Practical Reconstruction Algorithm Research Articles

A calibration-informed deep learning model for three-dimensional particle reconstruction of volumetric particle image velocimetry

Accurately reconstructing three-dimensional particle fields is essential in fluid velocity measurement research. This study addresses the limitations of current three-dimensional (3D) particle reconstruction methods, such as computational efficiency, precision at high particle density, and particle morphology issues, by introducing a calibration-informed deep learning model named the calibrated pixel to voxel convolutional neural network (CPV-CNN) for 3D Particle Reconstruction. This innovative neural network framework employs a unique Gaussian attention mechanism that bridges pixels and voxels, enabling the mapping of pixel features from two-dimensional (2D) particle images to 3D voxel features. This approach eliminates the need for an initial particle field for particle reconstruction, while significantly enhancing reconstruction efficiency. Additionally, the neural network incorporates camera calibration parameters and the physical coordinates of the reconstructed domain, thereby improving the model's generalization capability and flexibility. Numerical experiments demonstrate that CPV-CNN delivers superior results in terms of accuracy, generalization, and robustness in 3D particle reconstruction. The reconstructed particles exhibit favorable morphology, without the elongation issues commonly observed with conventional methods. This achievement illustrates a practical particle reconstruction algorithm based on artificial intelligence (AI) techniques and represents an important step toward developing an end-to-end AI-based particle reconstruction method in the future.

Development of a Solvability Map.

From time to time, it is necessary to determine whether there are sufficient measurements for the image reconstruction task especially when a non-standard scanning geometry is used. When the imaging system can be approximately modeled as a system of linear equations, the condition number of the system matrix indicates whether the entire system can be stably solved as a whole. When the system as a whole cannot be stably solved, the Moore-Penrose pseudo inverse matrix can be evaluated through the singular value decomposition (SVD) and then a generalized solution can be obtained. However, these methods are not practical because they require the computer memory to store the whole system matrix, which is often too large to store. Also, we do not know if the generalized solution is good enough for the application in mind. This paper proposes a practical image solvability map, which can be obtained for any practical image reconstruction algorithm. This image solvability map measures the reconstruction errors for each location using a large number of computer-simulated random phantoms. In other words, the map is generated by a Monte Carlo approach.

Identifiability Conditions for Compressive Multichannel Blind Deconvolution

In applications such as multi-receiver radars and ultrasound array systems, the observed signals are often modeled as the convolution of the transmit pulse signal and a set of sparse filters representing the sparse target scenes. A sparse multichannel blind deconvolution (MBD) problem simultaneously identifies the unknown signal and sparse filters, which is in general ill-posed. In this paper, we consider the identifiability problem of sparse-MBD and show that, similar to compressive sensing, it is possible to identify the sparse filters from compressive measurements of the output sequences. Specifically, we consider compressible measurements in the Fourier domain and derive deterministic identifiability conditions. Our main results demonstrate that $L$ -sparse filters can be identified from $\text{2}L^2$ Fourier measurements from two or more coprime channels. We also show that $\text{2}L$ measurements per channel are necessary. The sufficient condition sharpens as the number of channels increases and is asymptotically optimal, i.e., it suffices to acquire on the order of $L$ Fourier samples per channel. We also propose a kernel-based sampling scheme that acquires Fourier measurements from a commensurate number of time-domain samples. The gap between the sufficient and necessary conditions is illustrated through numerical experiments including comparing practical reconstruction algorithms. The proposed compressive MBD results require fewer measurements and fewer channels for identifiability compared to previous results, which aids in building cost-effective receivers.

Predicting Monsoon Intraseasonal Precipitation using a Low-Order Nonlinear Stochastic Model

Abstract The authors assess the predictability of large-scale monsoon intraseasonal oscillations (MISOs) as measured by precipitation. An advanced nonlinear data analysis technique, nonlinear Laplacian spectral analysis (NLSA), is applied to the daily precipitation data, resulting in two spatial modes associated with the MISO. The large-scale MISO patterns are predicted in two steps. First, a physics-constrained low-order nonlinear stochastic model is developed to predict the highly intermittent time series of these two MISO modes. The model involves two observed MISO variables and two hidden variables that characterize the strong intermittency and random oscillations in the MISO time series. It is shown that the precipitation MISO indices can be skillfully predicted from 20 to 50 days in advance. Second, an effective and practical spatiotemporal reconstruction algorithm is designed, which overcomes the fundamental difficulty in most data decomposition techniques with lagged embedding that requires extra information in the future beyond the predicted range of the time series. The predicted spatiotemporal patterns often have comparable skill to the MISO indices. One of the main advantages of the proposed model is that a short (3 year) training period is sufficient to describe the essential characteristics of the MISO and retain skillful predictions. In addition, both model statistics and prediction skill indicate that outgoing longwave radiation is an accurate proxy for precipitation in describing the MISO. Notably, the length of the lagged embedding window used in NLSA is crucial in capturing the main features and assessing the predictability of MISOs.

