Ptychographic image reconstruction with a phase-assisted alternating direction method of multipliers.

In this paper, a unified framework of iterative algebraic reconstruction for emission computed tomography (ECT) and its application to positron emission tomography (PET) is presented. The unified framework is based on an algebraic image restoration model and contains conventional iterative algebraic reconstruction algorithms: ART, SIRT, Landweber iteration (LWB), the generalized Landweber iteration (GLWB), the steepest descent method (STP), as well as iterative filtered backprojection (IFBP) reconstruction algorithms: Chang's method, Walters' method, and a modified iterative MAP. The framework provides an effective tool to systematically study conventional iterative algebraic algorithms and IFBP algorithms. Based on this framework, conventional iterative algebraic algorithms and IFBP algorithms are generalized. It is shown from the algebraic point of view that IFBP algorithms are not only excellent methods for correction of attenuation (either uniform or nonuniform) but are also good general iterative reconstruction algorithms (they can be applied to either attenuated or attenuation-free projections and converge very fast). The convergence behavior of iterative algebraic algorithms is discussed and insight is drawn into the fast convergence property of IFBP algorithms. A simulated PET system is used to evaluate IFBP algorithms and LWB in comparison with the maximum likelihood estimation via expectation maximization algorithm (MLE-EM) and the filtered backprojection (FBP) algorithm. The simulation results indicate that for both attenuation-free projection and attenuated projection cases IFBP algorithms have a significant computational advantage over LWB and MLE-EM, and have performance advantages over FBP in terms of contrast recovery and/or noise-to-signal ratios (NSRs) in regions of interest.

Iterative reconstruction algorithm based on finite element (FE) modeling is a powerful approach in photoacoustic tomography (PAT). However, an iterative inverse algorithm using conventional FE meshing of the entire imaging zone is computationally demanding, which hinders this powerful tool in applications where quick image acquisition and/or a large image matrix is needed. To address this challenge, parallel computing techniques are proposed and implemented in the field. Here, we present an alternative approach for 2D PAT, which locoregionally reconstructs the region of interest (ROI) instead of the full imaging zone. Our simulated and phantom experimental results demonstrate that this ROI reconstruction algorithm can produce almost the same image quality as the conventional full zone-based reconstruction algorithm; however, the computation time can be significantly reduced without any additional hardware cost by more than two orders of magnitude (100-fold). This algorithm is further applied and validated in an in vivo study. The major vessel structures in a rat’s brain can be imaged clearly using our ROI-based approach, coupled with a mesh of 11,801 nodes. This novel algorithm can also be parallelized using MPI or GPU acceleration techniques to further enhance the reconstruction performance of FE-based PAT.

A new reconstruction algorithm is introduced to obtain a high quality computerized tomography image from limited information. There are many practical cases in which only limited projection data can be collected due to the physical constraints of the hardware system and the object structure. In these cases, conventional reconstruction algorithms which require complete projections are often unacceptable because it causes severe streak artifacts and distortions. So image reconstruction from limited information is very important and many authors have contributed to it. But the methods presented are often time consuming, less efficient and some algorithm's convergency cannot be guaranteed. For iterative algorithms, it is more important to guarantee the convergency and accelerate the convergency speed. In this paper, a CT image reconstruction method which exploits the Helgason-Ludwig consistency condition is designed to consider obtainable information content about object and reconstruction error in the situation of a finite number of projections. Based on the consideration, we developed a new iterative algorithm which can reconstruct high quality artifactless CT image from limited information, and we design a new histogram constraint obtained from a priori knowledge to guarantee the convergency and to acquire high convergency speed. The results of simulated tests show the great advantages of this new method.

In digital holography, holograms are recorded by a CCD-array, and the complex amplitude of the object wave is numerically reconstructed via computer. For different recording conditions and different properties of objects, different reconstruction algorithms are required. The conventional reconstruction algorithms were conceived directly by replacing the diffraction integral with summation. Each method has its limitation in the valid range for correctly calculating the diffraction integral. The Single Fourier Transform method is valid for far Fresnel zone hologram, whereas the convolution method is appropriate for near Fresnel holograms. Here, we present a general reconstruction model from the perspective of “Generalized sampling theory”. Given that the function space in which the unknown complex amplitude lies, an approximation of the continuous complex amplitude at the CCD can be synthesized from a set of basis functions with the recorded samples as weights. Back-propagation of the approximated complex amplitude to the original object plane yields an expression relating the continuous complex amplitude of the object with the recorded samples. By adopting different basis functions and different formulas for describing the diffraction process, an optimal reconstruction algorithm can be developed for various recording conditions and different diffraction characteristics of the object. Contrary to the conventional algorithms where values are available only at specific grid, complex amplitude at any position of the object can be obtained using this model. In addition, the effect due to the non-zero fill factor of the CCD can also be incorporated into the reconstruction algorithm to be further compensated by over-weighting the high frequency components. Two basis functions: Dirac delta- and Sinc-, are studied in detail.

