Systematic approach for the design of reconstruction algorithm in digital holography

OA158] Noise equivalent number of quanta (NEQ): A tool for choosing the optimal reconstruction algorithm in computed tomography (CT)

The goal of this study was to suggest criteria for the determination of the optimal image reconstruction algorithm for image-based dosimetry of Cu-64 trastuzumab PET in a mouse model. Image qualities, such as recovery coefficient (RC), spill-over ratio (SOR), and non-uniformity (NU), were measured according to National Electrical Manufacturers Association (NEMA) NU4-2008. Mice bearing a subcutaneous tumor (, HER2 NCI N87) were injected with monoclonal antibodies (trastuzumab) with Cu-64. Preclinical mouse PET images were acquired at 4 time points after injection (2, 15, 40 and 64 h). Phantom and Cu-64 trastuzumab PET images were reconstructed using various reconstruction algorithms (filtered back projection (FBP), 3D reprojection algorithm (FBP-3DRP), 2D ordered subset expectation maximization (OSEM 2D), and OSEM 3D maximum a posteriori (OSEM3D-MAP)) and filters. The absorbed dose for the tumor and the effective dose for organs for Cu-64 trastuzumab PET were calculated using the OLINDA/EXM program with various reconstruction algorithms. Absorbed dose for the tumor ranged from 923 mGy/MBq to 1830 mGy/MBq with application of reconstruction algorithms and filters. When OSEM2D was used, the effective osteogenic dose increased from 0.0031 to 0.0245 with an increase in the iteration number (1 to 10). In the region of kidney, the effective dose increased from 0.1870 to 1.4100 when OSEM2D was used with iteration number 1 to 10. To determine the optimal reconstruction algorithms and filters, a correlation between RC and NU was plotted and selection criteria (0.9 < RC < 1.0 and < 10% of NU) were suggested. According to the selection criteria, OSEM2D (iteration 1) was chosen for the optimal reconstruction algorithm. OSEM2D (iteration 10) provided 154.7% overestimated effective dose and FBP with a Butterworth filter provided 20.9% underestimated effective dose. We suggested OSEM2D (iteration 1) for the calculation of the effective dose of Cu-64 trastuzumab on an Inveon PET scanner.

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.

In this thesis, we describe new approaches and methods for reconstructing complex-valued wave fields from digital holograms. We focus on Fresnel holograms recorded in an off-axis geometry, for which operational real-time acquisition setups readily exist. The three main research directions presented are the following. First, we derive the necessary tools to port methods and concepts of wavelet-based approaches to the field of digital holography. This is motivated by the flexibility, the robustness, and the unifying view that such multiresolution procedures have brought to many applications in image processing. In particular, we put emphasis on space-frequency processing and sparse signal representations. Second, we propose to decouple the demodulation from the propagation problem, which are both inherent to digital Fresnel holography. To this end, we derive a method for retrieving the amplitude and phase of the object wave through a local analysis of the hologram's interference fringes. Third, since digital holography reconstruction algorithms involve a number of parametric models, we propose automatic adjustment methods of the corresponding parameters. We start by investigating the Fresnel transform, which plays a central role in both the modeling of the acquisition procedure and the reconstruction of complex wave fields. The study of the properties that are central to wavelet and multiresolution analysis leads us to derive Fresnelets, a new family of wavelet-like bases. Fresnelets permit the analysis of holograms with a good localization in space and frequency, in a way similar to wavelets for images. Since the relevant information in a Fresnel off-axis hologram may be separated both in space and frequency, we propose an approach for selectively retrieving the information in the Fresnelet domain. We show that in certain situations, this approach is superior to others that exclusively rely on the separation in space or frequency. We then derive a least-squares method for the estimation of the object wave's amplitude and phase. The approach, which is reminiscent of phase-shifting techniques, is sufficiently general to be applied in a wide variety of situations, including those dictated by the use of microscopy objectives. Since it is difficult to determine the reconstruction distance manually, we propose an automatic procedure. We take advantage of our separate treatment of the phase retrieval and propagation problems to come up with an algorithm that maximizes a sharpness metric related to the sparsity of the signal's expansion in distance-dependent Fresnelet bases. Based on a simulation study, we suggest a number of guidelines for deciding which algorithm to apply to a given problem. We compare existing and the newly proposed solutions in a wide variety of situations. Our final conclusion is that the proposed methods result in flexible algorithms that are competitive with preexisting ones and superior to them in many cases. Overall, they may be applied in a wide range of experimental situations at a low computational cost.