Block-matching sparsity regularization-based image reconstruction for low-dose computed tomography.

Low-dose computed tomography (CT) imaging has been widely explored because it can reduce the radiation risk to human bodies. This presents challenges in improving the image quality because low radiation dose with reduced tube current and pulse duration introduces severe noise. In this study, we investigate block-matching sparsity regularization (BMSR) and devise an optimization problem for low-dose image reconstruction. The objective function of the program is built by combining the sparse coding of BMSR and analysis error, which is subject to physical data measurement. A practical reconstruction algorithm using hard thresholding and projection-onto-convex-set for fast and stable performance is developed. An efficient scheme for the choices of regularization parameters is analyzed and designed. In the experiments, the proposed method is compared with a conventional edge preservation method and adaptive dictionary-based iterative reconstruction. Experiments with clinical images and real CT data indicate that the obtained results show promising capabilities in noise suppression and edge preservation compared with the competing methods. A block-matching-based reconstruction method for low-dose CT is proposed. Improvements in image quality are verified by quantitative metrics and visual comparisons, thereby indicating the potential of the proposed method for real-life applications.

Performance Analysis and Simulation of Numerical Algorithm for Quadratic Basis Pursuit Problem

Signal reconstruction is an important technique for compressive sensing problem. At present, when the relationship between the measurements and the unknowns is non-linear, the quadratic basis pursuit (QBP) is a practical signal reconstruction algorithm to solve the problem. However, it is computationally demanding. In this paper, a modified QBP method based on alternating direction method of multipliers (ADMM) is proposed. The performance of this algorithm is investigated by numerical analysis. Compared with traditional convex optimization tool, it has smaller computational time.

Sparse Recovery in Magnetic Resonance Imaging With a Markov Random Field Prior.

Recent research in compressed sensing of magnetic resonance imaging (CS-MRI) emphasizes the importance of modeling structured sparsity, either in the acquisition or in the reconstruction stages. Subband coefficients of typical images show certain structural patterns, which can be viewed in terms of fixed groups (like wavelet trees) or statistically (certain configurations are more likely than others). Wavelet tree models have already demonstrated excellent performance in MRI recovery from partial data. However, much less attention has been given in CS-MRI to modeling statistically spatial clustering of subband data, although the potentials of such models have been indicated. In this paper, we propose a practical CS-MRI reconstruction algorithm making use of a Markov random field prior model for spatial clustering of subband coefficients and an efficient optimization approach based on proximal splitting. The results demonstrate an improved reconstruction performance compared with both the standard CS-MRI methods and the recent related methods.

Power-Constrained Sparse Gaussian Linear Dimensionality Reduction Over Noisy Channels

In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single--terminal setup as well as in a multi--terminal setup consisting of orthogonal or coherent multiple access channels (MAC). We adopt the mean square error (MSE) performance criterion for sparse source reconstruction in a system where source-to-sensor channel(s) and sensor-to-decoder communication channel(s) are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE in single-- and multiple--terminal setups. We propose a three-stage sensing matrix optimization scheme that combines semi-definite relaxation (SDR) programming, a low-rank approximation problem and power-rescaling. Under certain conditions, we derive closed-form solutions to the proposed optimization procedure. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the superiority of the proposed scheme by comparing it with other relevant methods. This performance improvement is achieved at the price of higher computational complexity. Hence, in order to address the complexity burden, we present an equivalent stochastic optimization method to the problem of interest that can be solved approximately, while still providing a superior performance over the popular methods.

A practical fan-beam design and reconstruction algorithm for Active and Passive Computed Tomography of radioactive waste barrels

Active and Passive CT (A&PCT) of waste barrels is mostly carried out in parallel beam configuration due to its relative ease of implementation. This necessitates either using a single detector–source pair and translating the barrel or using multiple detector–source pairs for increasing the scanning speed. Additionally, because the use of bulky HPGe detectors may limit the number of detectors used in both active and passive modes, we propose to use 1″×1″ LaBr3(Ce) scintillators. This paper describes a practical fan-beam reconstruction for A&PCT imaging of waste barrels. A fan beam system model has been computed analytically and reconstruction done using MLEM algorithm. The results are compared with analytical reconstruction.

