Existing Reconstruction Methods Research Articles

A novel thermal turbulence reconstruction method using proper orthogonal decomposition and compressed sensing coupled based on improved particle swarm optimization for sensor arrangement

With the development of offshore wind turbine single power toward levels beyond 10 MW, the increase in heat loss of components in the nacelle leads to a high local temperature in the nacelle, which seriously affects the performance of the components. Accurate reconstruction and control of thermal turbulence in the nacelle can alleviate this problem. However, the physical environment of thermal turbulence in the nacelle is very complex. Due to the intermittent and fluctuating nature of turbulence, the turbulent thermal environment is highly nonlinear when coupled with the temperature field. This leads to large reconstruction errors in existing reconstruction methods. Therefore, we improve the sparse reconstruction method for compressed sensing (CS) based on the concept of virtual time using proper orthogonal decomposition (POD). The POD-CS method links the turbulent thermal environment reconstruction with matrix decomposition to ensure computational accuracy and computational efficiency. The improved particle swarm optimization (PSO) is used to optimize the sensor arrangement to ensure stability of the reconstruction and to save sensor resources. We apply this novel and improved PSO-POD-CS coupled reconstruction method to the thermal turbulence reconstruction in the nacelle. The effects of different basis vector dimensions and different sensor location arrangements (boundary and interior) on the reconstruction errors are also evaluated separately, and finally, the desired reconstruction accuracy is obtained. The method is of research value for the reconstruction of conjugate heat transfer problems with high turbulence intensity.

Image fast reconstruction for sparse view computed tomography with reduced sampling integration time

Industrial computed tomography (CT) can detect the internal structure of objects nondestructively. Its scanning and image reconstruction are time-consuming, which limits its application in the fast detection field. In this work, we reduce the sampling integration time in sparse view CT to achieve ultra-fast scanning in only 5 s. However, this ultra-fast scanning method produces more noise and streak artifacts in the reconstructed CT images. The existing reconstruction methods cannot effectively reconstruct high quality CT images under this ultra-fast scanning. To solve this issue, a faster and higher quality CT image reconstruction method is proposed in this paper. We construct a novel objective function using multi-directional TV and adaptive non-local means (ANLM), and design a solution algorithm to solve the objective function. The multi-directional TV-norm takes into account the differences in horizontal, vertical, and 45° directional gradients to obtain more image detail information, while the ANLM-norm focuses on noise suppression. Simulation and practical experiments show that the proposed method can reconstruct higher quality CT images under faster CT scanning strategy, and the peak signal to noise ratio (PSNR) is 1.3 dB higher than the optimal baseline algorithm. On the other hand, our method converges faster and achieves a shorter CT image reconstruction time, which is 47 s shorter than the current popular iterative reconstruction methods. This reconstruction method provides a reliable scheme for faster CT scanning and image reconstruction.

M-NeuS: Volume rendering based surface reconstruction and material estimation

Although significant advances have been made in the field of multi-view 3D reconstruction using implicit neural field-based methods, existing reconstruction methods overlook the estimation of the material information (e.g. the base color, albedo, roughness, and metallic) during the learning process. In this paper, we propose a novel differentiable rendering framework, named as material NueS (M-NeuS), for simultaneously achieving precise surface reconstruction and competitive material estimation. For surface reconstruction, we perform multi-view geometry optimization by proposing an enhanced-low-to-high frequency encoding registration strategy (EFERS) and a second-order interpolated signed distance function (SI-SDF) for precise details and outline reconstruction. For material estimation, inspired by the NeuS, we first propose a volume-rendering-based material estimation strategy (VMES) to estimate the base color, albedo, roughness, and metallic accurately. And then, different from most material estimation methods that need ground-truth geometric priors, we use the geometry information reconstructed in the surface reconstruction stage and the directions of incidence from different viewpoints to model a neural light field, which can extract the lighting information from image observations. Next, the extracted lighting and the estimated base color, albedo, roughness, and metallic are optimized by the physics-based rendering equation. Extensive experiments demonstrate that our M-NeuS can not only reconstruct more precise geometry surface than existing state-of-the-art (SOTA) reconstruction methods but also can estimate competitive material information: the base color, albedo, roughness, and metallic.

