Two-dimensional Image Reconstruction Research Articles

Morphological heterogeneity of neurons in the human central amygdaloid nucleus.

The central amygdaloid nucleus (CeA) has an ancient phylogenetic development and functions relevant for animal survival. Local cells receive intrinsic amygdaloidal information that codes emotional stimuli of fear, integrate them, and send cortical and subcortical output projections that prompt rapid visceral and social behavior responses. We aimed to describe the morphology of the neurons that compose the human CeA (N = 8 adult men). Cells within CeA coronal borders were identified using the thionine staining and were further analyzed using the "single-section" Golgi method followed by open-source software procedures for two-dimensional and three-dimensional image reconstructions. Our results evidenced varied neuronal cell body features, number and thickness of primary shafts, dendritic branching patterns, and density and shape of dendritic spines. Based on these criteria, we propose the existence of 12 morphologically different spiny neurons in the human CeA and discuss the variability in the dendritic architecture within cellular types, including likely interneurons. Some dendritic shafts were long and straight, displayed few collaterals, and had planar radiation within the coronal neuropil volume. Most of the sampled neurons showed a few to moderate density of small stubby/wide spines. Long spines(thin and mushroom) were observed occasionally. These novel data address the synaptic processing and plasticity in the human CeA. Our morphological description can be combined with further transcriptomic, immunohistochemical, and electrophysiological/connectional approaches.It serves also to investigate how neurons are altered in neurological and psychiatric disorders with hindered emotional perception, in anxiety, following atrophy in schizophrenia, and along different stages of Alzheimer's disease.

The Fibre Resolved OpticAl and Near-Ultraviolet Czerny–Turner Imaging Spectropolarimeter (francis)

The solar physics community is entering a golden era that is ripe with next-generation ground- and space-based facilities, advanced spectral inversion techniques, and realistic simulations that are becoming more computationally streamlined and efficient. With ever-increasing resolving power stemming from the newest observational telescopes, it becomes more challenging to obtain (near-)simultaneous measurements at high spatial, temporal and spectral resolutions, while operating at the diffraction limit of these new facilities. Hence, in recent years there has been increased interest in the capabilities integral field units (IFUs) offer towards obtaining the trifecta of high spatial, temporal and spectral resolutions contemporaneously. To date, IFUs developed for solar physics research have focused on mid-optical and infrared measurements. Here, we present an IFU prototype that has been designed for operation within the near-ultraviolet to mid-optical wavelength range, which enables key spectral lines (e.g., Ca ii H/K, Hβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\beta $\\end{document}, Sr ii, Na i D1/D2, etc.) to be studied, hence providing additional spectral coverage to the instrument suites developed to date. The IFU was constructed as a low-budget proof-of-concept for the upcoming 2 m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$2\ ext{ m}$\\end{document} class Indian National Large Solar Telescope and employs circular cross-section fibres to guide light into a Czerny–Turner configuration spectrograph, with the resulting spectra captured using a high quantum efficiency scientific CMOS camera. Mapping of each input fibre allows for the reconstruction of two-dimensional spectral images, with frame rates exceeding 20 s−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$20\ ext{ s}^{-1}$\\end{document} possible while operating in a non-polarimetric configuration. Initial commissioning of the instrument was performed at the Dunn Solar Telescope, USA, during August 2022. The science verification data presented here highlights the suitability of fibre-fed IFUs operating at near-ultraviolet wavelengths for solar physics research. Importantly, the successful demonstration of this type of instrument paves the way for further technological developments to make a future variant suitable for upcoming ground-based and space-borne telescope facilities.

Single-pixel image reconstruction using coherent nonlinear optics.

We propose and experimentally demonstrate a novel, to the best of our knowledge, hybrid optoelectronic system that utilizes mode-selective frequency upconversion, single-pixel detection, and a deep neural network to achieve the reliable reconstruction of two-dimensional (2D) images from a noise-contaminated database of handwritten digits. Our system is designed to maximize the multi-scale structural similarity index measure (MS-SSIM) and minimize the mean absolute error (MAE) during the training process. Through extensive evaluation, we have observed that the reconstructed images exhibit high-quality results, with a peak signal-to-noise ratio (PSNR) reaching approximately 20 dB and a structural similarity index measure (SSIM) of around 0.85. These impressive metrics demonstrate the effectiveness and fidelity of our image reconstruction technique. The versatility of our approach allows its application in various fields, including Lidar, compressive imaging, volumetric reconstruction, and so on.