MLEM and OSEM Deviate From the Cramer-Rao Bound at Low Counts

Maximum Likelihood (ML) reconstruction estimators are non biased and achieve the lowest variance, called the Cramer-Rao lower bound (CRLB), in the asymptotic regime, which in positron emission tomography (PET) or in single photon emission tomography (SPECT) corresponds to measuring an infinite number of counts. At finite number of counts or iterations, practical reconstruction algorithms are however biased, and nothing guarantees that the minimum variance expressed by the CRLB is achieved. We study the two dimensional Ordered Subsets Expectation Maximization (2D OSEM) algorithm with a finite number of counts and iterations, and investigate the question: given its bias, does this algorithm achieve the minimum variance predicted by the biased Cramer-Rao lower bound? We found a threshold separating two regimes: an asymptotic regime at large counts, where the variance almost equals the biased CRLB, even for a finite number of iterations and in cold regions, and a low counts regime where the variance significatively exceeds the biased CRLB. We extended our analysis to a realistic image by introducing the neighborhood method that evaluates the Cramer-Rao lower bound by inverting a submatrix of the Fisher matrix. We finally showed, both with a simulation and a theoretical toy example, that MLEM shares with OSEM the existence of a threshold in number of counts. A further analysis is needed to investigate the reason of the difference at low counts, which might indicate that there exists an algorithm with a smaller variance than OSEM for the same bias, or that a higher bound could be found.

On the [formula omitted]-adaptive solution of complete electrode model forward problems of electrical impedance tomography

Electrical impedance tomography is a noninvasive imaging technique based on measurements of currents and voltages on the boundary of the object of interest. The most accurate forward model for impedance tomography is the complete electrode model that takes into account the electrode shapes and the contact impedances at the corresponding interfaces; many practical reconstruction algorithms of electrical impedance tomography require repetitive computation of accurate forward solutions for the complete model. In this work, we introduce an hp-adaptive finite element method for solving the complete electrode forward problem and demonstrate its functionality via two-dimensional numerical studies.

Precise two-dimensional D-bar reconstructions of human chest and phantom tank via sinc-convolution algorithm.

BackgroundElectrical Impedance Tomography (EIT) is used as a fast clinical imaging technique for monitoring the health of the human organs such as lungs, heart, brain and breast. Each practical EIT reconstruction algorithm should be efficient enough in terms of convergence rate, and accuracy. The main objective of this study is to investigate the feasibility of precise empirical conductivity imaging using a sinc-convolution algorithm in D-bar framework.MethodsAt the first step, synthetic and experimental data were used to compute an intermediate object named scattering transform. Next, this object was used in a two-dimensional integral equation which was precisely and rapidly solved via sinc-convolution algorithm to find the square root of the conductivity for each pixel of image. For the purpose of comparison, multigrid and NOSER algorithms were implemented under a similar setting. Quality of reconstructions of synthetic models was tested against GREIT approved quality measures. To validate the simulation results, reconstructions of a phantom chest and a human lung were used.ResultsEvaluation of synthetic reconstructions shows that the quality of sinc-convolution reconstructions is considerably better than that of each of its competitors in terms of amplitude response, position error, ringing, resolution and shape-deformation. In addition, the results confirm near-exponential and linear convergence rates for sinc-convolution and multigrid, respectively. Moreover, the least degree of relative errors and the most degree of truth were found in sinc-convolution reconstructions from experimental phantom data. Reconstructions of clinical lung data show that the related physiological effect is well recovered by sinc-convolution algorithm.ConclusionsParametric evaluation demonstrates the efficiency of sinc-convolution to reconstruct accurate conductivity images from experimental data. Excellent results in phantom and clinical reconstructions using sinc-convolution support parametric assessment results and suggest the sinc-convolution to be used for precise clinical EIT applications.

DART: A Practical Reconstruction Algorithm for Discrete Tomography

In this paper, we present an iterative reconstruction algorithm for discrete tomography, called discrete algebraic reconstruction technique (DART). DART can be applied if the scanned object is known to consist of only a few different compositions, each corresponding to a constant gray value in the reconstruction. Prior knowledge of the gray values for each of the compositions is exploited to steer the current reconstruction towards a reconstruction that contains only these gray values. Based on experiments with both simulated CT data and experimental μCT data, it is shown that DART is capable of computing more accurate reconstructions from a small number of projection images, or from a small angular range, than alternative methods. It is also shown that DART can deal effectively with noisy projection data and that the algorithm is robust with respect to errors in the estimation of the gray values.

Efficient reconstruction method for L1 regularization in fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is a promising technique for in vivo small animal imaging. In this paper, the sparsity of the fluorescent sources is considered as the a priori information and is promoted by incorporating L1 regularization. Then a reconstruction algorithm based on stagewise orthogonal matching pursuit is proposed, which treats the FMT problem as the basis pursuit problem. To evaluate this method, we compare it to the iterated-shrinkage-based algorithm with L1 regularization. Numerical simulations and physical experiments show that the proposed method can obtain comparable or even slightly better results. More importantly, the proposed method was at least 2 orders of magnitude faster in these experiments, which makes it a practical reconstruction algorithm.