CT image reconstruction via industrial CT fast scanning

In automated manufacturing and safety inspection, there is a high demand for fast computed tomography (CT) scanning and image reconstruction. Currently, faster scanning can be achieved by reducing the X-ray exposure time within sparse view CT. The faster scanning strategy introduces significant streak artefacts and noise during the sampling process. Consequently, streak artefacts and noise need to be simultaneously suppressed, which is poses a challenge for existing reconstruction methods. This paper presents a fast iterative reconstruction algorithm that can simultaneously suppress both streak artefacts and noise. This method can not only reconstruct high-fidelity images from rapidly acquired projection data, but also has a faster reconstruction speed than the existing iterative reconstruction algorithms. First, we present a high-order multi-directional total variation (HOM-TV) method that specifically focuses on preserving edge details of the image. Then, we present a fast iterative reconstruction model by incorporating HOM-TV and non-local means into the objective function. Finally, the effectiveness of the presented reconstruction model is validated by simulation and real experiments. The faster scanning method can complete the scan in only 5 seconds, and the structural similarity index (SSIM) of the CT image reconstructed by our method is 0.9755, which is higher than 0.0175 of the Fast Null Space Reconstruction (FNSR) algorithm. The peak signal-to-noise ratio (PSNR) index is 1.656, which is higher than that of the contrast algorithm. In terms of reconstruction time, our algorithm can achieve reconstruction in as little as 36 seconds, outperforming the baseline algorithms.

The Origin and Differentiation of CO2-Rich Primary Melts in Ocean Island Volcanoes: Integrating 3D X-Ray Tomography with Chemical Microanalysis of Olivine-Hosted Melt Inclusions from Pico (Azores).

ABSTRACT Constraining the initial differentiation of primary mantle melts is vital for understanding magmatic systems as a whole. Chemical compositions of olivine-hosted melt inclusions preserve unique information about the mantle sources, crystallisation behaviour and volatile budgets of such melts. Crucially, melt inclusion CO2 contents can be linked to mantle CO2 budgets and inform us on Earth's carbon fluxes and cycles. However, determining total inclusion CO2 contents is not straightforward, as they often need to be reconstructed from CO2 dissolved in melts and CO2 stored in a vapour bubble. Here, we improve upon existing reconstruction methods by combining 3D X-ray computed tomography (CT) with geochemical microanalyses of major, trace and volatile elements. We show that in comparison to CT data, traditional reconstruction methods using 2D photomicrographs can underestimate CO2 budgets by more than 40%. We applied our improved methods to basaltic olivine-hosted melt inclusions from Pico volcano (Azores) in order constrain the formation and differentiation of volatile-rich primary melts in the context of a mantle plume. Results for these inclusions yielded 1935 to 9275 μg/g reconstructed total CO2, some of the highest values reported for ocean island volcanoes to date. Using these CO2 concentrations, we calculate entrapment pressures of 105 to 754 MPa that indicate a magma reservoir comprising stacked sills straddling the crust–mantle boundary. In the magma reservoir, crystallisation of volatile saturated melts drives extensive degassing, leading to fractionated CO2/Ba ratios of 3.5 to 62.2 and a loss of over 79% of primary mantle-derived CO2. Variabilities in trace elements (La, Y) show that differentiation occurred by concurrent mixing and crystallisation of two endmember melts, respectively depleted and enriched in trace elements. Geochemical models show that enriched endmember melts constitute 33 wt % of all melts supplied to the crust at Pico and that primary melts underwent 60% crystallisation prior to eruption. Mantle melting models indicate that the enriched and depleted primary melt endmembers are low- and high-degree melts of carbon-poor lherzolite and carbon-rich pyroxenite, respectively. Moreover, since deep magmas at Pico island are dominantly pyroxenite derived, their CO2-enrichement is mainly controlled by mantle source carbon content. Overall, our study illustrates that by combining 3D imaging, geochemical microanalyses and numerical modelling, melt inclusions provide a unique record of differentiation and storage of deep magmas, as well as mantle melting.