Abstract 4707: LED photobleaching-based multiplex 3D microscopy of the tumor microenvironment

Abstract Multiplexing in immunofluorescence imaging is important for the spatial profiling of cells and molecules in tumor tissue samples. Cyclic immunofluorescence (IF) methods using oxidants (e.g. hydrogen peroxide) and enzymes (e.g. DNase) localize a great number of cellular makers and proteins in a tissue section while repeating a process of IF staining, imaging, and fluorescence deactivation. However, the repeated use of chemicals and enzymes might cause artifacts in tissue and cell morphologies. Furthermore, these methods are restricted to thin tissue sections (~5 μm thick) which are inappropriate to provide comprehensive structural information on tissue samples. Although reconstruction of two-dimensional (2D) images from serial tissue sections can provide a certain volumetric tissue image, it takes a huge amount of time and effort. Here we introduce a three-dimensional (3D) multiplex IF imaging method using LED photobleaching. We built high-power LED illuminators with 100W warm (emission wavelength: 480-700 nm), green (430-520 nm), and red (600- 680 nm) LED chips, which can efficiently bleach a broad or selected wavelength of fluorescence signals in tissue samples. We integrated this LED photobleaching with the Transparent Tissue Tomography (T3) protocol and created a 3D cyclic IF method involving tissue macrosectioning (400 μm), three-color IF staining, D-fructose-based tissue clearing, 3D confocal fluorescence microscopy, LED photobleaching, tissue washing, and three-color IF staining for other biomarkers, and repeating the process. By applying this method to mouse mammary tumor tissues, we could perform 8-plex fluorescence microscopy for visualizing cell nuclei (DAPI), vascular (CD31, SMA) and structural (ER-TR7) cells, immune cells (CD3, CD8, CD45), and cancer cells (CK8) in the tumor macrosections in 3D at tissue and cellular resolution. To validate the method as an evaluation tool for immunotherapy, we treated the mouse mammary tumor with a STING agonist (DMAXX) intratumorally and collected the tumor tissue 1 day after the treatment, and processed it for the 3D cyclic IF protocol. The quantitative multiplex image data showed immune-driven-cancer eradication and high tumor infiltration of a large number of CD3+CD8+CD45+ cytotoxic T cells. We also examined that Red and Green LED illumination can selectively bleach fluorophores in tissues, which would be useful for patterning fluorescence in tissue as well as studying fluorescent drug-cell interaction in a tissue. In summary, this chemical and enzyme-free 3D cyclic IF imaging method will be a powerful tissue assay tool to provide comprehensive spatial information of tissue (tumor) samples including cell types, cellular and molecular location, and their 3D organization in a tissue sample. Citation Format: Jingtian Zheng, Evan Phillips, Yi-Chien Wu, Steve Seung-Young Lee, Vytautas Bindokas. LED photobleaching-based multiplex 3D microscopy of the tumor microenvironment. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 4707.

Construction of Structured Random Measurement Matrices in Semi-Tensor Product Compressed Sensing Based on Combinatorial Designs.

A random matrix needs large storage space and is difficult to be implemented in hardware, and a deterministic matrix has large reconstruction error. Aiming at these shortcomings, the objective of this paper is to find an effective method to balance these performances. Combining the advantages of the incidence matrix of combinatorial designs and a random matrix, this paper constructs a structured random matrix by the embedding operation of two seed matrices in which one is the incidence matrix of combinatorial designs, and the other is obtained by Gram-Schmidt orthonormalization of the random matrix. Meanwhile, we provide a new model that applies the structured random matrices to semi-tensor product compressed sensing. Finally, compared with the reconstruction effect of several famous matrices, our matrices are more suitable for the reconstruction of one-dimensional signals and two-dimensional images by experimental methods.