The present full-angle, free-space fluorescence molecular tomography (FMT) system uses a step-by-step strategy to acquire measurements, which consumes time for both the rotation of the object and the integration of the charge-coupled device (CCD) camera. Completing the integration during the rotation is a more time-efficient strategy called synchronous data acquisition. However, the positions of sources and detectors in this strategy are not stationary, which is not taken into account in the conventional reconstruction algorithm. In this paper we propose a reconstruction algorithm based on the finite element method (FEM) to overcome this problem. Phantom experiments were carried out to validate the performance of the algorithm. The results show that, compared with the conventional reconstruction algorithm used in the step-by-step data acquisition strategy, the proposed algorithm can reconstruct images with more accurate location data and lower relative errors when used with the synchronous data acquisition strategy.

To characterize the noise and spatial resolution properties of a commercially available deep learning-based computed tomography (CT) reconstruction algorithm. Two phantom experiments were performed. The first used a multisized image quality phantom (Mercury v3.0, Duke University) imaged at five radiation dose levels (CTDIvol : 0.9, 1.2, 3.6, 7.0, and 22.3mGy) with a fixed tube current technique on a commercial CT scanner (GE Revolution CT). Images were reconstructed with conventional (FBP), iterative (GE ASiR-V), and deep learning-based (GE True Fidelity) reconstruction algorithms. Noise power spectrum (NPS), high-contrast (air-polyethylene interface), and intermediate-contrast (water-polyethylene interface) task transfer functions (TTF) were measured for each dose level and phantom size and summarized in terms of average noise frequency (fav ) and frequency at which the TTF was reduced to 50% (f50% ), respectively. The second experiment used a custom phantom with low-contrast rods and lung texture sections for the assessment of low-contrast TTF and noise spatial distribution. The phantom was imaged at five dose levels (CTDIvol : 1.0, 2.1, 3.0, 6.0, and 10.0mGy) with 20 repeated scans at each dose, and images reconstructed with the same reconstruction algorithms. The local noise stationarity was assessed by generating spatial noise maps from the ensemble of repeated images and computing a noise inhomogeneity index, , following AAPM TG233 methods. All measurements were compared among the algorithms. Compared to FBP, noise magnitude was reduced on average (± one standard deviation) by 74±6% and 68±4% for ASiR-V (at "100%" setting) and True Fidelity (at "High" setting), respectively. The noise texture from ASiR-V had substantially lower noise frequency content with 55±4% lower NPS fav compared to FBP while True Fidelity had only marginally different noise frequency content with 9±5% lower NPS fav compared to FBP. Both ASiR-V and True Fidelity demonstrated locally nonstationary noise in a lung texture background at all radiation dose levels, with higher noise near high-contrast edges of vessels and lower noise in uniform regions. At the 1.0mGy dose level values were 314% and 271% higher in ASiR-V and True Fidelity compared to FBP, respectively. High-contrast spatial resolution was similar between all algorithms for all dose levels and phantom sizes (<3% difference in TTF f50% ). Compared to FBP, low-contrast spatial resolution was lower for ASiR-V and True Fidelity with a reduction of TTF f50% of up to 42% and 36%, respectively. The deep learning-based CT reconstruction demonstrated a strong noise magnitude reduction compared to FBP while maintaining similar noise texture and high-contrast spatial resolution. However, the algorithm resulted in images with a locally nonstationary noise in lung textured backgrounds and had somewhat degraded low-contrast spatial resolution similar to what has been observed in currently available iterative reconstruction techniques.