Motion-aware Dynamic Graph Neural Network for Video Compressive Sensing.

Video snapshot compressive imaging (SCI) utilizes a 2D detector to capture sequential video frames and compress them into a single measurement. Various reconstruction methods have been developed to recover the high-speed video frames from the snapshot measurement. However, most existing reconstruction methods are incapable of efficiently capturing long-range spatial and temporal dependencies, which are critical for video processing. In this paper, we propose a flexible and robust approach based on the graph neural network (GNN) to efficiently model non-local interactions between pixels in space and time regardless of the distance. Specifically, we develop a motion-aware dynamic GNN for better video representation, i.e., represent each node as the aggregation of relative neighbors under the guidance of frame-by-frame motions, which consists of motion-aware dynamic sampling, cross-scale node sampling, global knowledge integration, and graph aggregation. Extensive results on both simulation and real data demonstrate both the effectiveness and efficiency of the proposed approach, and the visualization illustrates the intrinsic dynamic sampling operations of our proposed model for boosting the video SCI reconstruction results. The code and model will be released.

Frequency-Enhanced Geometric-Constrained Reconstruction for Localizing Myocardial Infarction in 12-Lead Electrocardiograms.

Determining the location of myocardial infarction is crucial for clinical management and therapeutic stratagem. However, existing diagnostic tools either sacrifice ease of use or are limited by their spatial resolution. Addressing this, we aim to refine myocardial infarction localization via surface potential reconstruction of the ventricles in 12-lead electrocardiograms (ECG). A notable obstacle is the ill-posed nature of such reconstructions. To overcome this, we introduce the frequency-enhanced geometric-constrained iterative network (FGIN). FGIN begins by mining the latent features from ECG data across both time and frequency domains. Subsequently, it increases the data dimensionality of ECG and captures intricate features using convolutional layers. Finally, FGIN incorporates ventricular geometry as a constraint on surface potential distribution. It allocates variable weights to distinct edges. Experimental validation of FGIN confirms its efficacy over synthetic and clinical datasets. On the synthetic dataset, FGIN outperforms seven existing reconstruction methods, attaining the highest Pearson Correlation Coefficient of 0.8624, the lowest Root Mean Square Error of 0.1548, and the highest Structural Similarity Index Measure of 0.7988. On the clinical public dataset (2007 PhysioNet/Computers in Cardiology Challenge), FGIN achieves better localization results than other approaches, according to the clinical standard 17-segment model, achieving an average Segment Overlap of 87.2%. Clinical trials on 50 patients demonstrate FGIN's effectiveness, showing an average accuracy of 91.6% and an average Segment Overlap of 88.2%.

Attention Network with Outdoor Illumination Variation Prior for Spectral Reconstruction from RGB Images

Hyperspectral images (HSIs) are widely used to identify and characterize objects in scenes of interest, but they are associated with high acquisition costs and low spatial resolutions. With the development of deep learning, HSI reconstruction from low-cost and high-spatial-resolution RGB images has attracted widespread attention. It is an inexpensive way to obtain HSIs via the spectral reconstruction (SR) of RGB data. However, due to a lack of consideration of outdoor solar illumination variation in existing reconstruction methods, the accuracy of outdoor SR remains limited. In this paper, we present an attention neural network based on an adaptive weighted attention network (AWAN), which considers outdoor solar illumination variation by prior illumination information being introduced into the network through a basic 2D block. To verify our network, we conduct experiments on our Variational Illumination Hyperspectral (VIHS) dataset, which is composed of natural HSIs and corresponding RGB and illumination data. The raw HSIs are taken on a portable HS camera, and RGB images are resampled directly from the corresponding HSIs, which are not affected by illumination under CIE-1964 Standard Illuminant. Illumination data are acquired with an outdoor illumination measuring device (IMD). Compared to other methods and the reconstructed results not considering solar illumination variation, our reconstruction results have higher accuracy and perform well in similarity evaluations and classifications using supervised and unsupervised methods.