Volumetric imaging from a multisegment straight-line trajectory and a practical reconstruction algorithm

A new imaging configuration whose trajectory is a multisegment straight line is investigated, and a practical reconstruction algorithm is proposed. It is a natural extension of an imaging configuration with a straight-line trajectory. These kinds of scanning systems may be useful in industry and security inspections. As is known, projection data from a single straight-line trajectory are incomplete and their reconstruction suffers from a limited-angle problem. A multisegment straight-line trajectory can be used to compensate for this deficiency. To reconstruct images, a practical reconstruction algorithm is derived. It is of the Feldkamp-Davis-Kress (FDK) type, and is efficient and straightforward. Like the FDK algorithm, our reconstruction is exact in the midplane and can be exact everywhere if the density of the scanned object is independent of the direction z, though the integral of the reconstructed image along z is no longer preserved. Numerical simulations validate our method.

Triangulation for points on lines

Triangulation consists in finding a 3D point reprojecting the best as possible onto corresponding image points. It is classical to minimize the reprojection error, which, in the pinhole camera model case, is nonlinear in the 3D point coordinates. We study the triangulation of points lying on a 3D line, which is a typical problem for Structure-From-Motion in man-made environments. We show that the reprojection error can be minimized by finding the real roots of a polynomial in a single variable, which degree depends on the number of images. We use a set of transformations in 3D and in the images to make the degree of this polynomial as low as possible, and derive a practical reconstruction algorithm. Experimental comparisons with an algebraic approximation algorithm and minimization of the reprojection error using Gauss–Newton are reported for simulated and real data. Our algorithm finds the optimal solution with high accuracy in all cases, showing that the polynomial equation is very stable. It only computes the roots corresponding to feasible points, and can thus deal with a very large number of views – triangulation from hundreds of views is performed in a few seconds. Reconstruction accuracy is shown to be greatly improved compared to standard triangulation methods that do not take the line constraint into account.

A generalized sampling theory without band-limiting constraints

We consider the problem of the reconstruction of a continuous-time function f(x)/spl isin/H from the samples of the responses of m linear shift-invariant systems sampled at 1/m the reconstruction rate. We extend Papoulis' generalized sampling theory in two important respects. First, our class of admissible input signals (typ. H=L/sub 2/) is considerably larger than the subspace of band-limited functions. Second, we use a more general specification of the reconstruction subspace V(/spl psi/), so that the output of the system can take the form of a band-limited function, a spline, or a wavelet expansion. Since we have enlarged the class of admissible input functions, we have to give up Shannon and Papoulis' principle of an exact reconstruction. Instead, we seek an approximation f/spl isin/V(/spl psi/) that is consistent in the sense that it produces exactly the same measurements as the input of the system. This leads to a generalization of Papoulis' sampling theorem and a practical reconstruction algorithm that takes the form of a multivariate filter. In particular, we show that the corresponding system acts as a projector from H onto V(/spl psi/). We then propose two complementary polyphase and modulation domain interpretations of our solution. The polyphase representation leads to a simple understanding of our reconstruction algorithm in terms of a perfect reconstruction filter bank. The modulation analysis, on the other hand, is useful in providing the connection with Papoulis' earlier results for the band-limited case. Finally, we illustrate the general applicability of our theory by presenting new examples of interlaced and derivative sampling using splines.

List-mode likelihood.

As photon-counting imaging systems become more complex, there is a trend toward measuring more attributes of each individual event. In various imaging systems the attributes can include several position variables, time variables, and energies. If more than about four attributes are measured for each event, it is not practical to record the data in an image matrix. Instead it is more efficient to use a simple list where every attribute is stored for every event. It is the purpose of this paper to discuss the concept of likelihood for such list-mode data. We present expressions for list-mode likelihood with an arbitrary number of attributes per photon and for both preset counts and preset time. Maximization of this likelihood can lead to a practical reconstruction algorithm with list-mode data, but that aspect is covered in a separate paper [IEEE Trans. Med. Imaging (to be published)]. An expression for lesion detectability for list-mode data is also derived and compared with the corresponding expression for conventional binned data.

On the possibility of using the velocity of recorded signal for tomographic study of excited media

In this paper, by the example of optical and acoustic study of nonlinear crystals, we solve the problem of dynamic reconstruction of the internal structure of an object using a set of linear integrals, which depend parametrically on the time and velocity of integrated signals. Possible practical reconstruction algorithms are discussed. The results of model experiments with one of the above algorithms are given.

Interpolation of lowpass signals at half the Nyquist rate

Describes the interpolation of low-pass signals from a class of stable sampling sets at half the Nyquist rate. Practical reconstruction algorithms are also suggested.