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.

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.

A color digital Fresnel hologram has been recorded those complex amplitudes can be measured by six-step phase-shifting interferometry with the wavelength shifts of R, G and B tunable lasers. A six-step calculation is insensitive to the power change in tunable lasers. The wavelengths can be tuned by a current change of a red laser diode (LD), a cavity-length change of a green laser and an angle change in a grating of a Littman-type blue LD. Three monochromatic images are reconstructed from the numerical Fresnel diffraction integral and combined into a full-color image with CIE chromaticity. The experimental result of a full-color image reconstruction based on digital holography is shown.

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.

The aim was to explore the application value of computed tomography (CT) images based on optimized reconstruction algorithm (ORA) in knee osteoarthritis (KOA) and to analyze the rehabilitation effect of exercise therapy combined with celecoxib capsules on KOA. On the basis of iterative reconstruction algorithm, sparse data and compressed sensing (CS) algorithm were introduced in this study for the image reconstruction and were compared with the reconstruction effects of other algorithms. 105 patients with KOA were selected as the subjects investigated, who were treated in the hospital from December 2018 to January 2020. They were divided randomly into group A (exercise therapy), group B (celecoxib capsule therapy), and group C (exercise therapy combined with celecoxib capsules), with 35 patients in each group. All the patients were scanned by CT. Visual analogue score (VAS) method was adopted to compare the pain symptoms of patients in the three groups before and after treatment. The Lysholm knee function score was employed to evaluate the knee function of the patient before and after treatment, and finally the difference in the total effective rate of treatment was compared. The results showed that the reconstruction algorithm in this study had a higher degree of coincidence with the original image, and its root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) were greatly higher than those of filtered back-projection (FBP) algorithm. There was no huge difference between Lysholm score and VAS in patients of the three groups before treatment ( P &gt; 0.05 ). Besides, Lysholm score in all dimensions and its total score after treatment were higher than those of patients in the three groups before treatment ( P &lt; 0.05 ), and those of patients in group C increased extremely in contrast to group A ( P &lt; 0.05 ). VAS after treatment were all lower in patients of the three groups than those before treatment ( P &lt; 0.05 ), and VAS of patients in group C were sharply lower than those of group A ( P &lt; 0.05 ), but the total effective rate of patients in group C was dramatically higher than the rate of group A ( P &lt; 0.05 ). It indicated that an algorithm with short scanning time and good image quality was established based on iterative reconstruction algorithm. Exercise therapy combined with celecoxib capsules could alleviate the pain symptoms and improve the function of knee joint, which was more advantageous than the simple rehabilitation comprehensive therapy. Therefore, it had higher clinical value for the patients with KOA.

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.

Ptychography is a widely used coherent imaging technique across many imaging modalities, especially microscopy. Reconstruction algorithms are important to obtain the final imaging results from a series of captured diffraction patterns. Conventional reconstruction algorithms only regard phase retrieval as an intermediate step in each iteration. The retrieved phase is lost and cannot be used in the following iterations. In this Letter, we introduce an auxiliary variable related to the phase information of the diffraction patterns in the iterative algorithms, which can make the history phase information available for future iterations. Simulation and experimental results show that our algorithm can achieve higher-quality reconstruction results than other commonly used algorithms.

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