Prominent expression method for line features in multiview reconstruction

In multi-view reconstruction, mesh models are one of the most important data carriers. However, existing reconstruction methods have not adequately considered the existence of real-world edge features, resulting in insufficient utilization of geometric feature information from images. This leads to issues such as surface distortion and a lack of prominent edge features in the reconstructed mesh models. To address these challenges, this paper proposes a method of line features prominent expression during the multi-view reconstruction process. This algorithm integrates image line features and the mesh model to enhance geometric features. Specifically, in this paper, the line features on the image are first extracted, and the 2D line features are sampled and fitted to synthesize 3D line features by depth map. Then, it clusters the 3D line features and establishes minimum bounding boxes. Finally, the mesh line features are determined based on graph cut methods and are prominently expressed in the mesh model. Experimental validation demonstrates that in terms of the accuracy of line feature expression, the average reprojection pass rate for line features in five datasets reaches 93.7 %. This proves that this method significantly mitigates the issue of unclear edge features on the model surface, greatly improving the visual quality of mesh models while maintaining a high accuracy.

Reconstruction Algorithm for Complex Dexel Models Based on Composite Block Partition

Abstract In machining simulations, dexel models are often used to represent objects to achieve high accuracy and real-time performance. However, this approach leads to the loss of original surface information and topological relationships, thereby affecting the visualization effect of simulations. Furthermore, existing reconstruction methods have the drawbacks of generalization or redundancy. To reconstruct the surface of dexel models efficiently and accurately, this paper proposes an algorithm based on “composite block” partition, which converts the dexel model into a polyhedral model. The algorithm begins by partitioning the entire dexel model within the grids into several composite blocks based on the “Connectivity Principle” and generating their end faces. Subsequently, the transitional zone’s surface is reconstructed based on the connectivity relationships of the boundaries of composite blocks. Finally, an optimization process refines the boundaries to generate smoother side faces at a low computational cost. The paper first validates the algorithm’s reconstruction capability and the effectiveness of edge refinement through the reconstruction of various dexel models with different precision levels. It is observed that edge refinement does not introduce excessive additional computation, doubling the overall efficiency compared to existing algorithms. Furthermore, by changing model volumes and performing separate reconstructions, it’s noted that as the volume increases, the incremental growth in conversion time gradually decreases. This makes the algorithm particularly suitable for reconstructing large-scale complex dexel models. Finally, the application of this algorithm in virtual-real simulation systems and industrial digital twin systems is briefly introduced.

Digital core reconstruction based on discrete element and Markov chain-Monte Carlo methods

The digital core is an essential platform for pore-scale flow simulation in geoenergy exploitation, CO2 storage, and hydrogen storage. However, the existing reconstruction methods, such as the Markov chain-Monte Carlo (MCMC) method, can not obtain the digital core reflecting the influence of complex stress. Moreover, the discrete element method (DEM)-based reconstruction, which can consider the effect of stress, has yet to be reported to consider the actual particle shape. To this end, a hybrid reconstruction method based on DEM and MCMC methods is proposed in this study. Firstly, watershed and level set algorithms are used to segment and extract the contours of rock particles, and clump in PFC2D is used to fill the contours to establish a clump template library. Then, the initial condition (ground condition) digital core slice is established with clump packing based on porosity and particle size distribution. Subsequently, the stress loading simulation is carried out to obtain 2D digital core slices with different stress combinations. Finally, the MCMC method obtains 3D digital cores. This proposed method is used to reconstruct the digital core of Belgian fieldstone with different stresses and effective moduli, and the evolution of pore structure characteristics is analyzed. Results show that the stress compresses the range of the pore radius distribution curve, resulting in the shortening of the throat length distribution; the conductivity of the model is poor. The maximum reduction of porosity and permeability is 6.56% and 24.81%, respectively. The model with a large effective modulus has a stronger resistance to deformation and can protect the pore structure. These results prove that the method proposed can obtain the digital core reflecting the stress effects and provide a reference for accurately describing the in-situ rocks' pore structure and the pore-scale flow simulation.

Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data

Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave surfaces from sparse measurements like radar. Existing reconstruction methods either rely on computationally intensive optimization procedures or simplistic modelling assumptions that compromise the real-time capability or accuracy of the subsequent prediction process. We therefore address these issues by proposing a novel approach for phase-resolved wave surface reconstruction using neural networks based on the U-Net and Fourier neural operator (FNO) architectures. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids, that is generated by the high-order spectral method for wave simulation and a geometric radar modelling approach. The investigation reveals that both models deliver accurate wave reconstruction results and show good generalization for different sea states when trained with spatio-temporal radar data containing multiple historic radar snapshots in each input. Notably, the FNO demonstrates superior performance in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and output in Fourier space.

A New Framework for the Reconstruction of Daily 1 km Land Surface Temperatures from 2000 to 2022

Accurate, seamless, and long-term land surface temperature (LST) data sets are crucial for investigating climate change and agriculture production. However, factors like cloud contamination have led to invalid values in the LST product, which has restricted the application of the LST dataset. Therefore, the reconstruction of LST products is challenging, and it is attracting widespread attention. This study compared the performance of different algorithms (XGBoost, GBDT, RF, POLY, MLR) and different training sets (using only good-quality pixels or using both good-quality and other-quality pixels) in the estimation of missing pixels in the LST data, obtaining a seamless daily 1 km LST dataset of MODIS Terra-day, Aqua-day, Terra-night, and Aqua-night data for Zhejiang Province and its surrounding areas from 2000 to 2022. The results demonstrated that the performance of machine-learning models is significantly better than that of linear models, and among the five models, XGBoost performed the best, with an RMSE of less than 1 °C. The Wilcoxon test between the reconstructed LST and the true LST values revealed that including both good-quality and other-quality pixels for reconstruction resulted in a 33% increase in the number of days with non-significant differences compared with using only good-quality pixels. Moreover, the reconstructed nighttime LST has a lower RMSE compared with the reconstructed daytime LST, and the RMSE of the reconstructed LST on the Terra satellite is lower than the RMSE of the reconstructed LST on the Aqua satellite. The RMSEs for the reconstructed LSTs are 0.50 °C, 0.61 °C, 0.36 °C, and 0.39 °C, corresponding to Terra-day, Aqua-day, Terra-night, and Aqua-night for images with coverage reaching 70%, 0.65 °C, 0.83 °C, 0.49 °C, respectively, and 0.52 °C for images with coverage less than 70%. The accuracy of the reconstructed LSTs using our proposed framework outperforms the existing reconstruction methods. The 1 km daily seamless LST products can be applied in various fields, such as air temperature estimation, climate change, urban heat island, and crop temperature stress monitoring.

MosReformer: Reconstruction and Separation of Multiple Moving Targets for Staggered SAR Imaging

Maritime moving target imaging using synthetic aperture radar (SAR) demands high resolution and wide swath (HRWS). Using the variable pulse repetition interval (PRI), staggered SAR can achieve seamless HRWS imaging. The reconstruction should be performed since the variable PRI causes echo pulse loss and nonuniformly sampled signals in azimuth, both of which result in spectrum aliasing. The existing reconstruction methods are designed for stationary scenes and have achieved impressive results. However, for moving targets, these methods inevitably introduce reconstruction errors. The target motion coupled with non-uniform sampling aggravates the spectral aliasing and degrades the reconstruction performance. This phenomenon becomes more severe, particularly in scenes involving multiple moving targets, since the distinct motion parameter has its unique effect on spectrum aliasing, resulting in the overlapping of various aliasing effects. Consequently, it becomes difficult to reconstruct and separate the echoes of the multiple moving targets with high precision in staggered mode. To this end, motivated by deep learning, this paper proposes a novel Transformer-based algorithm to image multiple moving targets in a staggered SAR system. The reconstruction and the separation of the multiple moving targets are achieved through a proposed network named MosReFormer (Multiple moving target separation and reconstruction Transformer). Adopting a gated single-head Transformer network with convolution-augmented joint self-attention, the proposed MosReFormer network can mitigate the reconstruction errors and separate the signals of multiple moving targets simultaneously. Simulations and experiments on raw data show that the reconstructed and separated results are close to ideal imaging results which are sampled uniformly in azimuth with constant PRI, verifying the feasibility and effectiveness of the proposed algorithm.

