Estimation-free spatial-domain image reconstruction of structured illumination microscopy

Structured illumination microscopy(SIM)achieves super-resolution(SR)by modulating the high-frequency information of the sample into the passband of the optical system and subsequent image reconstruction.The traditional Wiener-filtering-based reconstruction algorithm operates in the Fourier domain,it requires prior knowledge of the sinusoidal illumination patterns which makes the time-consuming procedure of parameter estimation to raw datasets necessary,besides,the parameter estimation is sensitive to noise or aberration-induced pattern distortion which leads to reconstruction artifacts.Here,we propose a spatial-domain image reconstruction method that does not require parameter estimation but calculates patterns from raw datasets,and a reconstructed image can be obtained just by calculating the spatial covariance of differential calculated patterns and differential filtered datasets(the notch filtering operation is performed to the raw datasets for attenuating and compensating the optical transfer function(OTF)).Experiments on reconstructing raw datasets including nonbiological,biological,and simulated samples demonstrate that our method has SR capability,high reconstruction speed,and high robustness to aberration and noise.

Triple-path feature transform network for ring-array photoacoustic tomography image reconstruction

Photoacoustic imaging(PAI)is a noninvasive emerging imaging method based on the photoacoustic effect,which provides necessary assistance for medical diagnosis.It has the characteristics of large imaging depth and high contrast.However,limited by the equipment cost and reconstruction time requirements,the existing PAI systems distributed with annular array transducers are difficult to take into account both the image quality and the imaging speed.In this paper,a triple-path feature transform network(TFT-Net)for ring-array photoacoustic tomography is proposed to enhance the imaging quality from limited-view and sparse measurement data.Specifically,the network combines the raw photoacoustic pressure signals and conventional linear reconstruction images as input data,and takes the photoacoustic physical model as a prior information to guide the reconstruction process.In addition,to enhance the ability of extracting signal features,the residual block and squeeze and excitation block are introduced into the TFT-Net.For further efficient reconstruction,the final output of photoacoustic signals uses‘filter-then-upsample’operation with a pixel-shuffle multiplexer and a max out module.Experiment results on simulated and in-vivo data demonstrate that the constructed TFT-Net can restore the target boundary clearly,reduce background noise,and realize fast and high-quality photoacoustic image reconstruction of limited view with sparse sampling.

Artificial Intelligence-Based Image Reconstruction for Computed Tomography: A Survey

Computed tomography has made significant advances since its intro-duction in the early 1970s,where researchers have mainly focused on the quality of image reconstruction in the early stage.However,radiation exposure poses a health risk,prompting the demand of the lowest possible dose when carrying out CT examinations.To acquire high-quality reconstruction images with low dose radiation,CT reconstruction techniques have evolved from conventional reconstruction such as analytical and iterative reconstruction,to reconstruction methods based on artificial intelligence(AI).All these efforts are devoted to con-structing high-quality images using only low doses with fast reconstruction speed.In particular,conventional reconstruction methods usually optimize one aspect,while AI-based reconstruction has finally managed to attain all goals in one shot.However,there are limitations such as the requirements on large datasets,unstable performance,and weak generalizability in AI-based reconstruction methods.This work presents the review and discussion on the classification,the commercial use,the advantages,and the limitations of AI-based image reconstruction methods in CT.

Accelerating SAGE algorithm in PET image reconstruction by rescaled block-iterative method

A new method to accelerate the convergent rate of the space-alternatinggeneralized expectation-maximization (SAGE) algorithm is proposed. The new rescaled block-iterativeSAGE (RBI-SAGE) algorithm combines the RBI algorithm with the SAGE algorithm for PET imagereconstruction. In the new approach, the projection data is partitioned into disjoint blocks; eachiteration step involves only one of these blocks. SAGE updates the parameters sequentially in eachblock. In experiments, the RBI-SAGE algorithm and classical SAGE algorithm are compared in theapplication on positron emission tomography (PET) image reconstruction. Simulation results show thatRBI-SAGE has better performance than SAGE in both convergence and image quality.