The Method of Reconstructing Three-Dimensional Human Posture from Two-Dimensional Images in Film and Television Production.

With the development of computer software and hardware technology, film and television production has made a breakthrough. More and more film and television works have changed from the traditional plane two-dimensional space projection to three-dimensional space projection. Three-dimensional works give the audience an immersive feeling. Taking human posture, one of the most important components in film and television works, as an example, this paper discusses the method of reconstructing three-dimensional human posture from two-dimensional images in film and television production. Starting from the research significance of two-dimensional image reconstruction of three-dimensional human posture in film and television production, the existing three-dimensional human posture in film and television production is analyzed. The audience can watch the film and television works in an all-round way to keep the film and television works fresh to the greatest extent. This paper provides a certain reference value for 3D stereoscopic projection.

Super-resolution reconstruction of digital rock CT images based on residual attention mechanism

Computer tomography technology is widely used in geological exploration because it is a nondestructive and three-dimensional imaging method that can be integrated with computer simulation. However, the large-scale application of the computer tomography technique is limited by economic costs and time consumption. Therefore, it is challenging and intractable to indicate the pore structure characteristics of rock. To address this issue, a super-resolution reconstruction algorithm based on convolutional neural networks, residual learning, and attention mechanism was proposed to generate super-resolution images in this study. This algorithm was applied to the reconstruction of carbonate rock and sandstone. The performance of two-dimensional image reconstruction was evaluated by quantitative extraction and qualitative visualization. The results from experiments indicate that the built model performs well on different upscaling factors and is superior to the existing super-resolution approaches based on convolutional neural network. Cited as: Shan, L., Bai, X., Liu, C., Feng, Y., Liu, Y., Qi, Y. Super-resolution reconstruction of digital rock CT images based on residual attention mechanism. Advances in Geo-Energy Research, 2022, 6(2): 157-168. https://doi.org/10.46690/ager.2022.02.07

Reconstruction of Two-dimensional Image to Three-dimensional Point Cloud Data for Detection of Empty Rot Defects in Tree Growth

In the application of nondestructive detecting of trees, it is a technical problem to use radar waves to detect tree specimens with growth defects, how to segment defect areas after obtaining two-dimensional images, and reverse simulate the detection results with three-dimensional point cloud data. Therefore, the method of extracting boundary information according to color features is studied to extract the boundary curve of empty rot area, and the selection of higher precision extraction algorithm is determined by comparing the boundary extraction results of HSV color space and RGB color space in laboratory According to the extracted void boundary curve, the reverse modeling is carried out, and the mapping from 2D inspection gray image to 3D space is realized, The point cloud data reconstruction needed for 3D modeling of multi-curved surfaces is obtained in reverse. The boundary curve extraction algorithm in this study is used to process the images of nondestructive testing of trees. Through comparative experiments and error analysis, the accurate modeling conclusion from inversion of 2D images to 3D point cloud data reconstruction by radar wave detection is verified, and the Core issue problem of point cloud reconstruction in the ill-conditioned area of tree growth and decay detected by radar wave is solved.

Incomplete PET projection data reconstruction method and simulation experiment

In positron emission tomography (PET) imaging, the whole body reconstruction is not required if the region of interest (ROI) is only a part of the object. This paper researched a local image reconstruction algorithm based on the PI-lines, and proposed the derivative-backprojection-Hilbert (DBH) algorithm which can use the incomplete PET projection data to achieve accurate reconstruction of ROI. We designed simulation experiments to evaluate the performance of the DBH algorithm with thorax model as the object of PET image reconstruction, and compared root mean square error (RMSE) of DBH reconstruction and RMSE of filtered backprojection (FBP) reconstruction from simulations data sets with and without noise. The result shows that DBH algorithm has advantages over traditional FBP algorithm, the RMSE decreases by 49.07% and 51.19% with the coincidence events number of 20 million and 40 million, respectively. Compared with traditional maximum-likelihood expectation-maximization (ML-EM), the local iteration algorithm which uses DBH reconstruction as the initial image produces a better reconstructed image at fewer iterations with the coincidence events number of 60 million. DBH algorithm is expected to be applied to fast two-dimensional local image reconstruction and optimize the local iterative reconstruction algorithm in clinical diagnosis.

