algorithms and the classical SART algorithm.

A practical and effective regularized polynomial smoothing (RPS) method for high-gradient strain field measurement in digital image correlation

Digital image correlation (DIC) is an effective tool for studying the deformation of tested materials. However, high-gradient strain field (HSF) measurement remains a challenging issue in DIC, because multifold factors have a significant effect on the first correlation calculation step of the original displacement and the exact strain reconstruction in the second post-processing step. In this study, we focus on the second step. The formerly proposed local Hermite has been proven as an accurate and robust method, yet substantial programming work is involved in constructing a Hermite element. To solve this issue, a regularized polynomial smoothing (RPS) method is proposed, which replaces the Hermite function of the polynomial. The RPS applies the same kernel function as the point-wise least-squares (PLS) method for easy implementation. Tikhonov regularization and the generalized cross-validation (GCV) function are also used to decrease unavoidable noise and weaken the dependence on window size. The experiments demonstrate that, in the matched/overmatched case, Tikhonov regularization in RPS can greatly decrease the degree of morbidity caused by ill-posed problems in the PLS method, thereby ensuring smoothness and stability of the solution. Moreover, the influences of window size and polynomial order of both the RPS and PLS are also closely studied. In conclusion, the proposed RPS provides a practical, robust and accurate method for HSF measurement.