Investigation of prior image constrained compressed sensing-based spectral X-ray CT image reconstruction

To improve spectral X-ray CT reconstructed image quality, the energy-weighted reconstructed image xbins^W and the separable paraboloidal surrogates（SPS） algorithm are proposed for the prior image constrained compressed sensing（PICCS）-based spectral X-ray CT image reconstruction. The PICCS-based image reconstruction takes advantage of the compressed sensing theory, a prior image and an optimization algorithm to improve the image quality of CT reconstructions.To evaluate the performance of the proposed method, three optimization algorithms and three prior images are employed and compared in terms of reconstruction accuracy and noise characteristics of the reconstructed images in each energy bin.The experimental simulation results show that the image xbins^W is the best as the prior image in general with respect to the three optimization algorithms; and the SPS algorithm offers the best performance for the simulated phantom with respect to the three prior images. Compared with filtered back-projection（FBP）, the PICCS via the SPS algorithm and xbins^W as the prior image can offer the noise reduction in the reconstructed images up to 80. 46%, 82. 51%, 88. 08% in each energy bin,respectively. M eanwhile, the root-mean-squared error in each energy bin is decreased by 15. 02%, 18. 15%, 34. 11% and the correlation coefficient is increased by 9. 98%, 11. 38%,15. 94%, respectively.

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

An algorithm for computed tomography image reconstruction from limited-view projections

With the development of the compressive sensing theory, the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology. This paper develops an iterative algorithm for image reconstruction, which can fit the most cases. This method gives an image reconstruction flow with the difference image vector, which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough. Then the l1-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles. The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data. Moreover, all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.

Image Zernike Moments Shape Feature Evaluation Based on Image Reconstruction

The evaluation approach to the accuracy of the image feature descriptors plays an important role in image feature extraction. We point out that the image shape feature can be described by the Zernike moments set while briefly introducing the basic concept of the Zernike moment. After talking about the image reconstruction technique based on the inverse transformation of Zernike moment, the evaluation approach to the accuracy of the Zernike moments shape feature via the dissimilarity degree and the reconstruction ratio between the original image and the reconstructed image is proposed. The experiment results demonstrate the feasibility of this evaluation approach to image Zernike moments shape feature.

Image reconstruction for cone-beam computed tomography using total p-variation plus Kullback-Leibler data divergence

Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp（0〈p〈1） quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation（TpV）. This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback-Leibler（KL） data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method（ADM） which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections（7 views evenly acquired within 180°）. The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications.

Optimization-based image reconstruction in x-ray computed tomography by sparsity exploitation of local continuity and nonlocal spatial self-similarity

The additional sparse prior of images has been the subject of much research in problems of sparse-view computed tomography（CT） reconstruction. A method employing the image gradient sparsity is often used to reduce the sampling rate and is shown to remove the unwanted artifacts while preserve sharp edges, but may cause blocky or patchy artifacts.To eliminate this drawback, we propose a novel sparsity exploitation-based model for CT image reconstruction. In the presented model, the sparse representation and sparsity exploitation of both gradient and nonlocal gradient are investigated.The new model is shown to offer the potential for better results by introducing a similarity prior information of the image structure. Then, an effective alternating direction minimization algorithm is developed to optimize the objective function with a robust convergence result. Qualitative and quantitative evaluations have been carried out both on the simulation and real data in terms of accuracy and resolution properties. The results indicate that the proposed method can be applied for achieving better image-quality potential with the theoretically expected detailed feature preservation.

Image Reconstruction of Ghost Imaging Based on Improved Generative Adversarial Networks

In this paper, we improve traditional generative adversarial networks (GAN) with reference to residual networks and convolutional neural networks to facilitate the reconstruction of complex objects that cannot be reconstructed by traditional associative imaging methods. Unlike traditional ghost imaging to reconstruct objects from bucket signals, our proposed method can use simple objects (such as EMNIST) as a training set for GAN, and then recognize objects (such as faces) of completely different complexity than the training set. We use traditional ghost imaging and neural network to reconstruct target objects respectively. According to the research results in this paper, the method based on neural network can reconstruct complex objects very well, but the method based on traditional ghost imaging cannot reconstruct complex objects. The research scheme in this paper is of great significance for the reconstruction of complex object-related imaging under low sampling conditions.