Adaptive sparsity level and dictionary size estimation for image reconstruction in accelerated 2D radial cine MRI.

In the past, dictionary learning (DL) and sparse coding (SC) have been proposed for the regularization of image reconstruction problems. The regularization is given by a sparse approximation of all image patches using a learned dictionary, that is, an overcomplete set of basis functions learned from data. Despite its competitiveness, DL and SC require the tuning of two essential hyperparameters: the sparsity level S - the number of basis functions of the dictionary, called atoms, which are used to approximate each patch, and K - the overall number of such atoms in the dictionary. These two hyperparameters usually have to be chosen a priori and are determined by repetitive and computationally expensive experiments. Furthermore, the final reported values vary depending on the specific situation. As a result, the clinical application of the method is limited, as standardized reconstruction protocols have to be used. In this work, we use adaptive DL and propose a novel adaptive sparse coding algorithm for two-dimensional (2D) radial cine MR image reconstruction. Using adaptive DL and adaptive SC, the optimal dictionary size K as well as the optimal sparsity level S are chosen dependent on the considered data. Our three main results are the following: First, adaptive DL and adaptive SC deliver results which are comparable or better than the most widely used nonadaptive version of DL and SC. Second, the time needed for the regularization is accelerated due to the fact that the sparsity level S is never overestimated. Finally, the a priori choice of S and K is no longer needed but is optimally chosen dependent on the data under consideration. Adaptive DL and adaptive SC can highly facilitate the application of DL- and SC-based regularization methods. While in this work we focused on 2D radial cine MR image reconstruction, we expect the method to be applicable to different imaging modalities as well.

Sparse Reconstruction for Microdefect Detection of Two-Dimensional Ultrasound Image Based on Blind Estimation

The sparse reconstruction of two-dimensional (2-D) ultrasound images has proven effective in detecting microdefects in acoustic microimaging (AMI). However, in terms of the acquisition method of a blur kernel for the AMI detection of microdefects, it is difficult for the experimental method to prepare a micrometer-level point source, and the simulation method needs to build different simulation models for different ultrasonic probes. These two methods are troublesome and limit the blur kernel function for sparse reconstruction. This article develops a super-resolution blind estimation algorithm for AMI to generalize the sparse model to different ultrasonic imaging devices and probes. The original blurred image is denoised based on the 2-D sparse representation to perform blur kernel estimation normally. Then, the blur kernel function based on the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> estimation is estimated in the denoised image. We reconstruct the deblurred <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> -scan images of complex defects with the blur kernel function. The results indicate that the sparse reconstruction for the microdefect detection of a 2-D ultrasound image based on the blind estimation is effective for resolution improvement and signal-to-noise ratio enhancement of microdefect detection.

View-driven compressed sensing method of CT image reconstruction

In order to significantly reducing the X-ray dose of CT examination, this study focuses on reconstructing the tomographic images from sparse projection data with sufficient accuracy. Aiming at two-dimensional (2D) image reconstruction of fan-beam projection under circular scanning, this paper proposes the view-driven system model and designs a CT iterative image reconstruction method by combining the iterative algorithm and the compressed sensing theory. The simulation results show that the algorithm has high numerical accuracy, low computational complexity, less memory overhead, and strong engineering practicability under the condition of ultra-sparse projection data (no more than 20 view angles for fan-beam scanning in the range of [0,2π)).