Neural Volumetric Reconstruction for Coherent Synthetic Aperture Sonar

Synthetic aperture sonar (SAS) measures a scene from multiple views in order to increase the resolution of reconstructed imagery. Image reconstruction methods for SAS coherently combine measurements to focus acoustic energy onto the scene. However, image formation is typically under-constrained due to a limited number of measurements and bandlimited hardware, which limits the capabilities of existing reconstruction methods. To help meet these challenges, we design an analysis-by-synthesis optimization that leverages recent advances in neural rendering to perform coherent SAS imaging. Our optimization enables us to incorporate physics-based constraints and scene priors into the image formation process. We validate our method on simulation and experimental results captured in both air and water. We demonstrate both quantitatively and qualitatively that our method typically produces superior reconstructions than existing approaches. We share code and data for reproducibility.

Reconstructing cloud-contaminated NDVI images with SAR-Optical fusion using spatio-temporal partitioning and multiple linear regression

Optical satellite imagery is an important Earth observation data source, yet when clouds are present, they provide limited utility for land surface applications. Synthetic Aperture Radar (SAR)-Optical data fusion models predict the missing reflectance values through the correlation between optical images and cloud-insensitive SAR images often using deep learning to train the model. However, most existing SAR-Optical data fusion methods did not incorporate temporal correlation optimally as they were not trained on dense and localized time-series data. Herein, we develop a new SAR-Optical data fusion method that incorporated spatial, temporal, and cross-data-source correlation in the same framework. The method uses spatio-temporal (ST) partitioning and pixel-wise multiple linear regression (MLR) and is named ST-MLR. The parsimonious structure of ST-MLR provides training-efficient model development, enabling the incorporation of full spatio-temporal information for a specific site. ST-MLR was validated with NDVI as the target in seven sites across a wide range of environments and landcovers. Both quantitative and qualitative results demonstrated the potential of ST-MLR to reproduce the target variable accurately with respect to both spatial and temporal dynamics. Although ST-MLR had relatively less accuracy when reconstructing multi-band images than when reconstructing the NDVI, its results were comparable to existing reconstruction methods in this regard. Compared with traditional optical image reconstruction methods and deep learning SAR-Optical fusion methods, ST-MLR is a simple, fast and reasonably accurate model, especially when filling large spatial gaps. ST-MLR is accessible to anyone regardless of compute capability as it can be implemented on Google Earth Engine — a public cloud computing platform. ST-MLR can be used as a benchmark to evaluate the performance of more complicated models such as those based on deep learning. The ST-MLR code is publicly available at https://github.com/yongjingmao/SAR-OPT_fusion_GEE.

Conductivity reconstruction from power density data in limited view

In acousto-electric tomography, the objective is to extract information about the interior electrical conductivity in a physical body from knowledge of the interior power density data generated from prescribed boundary conditions for the governing elliptic partial differential equation. In this note, we consider the problem when the controlled boundary conditions are applied only on a small subset of the full boundary. We demonstrate using the unique continuation principle that the Runge approximation property is valid also for this special case of limited view data. As a consequence, we guarantee the existence of finitely many boundary conditions such that the corresponding solutions locally satisfy a non-vanishing gradient condition. This condition is essential for conductivity reconstruction from power density data. In addition, we adapt an existing reconstruction method intended for the full data situation to our setting. We implement the method numerically and investigate the opportunities and shortcomings when reconstructing from two fixed boundary conditions.

Multi-target reconstruction strategy based on blind source separation of surface measurement signals in FMT.