To explore the application value of the reconstruction algorithm based on an iterative algorithm in the analysis of CT image and analyze the therapeutic effect of honey-fried Herba Ephedrae combined with Western medicine on acute exacerbation chronic obstructive pulmonary disease (AECOPD), a total of 96 AECOPD patients admitted to our hospital from January 2018 to December 2019 were selected as research subjects. According to a different treatment method, the subjects were divided into a control group (Ctrl group, conventional therapy) and an observation group (OG, conventional therapy + honey-fried Herba Ephedrae), with 48 in each group. The CT image algorithm was established based on the iterative algorithm, and the CT dose indexes of the reconstruction algorithm and the Filtered Back Projection (FBP) algorithm under the same conditions were compared ( P &lt; 0.05 ). After using CT to confirm the diagnosis of the subjects, the difference in indicators of forced expiratory volume in one second (FEV1), forced expiratory volume in one second to forced vital capacity ratio (FEV1%), and forced vital capacity (FVC), inflammatory factors of serum interleukin-8 (IL-8), serum interleukin-10 (IL-10), and tumor necrosis factor (TNF-α), the bronchial wall area, and the total treatment efficiency before and after different treatment was analyzed. The results suggested that the Computed Tomography Dose Index (CTDI) of iterative reconstruction (IR) algorithm when scanning different parts was higher than that of the FBP algorithm. The pulmonary function indexes and the expression of IL-8 and TNF-α in the OG were higher than those in the Ctrl group ( P &lt; 0.05 ); the bronchial wall area, bronchial wall area percentage, and IL-10 expression in the OG were all lower than those in the Ctrl group ( P &lt; 0.05 ). The effectiveness and improvement rates of the Ctrl group were 47.92% and 25%, respectively, significantly lower than those in the OG group, 56.25% and 31.25% ( P &lt; 0.05 ), and the total efficiency of the observation group was 87.5%, which was significantly higher than that in the Ctrl group (72.92%) ( P &lt; 0.05 ). In conclusion, based on the iterative algorithm, a CT reconstruction algorithm with better noise reduction performance was established, and the use of honey-fried Herba Ephedrae combined with Western medicine can improve the effective rate of treatment.

Imaging plays a vital role in radiation therapy and with recent advances in technology considerable emphasis has been placed on cone-beam CT (CBCT). Attaching a kV x-ray source and a flat panel detector directly to the linear accelerator gantry has enabled progress in target localization techniques, which can include daily CBCT setup scans for some treatments. However, with an increasing number of CT scans there is also an increasing concern for patient exposure. An intensity-weighted region-of-interest (IWROI) technique, which has the potential to greatly reduce CBCT dose, in conjunction with the chord-based backprojection-filtration (BPF) reconstruction algorithm, has been developed and its feasibility in clinical use is demonstrated in this article. A nonuniform filter is placed in the x-ray beam to create regions of two different beam intensities. In this manner, regions outside the target area can be given a reduced dose but still visualized with a lower contrast to noise ratio. Image artifacts due to transverse data truncation, which would have occurred in conventional reconstruction algorithms, are avoided and image noise levels of the low- and high-intensity regions are well controlled by use of the chord-based BPF reconstruction algorithm. The proposed IWROI technique can play an important role in image-guided radiation therapy.

Effects of reconstruction technique on the quality of abdominal CT angiography: A comparison between forward projected model-based iterative reconstruction solution (FIRST) and conventional reconstruction methods

Tomography is a powerful technique to obtain accurate images of the interior of an object in a nondestructive way. Conventional reconstruction algorithms, such as filtered backprojection, require many projections to obtain high quality reconstructions. If the object of interest is known in advance to consist of only a few different materials, corresponding to known image intensities, the use of this prior knowledge in the reconstruction procedure can dramatically reduce the number of required projections. In previous work we proposed a network flow algorithm for reconstructing a binary image defined on a lattice from its projections. In this paper we propose a new algorithm for the reconstruction of binary images that do not have an intrinsic lattice structure and are defined on a continuous domain, from a small number of their projections. Our algorithm relies on the fact that the problem of reconstructing an image from only two projections can be formulated as a network flow problem in a graph. We derive this formulation for parallel beam and fan beam tomography and show how it can be used to compute binary reconstructions from more than two projections. Our algorithm is capable of computing high quality reconstructions from very few projections. We evaluate its performance on both simulated and real experimental projection data and compare it to other reconstruction algorithms.