Comparison of stand-alone cage and cage-with-plate for monosegmental cervical fusion and impact of virtual reality in evaluating surgical results

ObjectivesAfter ventral decompression of monosegmental cervical spondylotic stenosis, a stand-alone cage (SC) or cage-with-plate (CP) can be inserted for fusion. Postoperative radiological evaluation can be achieved using different imaging modalities. We retrospectively compared complications, as well as clinical and radiological outcomes for both fusion techniques, and analyzed the possible role of virtual reality (VR) in evaluating the postoperative results. Patients and methodsOne hundred seventeen patients were included (SC/CP: 54/63). Complications, as well as clinical and radiological outcomes of both fusion techniques were compared. Computed tomography (CT) scans were visualized via VR to measure the smallest cross-sectional area of the intervertebral neuroforamen in the lateral resection region, and to assess the degree of the intersegmental ossification. ResultsThere were no significant differences between the two fusion techniques regarding perioperative complication rates, fusion rates, or pain parameter (visual analogue scale (VAS) of arm pain, neck disability index). However, advantages regarding subsidence, kyphosis, and VAS of neck pain were found when using the CP versus SC. Using the VR technique, there was no significant difference between the two fusion techniques in the mean size of the cross-sectional area at the end of follow-up. ConclusionDue to the long-term advantages of CP fusion, we prefer a monosegmental cervical spinal fusion using CP. Reconstruction of postsurgical two-dimensional CT images into three-dimensional images, and the spatial and anatomical presentation in VR models, improved the evaluation of these postoperative results.

Modulating relaxation responses of magnetic nanotracers for submillimeter imaging

Frequency-dependent magnetization characteristics potentially promote magnetic nanoparticles as prominent nanotracers for tomographic imaging. Owing to fast Neel dynamics relative to Brownian rotation of colloidal magnetic nanoparticles, we can demonstrate a two-dimensional image reconstruction from the Néel and Brownian relaxation responses modulated by external oscillatory field bursts with two distinctive frequencies. To realize a micrometer-scale resolution, a field-free-point (FFP) is manipulated to move in a dense Lissajous trajectory by low-frequency perpendicular sinusoidal fields across a steep field gradient between two permanent magnets. Instead of directly recording the resulting harmonic responses, we use an orthogonal high-frequency field to probe the time-varying FFP movement coupled with the moment relaxation. The proposed method achieves high spatial resolution, irrespective of the nonlinearity of the magnetization response, making it practical for bioanalytical imaging of cells and small animal models.

Coherent Bragg imaging of 60 nm Au nanoparticles under electrochemical control at the NanoMAX beamline.

Nanoparticles are essential electrocatalysts in chemical production, water treatment and energy conversion, but engineering efficient and specific catalysts requires understanding complex structure-reactivity relations. Recent experiments have shown that Bragg coherent diffraction imaging might be a powerful tool in this regard. The technique provides three-dimensional lattice strain fields from which surface reactivity maps can be inferred. However, all experiments published so far have investigated particles an order of magnitude larger than those used in practical applications. Studying smaller particles quickly becomes demanding as the diffracted intensity falls. Here, in situ nanodiffraction data from 60 nm Au nanoparticles under electrochemical control collected at the hard X-ray nanoprobe beamline of MAX IV, NanoMAX, are presented. Two-dimensional image reconstructions of these particles are produced, and it is estimated that NanoMAX, which is now open for general users, has the requisites for three-dimensional imaging of particles of a size relevant for catalytic applications. This represents the first demonstration of coherent X-ray diffraction experiments performed at a diffraction-limited storage ring, and illustrates the importance of these new sources for experiments where coherence properties become crucial.

A New Regularized Reconstruction Algorithm Based on Compressed Sensing for the Sparse Underdetermined Problem and Applications of One-Dimensional and Two-Dimensional Signal Recovery

The compressed sensing theory has been widely used in solving undetermined equations in various fields and has made remarkable achievements. The regularized smooth L0 (ReSL0) reconstruction algorithm adds an error regularization term to the smooth L0(SL0) algorithm, achieving the reconstruction of the signal well in the presence of noise. However, the ReSL0 reconstruction algorithm still has some flaws. It still chooses the original optimization method of SL0 and the Gauss approximation function, but this method has the problem of a sawtooth effect in the later optimization stage, and the convergence effect is not ideal. Therefore, we make two adjustments to the basis of the ReSL0 reconstruction algorithm: firstly, we introduce another CIPF function which has a better approximation effect than Gauss function; secondly, we combine the steepest descent method and Newton method in terms of the algorithm optimization. Then, a novel regularized recovery algorithm named combined regularized smooth L0 (CReSL0) is proposed. Under the same experimental conditions, the CReSL0 algorithm is compared with other popular reconstruction algorithms. Overall, the CReSL0 algorithm achieves excellent reconstruction performance in terms of the peak signal-to-noise ratio (PSNR) and run-time for both a one-dimensional Gauss signal and two-dimensional image reconstruction tasks.