A Compton scattering image reconstruction algorithm based on total variation minimization

Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process.The reconstruction problem of Compton scattering imaging is the inverse problem to solve electron densities from nonlinear equations,which is ill-posed.This means the solution exhibits instability and sensitivity to noise or erroneous measurements.Using the theory for reconstruction of sparse images,a reconstruction algorithm based on total variation minimization is proposed.The reconstruction problem is described as an optimization problem with nonlinear data-consistency constraint.The simulated results show that the proposed algorithm could reduce reconstruction error and improve image quality,especially when there are not enough measurements.

Image Reconstruction for Invasive ERT in Vertical Oil Well Logging

An invasive electrical resistance tomographic sensor was proposed for production logging in vertical oil well.The sensor consists of 24 electrodes that are fixed to the logging tool,which can move in the pipeline to acquire data on the conductivity distribution of oil/water mixture flow at different depths.A sensitivity-based algorithm was introduced to reconstruct the cross-sectional images.Analysis on the sensitivity of the sensor to the distribution of oil/water mixture flow was carried out to optimize the position of the imaging cross-section.The imaging results obtained using various boundary conditions at the pipe wall and the logging tool were compared.Eight typical models with various conductivity distributions were created and the measurement data were obtained by solving the forward problem of the sensor system.Image reconstruction was then implemented by using the simulation data for each model.Comparisons between the models and the reconstructed images show that the number and spatial distribution of the oil bubbles can be clearly identified.

Super-resolution image reconstruction based on three-step-training neural networks

A new method of super-resolution image reconstruction is proposed, which uses a three-step-training error backpropagation neural network （BPNN） to realize the super-resolution reconstruction （SRR） of satellite image. The method is based on BPNN. First, three groups learning samples with different resolutions are obtained according to image observation model, and then vector mappings are respectively used to those three group learning samples to speed up the convergence of BPNN, at last, three times consecutive training are carried on the BPNN. Training samples used in each step are of higher resolution than those used in the previous steps, so the increasing weights store a great amount of information for SRR, and network performance and generalization ability are improved greatly. Simulation and generalization tests are carried on the well-trained three-step-training NN respectively, and the reconstruction results with higher resolution images verify the effectiveness and validity of this method.

Method of lateral image reconstruction in structured illumination microscopy with super resolution

The image reconstruction process in super-resolution structured illumination microscopy(SIM)is investigated.The structured pattern is generated by the interference of two Gaussian beams to encode undetectable spectra into detectable region of microscope.After parameters estimation of the structured pattern,the encoded spectra are computationally decoded and recombined in Fourier domain to equivalently increase the cut-off frequency of microscope,resulting in the extension of detectable spectra and a reconstructed image with about two-fold enhanced resolution.Three di®erent methods to estimate the initial phase of structured pattern are compared,verifying the auto-correlation algorithm a®ords the fast,most precise and robust measurement.The artifacts sources and detailed reconstruction°owchart for both linear and nonlinear SIM are also presented.

IMAGE RECONSTRUCTION AND OBJECT CLASSIFICATION IN CT IMAGING SYSTEM

By obtaining a feasible filter function,reconstructed images can be got with linear interpolation and liftered backprojection techniques.Considering the gray and spstial correlation neighbour informations of each pixel,a new supervised classification method is put forward for the reconstructed images,and an experiment with noise image is done,the result shows that the method is feasible and accurate compared with ideal phantoms.