The spectrally constrained diffuse optical tomography (DOT) method relies on incorporating spectral prior information directly into the image reconstruction algorithm, thereby correlating the underlying optical properties across multiple wavelengths. Although this method has been shown to provide a solution that is stable, the use of conventional Tikhonov-type regularization techniques can lead to additional crosstalk between parameters, particularly in linear, single-step dynamic imaging applications. This is due mainly to the suboptimal regularization of the spectral Jacobian matrix, which smoothes not only the image-data space, but also the spectral mapping space. In this work a novel regularization technique based on the singular value decomposition (SVD) is presented that preserves the spectral prior information while regularizing the Jacobian matrix, leading to dramatically reduced crosstalk between the recovered parameters. Using simulated data, images of changes in oxygenated and deoxygenated hemoglobin concentrations are reconstructed via the SVD-based approach and compared with images reconstructed by using non-spectral and conventional spectral methods. In a 2D, two wavelength example, it is shown that the proposed approach provides a 98% reduction in crosstalk between recovered parameters as compared with conventional spectral reconstruction algorithms, and 60% as compared with non-spectrally constrained algorithms. Using a subject specific multilayered model of the human head, a noiseless dynamic simulation of cortical activation is performed to further demonstrate such improvement in crosstalk. However, with the addition of realistic noise in the data, both non-spectral and proposed algorithms perform similarly, indicating that the use of spectrally constrained reconstruction algorithms in dynamic DOT may be limited by the contrast of the signal as well as the noise characteristics of the system.

Tunable diode laser absorption tomography (TDLAT) is a well-established method for combustion diagnostics. However, conventional linear reconstruction algorithms tend to yield unsatisfactory results in scenarios where optical access is severely restricted. Although nonlinear tomography combined with line-of-sight measurements can fully exploit the nonlinear relationship between the reconstructed target field and the projection data to image temperature distributions, its high computational cost restricts its practical application. The advent of deep learning technology has provided a new avenue for addressing this challenge. Neural network algorithms can effectively establish a mapping relationship between the projection data and the reconstructed target field, enabling fast and accurate reconstruction. Leveraging this progress, this paper proposes a novel temperature field reconstruction algorithm based on a deep learning framework. This approach offers a new solution to the nonlinear laminar problem associated with two-dimensional temperature field reconstruction in laser absorption spectroscopy. The results demonstrate that the reconstruction quality of the temperature field steadily improves with an increasing number of projection angles (N). When N = 16, the average error of the reconstructed temperature field is only 1.38%, and the peak signal-to-noise ratio (PSNR) reaches 40.69. Moreover, the algorithm maintains robust reconstruction performance even with fewer projection angles. Compared to existing popular neural network reconstruction algorithms, the proposed approach demonstrates superior noise immunity, making it particularly well-suited for real-time monitoring of actual combustion environments.

Automatic correction of nonlinear damping effects in HAADF–STEM tomography for nanomaterials of discrete compositions

The paper describes the basic principles of an artificial neuron, the multilayer perceptron network and the back-propagation training algorithm, applied to electrical capacitance tomography systems for real-time, noninvasive imaging and measurement of multicomponent flows. Particular attention is given to the problems of distortion of the field ('soft field' error) and limitations on spatial resolution (imposed by the number of electrodes) in conventional image reconstruction algorithms for current systems. In addressing these issues, for the first time, an artificial neural network is employed to replace conventional image reconstruction algorithms. The system consists of a simulation program for a single layer multiple output network, using a variant of the back-propagation training algorithm with the principle of pattern association. The input vector consists of preprocessed capacitance measurements, and the output of the network directly corresponds to the spatial image. Two similar networks are trained for gas/oil flow (small difference in permittivity) and water/oil flow (large difference in permittivity) with results compared.

X-ray free-electron lasers (XFELs) provide high-brilliance pulses, which offer unique opportunities for coherent X-ray imaging techniques, such as in-line holography. One of the fundamental steps to process in-line holographic data is flat-field correction, which mitigates imaging artifacts and, in turn, enables phase reconstructions. However, conventional flat-field correction approaches cannot correct single XFEL pulses due to the stochastic nature of the self-amplified spontaneous emission (SASE), the mechanism responsible for the high brilliance of XFELs. Here, we demonstrate on simulated and megahertz imaging data, measured at the European XFEL, the possibility of overcoming such a limitation by using two different methods based on principal component analysis and deep learning. These methods retrieve flat-field corrected images from individual frames by separating the sample and flat-field signal contributions; thus, enabling advanced phase-retrieval reconstructions. We anticipate that the proposed methods can be implemented in a real-time processing pipeline, which will enable online data analysis and phase reconstructions of coherent full-field imaging techniques such as in-line holography at XFELs.