Robust mixed one-bit compressive sensing

When a measurement falls outside the quantization or measurable range, it becomes saturated and cannot be used in conventional signal recovery methods. Aiming at acquiring information from noisy saturated and regular measurements, we in this paper propose a new signal recovery method called mixed one-bit compressive sensing (M1bit-CS) and develop an efficient algorithm in the framework of alternating direction methods of multipliers. Numerical experiments on one-dimensional symmetric signals and two-dimensional image reconstruction from computed tomography verify the effectiveness of M1bit-CS on signal recovery from saturated measurements.

Mechanical arm assisted lumbar puncture ultrasound scanning control and structural reconstruction

Objective To design a mechanical arm assisted lumbar puncture ultrasound scanning system to realize automatic scanning imaging of the lumbar vertebrae and visualize the three-dimensional reconstruction of the acquired two-dimensional ultrasound image, so as to obtain the three-dimensional image of the scanning lumbar and provide a basis for path planning and assisted puncture. Methods The main control program of the robotic arm was programmed by C language which can control the robotic arm to scan the lumbar vertebrae of the patient by a clamped ultrasound. The acquired 2D ultrasound image was reconstructed and visualized using a VTK-based 3D reconstruction visualization program. The lumbar vertebrae model reconstruction was conducted by Enovo Medical Model in water and CIRS 034 lumbar vertebral phantom, respectively, and the experimental results were compared and analyzed. Results By using the lumbar puncture ultrasound scanning system, the obtained two-dimensional ultrasound image of the lumbar spine model was clear and the anatomy was basically complete. The results of three-dimensional reconstruction showed that the spinous processes and their gaps of the scanned lumbar model were clearly visible, and the structure was intact, indicating that the system was operating normally and could achieve the expected function. By comparing the reconstruction results of the bent-knee lateral position and prone position, it can be concluded that the body position has an important influence on the reconstruction results of the lumbar spine ultrasound image. The bent-knee lateral position should be used in the follow-up study of lumbar puncture. Conclusions A lumbar puncture ultrasound scanning system assisted by a mechanical arm was proposed. The system can effectively capture the clear ultrasound image of the model and realize the visualization of 3D reconstruction, which can provide a basis for puncture path planning and assisted puncture. Key words: Lumbar puncture; Mechanical arm; Ultrasound; VTK; 3D reconstruction

Inversion of the Attenuated V-Line Transform With Vertices on the Circle

The Compton camera is a promising alternative to the Anger camera for imaging gamma radiation, with the potential to significantly increase the sensitivity of SPECT. Two-dimensional Compton camera image reconstruction can be implemented by inversion of the V-line transform, which integrates the emission distribution over V-lines (unions of two half-lines) that have vertices on a surrounding detector array. Inversion of the V-line transform without attenuation has recently been addressed by several authors. However, it is well known from standard SPECT that ignoring attenuation can significantly degrade the quality of the reconstructed image. In this paper, we address this issue and study the attenuated V-line transform accounting for attenuation of photons in SPECT with Compton cameras. Assuming vertices of V-lines on a circle, we derive an analytic inversion approach based on circular harmonics expansion, and show uniqueness of reconstruction for the attenuated V-line transform. We further develop a discrete image reconstruction algorithm based on our analytic studies, and present numerical results that demonstrate the effectiveness of our algorithm.

Fast and exact 2d image reconstruction based on Hakopian interpolation

A new algorithm for the reconstruction of two-dimensional (2D) images from projections is given. The algorithm is based on the expansions of Hakopian interpolation polynomial into Chebyshev–Fourier series. The computer simulation experiments show that the new algorithm is effective.