Research on Multi-View Image Reconstruction Technology Based on Auto-Encoding Learning

Traditional three-dimensional(3D)image reconstruction method,which highly dependent on the environment and has poor reconstruction effect,is easy to lead to mismatch and poor real-time performance.The accuracy of feature extraction from multiple images affects the reliability and real-time performance of 3D reconstruction technology.To solve the problem,a multi-view image 3D reconstruction algorithm based on self-encoding convolutional neural network is proposed in this paper.The algorithm first extracts the feature information of multiple two-dimensional(2D)images based on scale and rotation invariance parameters of Scale-invariant feature transform(SIFT)operator.Secondly,self-encoding learning neural network is introduced into the feature refinement process to take full advantage of its feature extraction ability.Then,Fish-Net is used to replace the U-Net structure inside the self-encoding network to improve gradient propagation between U-Net structures,and Generative Adversarial Networks(GAN)loss function is used to replace mean square error(MSE)to better express image features,discarding useless features to obtain effective image features.Finally,an incremental structure from motion(SFM)algorithm is performed to calculate rotation matrix and translation vector of the camera,and the feature points are triangulated to obtain a sparse spatial point cloud,and meshlab software is used to display the results.Simulation experiments show that compared with the traditional method,the image feature extraction method proposed in this paper can significantly improve the rendering effect of 3D point cloud,with an accuracy rate of 92.5%and a reconstruction complete rate of 83.6%.

Multi-channel fast super-resolution image reconstruction based on matrix observation model

A multi-channel fast super-resolution image reconstruction algorithm based on matrix observation model is proposed in the paper,which consists of three steps to avoid the computational complexity: a single image SR reconstruction step,a registration step and a wavelet-based image fusion. This algorithm decomposes two large matrixes to the tensor product of two little matrixes and uses the natural isomorphism between matrix space and vector space to transform cost function based on matrix-vector products model to matrix form. Furthermore,we prove that the regularization part can be transformed to the matrix formed. The conjugate-gradient method is used to solve this new model. Finally,the wavelet fusion is used to integrate all the registered highresolution images obtained from the single image SR reconstruction step. The proposed algorithm reduces the storage requirement and the calculating complexity,and can be applied to large-dimension low-resolution images.

SDOCT IMAGE RECONSTRUCTION BY INTERFEROMETRIC SYNTHETIC APERTURE MICROSCOPY

Spectral domain optical coherence tomography(SDOCT)is a noninvasive,cross-sectional imaging technique that measures depth resolved reflectance of tissue by Fourier transforming the spectral interferogram with the scanning of the reference avoided.Interferometric synthetic aperture microscopy(ISAM)is an optical microscopy computed-imaging technique for measuring the optical properties of biological tissues,which can overcome the compromise between depth of focus and transverse resolution.This paper describes the principle of SDOCT and ISAM,which multiplexes raw acquisitions to provide quantitatively meaningful data with reliable spatially invariant resolution at all depths.A mathematical model for a coherent microscope with a planar scanning geometry and spectral detection was described.The two-dimensional fast Fourier transform(FFT)of spectral data in the transverse directions was calculated.Then the nonuniform ISAM resampling and filtering was implemented to yield the scattering potential within the scalar model.Inverse FFT was used to obtain the ISAM reconstruction.One scatterer,multiple scatterers,and noisy simulations were implemented by use of ISAM to catch spatially invariant resolution.ISAM images were compared to those obtained using standard optical coherence tomography(OCT)methods.The high quality of the results validates the rationality of the founded model and that diffraction limited resolution can be achieved outside the focal plane.

Non-iterative image reconstruction from sparse magnetic resonance imaging radial data without priors

The state-of-the-art approaches for image reconstruction using under-sampled k-space data are compressed sensing based.They are iterative algorithms that optimize objective functions with spatial and/or temporal constraints.This paper proposes a non-iterative algorithm to estimate the un-measured data and then to reconstruct the image with the efficient filtered backprojection algorithm.The feasibility of the proposed method is demonstrated with a patient magnetic resonance imaging study.The proposed method is also compared with the state-of-the-art iterative compressed-sensing image reconstruction method using the total-variation optimization norm.