Fluorescence molecular tomography (FMT) is a promising molecular imaging technique for tumor detection in the early stage. High-precision multi-target reconstructions are necessary for quantitative analysis in practical FMT applications. The existing reconstruction methods perform well in retrieving a single fluorescent target but may fail in reconstructing a multi-target, which remains an obstacle to the wider application of FMT. In this paper, a novel multi-target reconstruction strategy based on blind source separation (BSS) of surface measurement signals was proposed, which transformed the multi-target reconstruction problem into multiple single-target reconstruction problems. Firstly, by multiple points excitation, multiple groups of superimposed measurement signals conforming to the conditions of BSS were constructed. Secondly, an efficient nonnegative least-correlated component analysis with iterative volume maximization (nLCA-IVM) algorithm was applied to construct the separation matrix, and the superimposed measurement signals were separated into the measurements of each target. Thirdly, the least squares fitting method was combined with BSS to determine the number of fluorophores indirectly. Lastly, each target was reconstructed based on the extracted surface measurement signals. Numerical simulations and in vivo experiments proved that it has the ability of multi-target resolution for FMT. The encouraging results demonstrate the significant effectiveness and potential of our method for practical FMT applications.

Quantitative image reconstruction for microscopy with correct sub-pixel photon statistics.

The diffraction of light forces a lower limit on spatial resolution available with conventional optical microscopes. However, sophisticated computational techniques in conjunction with inhomogeneous illumination have facilitated image acquisition without this limitation. Typical image reconstruction algorithms for such superresolution microscopy techniques, including structured illumination microscopy (SIM), involve combining multiple diffraction-limited raw images in Fourier space via minimization of some cost function. This leads to undesired artifacts including loss of correct noise properties for the photons collected by the camera and loss of temporal resolution. Here, we propose a Bayesian framework performing reconstructions in real space while incorporating all sources of noise such as camera electronics and incoming photon Poisson statistics. Furthermore, this framework inherently allows corrections for inhomogeneous illumination incident on a biological sample. As a result, superresolution reconstructions can now be performed with fewer images otherwise needed by existing reconstruction methods while maintaining Poisson statistics for collected photons at the sub-pixel level. We benchmark our framework using both simulated and experimentally generated images.

Reconstructing 2-D Gas Temperature Distribution With Deep Neural Networks

Acoustic tomography (AT) is considered a promising visualization technique for gas temperature distribution (TD). Generally, a temperature map of a region of interest (ROI) is reconstructed with acoustic velocities of multiple routes inside the ROI using an AT reconstruction algorithm. To improve the accuracy of the reconstruction, increasing the number of iterations is inevitable, which may be time-consuming. Besides, existing reconstruction algorithms rarely consider utilizing practical measurements to improve their performance. In this study, a convolutional neural network (CNN) is proposed to train a machine-learning model that can reconstruct a gas TD from acoustic velocities. By adjusting the label and the loss function, a practical training approach was found. Six models were successfully trained to reconstruct a gas TD. Two were trained with the ideal TD, three were trained with a reconstructed TD, and one was trained with temperatures from specific locations. After that, a TD with peak temperatures located in 13 different positions was applied to test the models’ performance in tracking the hot spot. The results were compared with an existing reconstruction method. Besides, the acoustic velocities from three gas TDs were applied to evaluate the 2-D visualization performance. One of them was similar to the training data and the other two were different. The results indicated that the models trained with the ideal gas TD could track the hot spot more closely, and the models trained with reconstructed gas TDs had similar performance as the selected reconstruction algorithm. However, the 2-D visualization results using models trained with the ideal gas TD were poor compared with models trained with reconstructed TDs when the input acoustic velocities were different from the training data. This indicated that the proposed method could successfully learn the relationship between TD and acoustic velocities from an ordinary reconstruction algorithm. Furthermore, the execution time of the proposed model was 0.109 s, which is 96% less than the selected iterative reconstruction method. Consequently, the proposed neural networks should be considered a reliable and efficient 2-D gas TD reconstruction methodology.