Reconstructed 2D Images Research Articles

Optimal Reconstruction of Single-Pixel Images through Feature Feedback Mechanism and Attention

The single-pixel imaging technique can reconstruct high-quality images using only a bucket detector with no spatial resolution, and the image quality is degraded in order to meet the demands of real-time applications. According to some studies of algorithm performance, the network model performs differently in simulated and real-world experiments. We propose an end-to-end neural network capable of reconstructing 2D images from experimentally obtained 1D signals optimally. In order to improve the image quality of real-time single-pixel imaging, we built a feedback module in the hidden layer of the recurrent neural network to implement feature feedback. The feedback module fuses high-level features of undersampled images with low-level features through dense jump connections and multi-scale balanced attention modules to gradually optimize the feature extraction process and reconstruct high-quality images. In addition, we introduce a learning strategy that combines mean loss with frequency domain loss to improve the network’s ability to reconstruct complex undersampled images. In this paper, the factors that lead to the degradation of single-pixel imaging are analyzed, and a network degradation model suitable for physical imaging systems is designed. The experiment results indicate that the reconstructed images utilizing the proposed method have better quality metrics and visual effects than the excellent methods in the field of single-pixel imaging.

Transformation of coherence-dependent bokeh for incoherent digital holography

Incoherent digital holography (IDH) enables the recording of holograms with incoherent light. However, there is unnatural bokeh with ringing on reconstructed 2D images, owing to the diffraction calculation based on the coherent nature of the light. Thus, we propose a transformation method that converts it into incoherent bokeh. This proposed method can generate 2D images without ringing from recorded holograms through a virtual incoherent imaging system, while focusing on the non-linearity problem of reconstruction distances in IDH. Flexible depth-of-field control is also made possible by the judicious selection of parameters in this method. A proof-of-principle demonstration verifies its feasibility.

An Investigation of Microwave Tomography Technique to Detect Brain Tumour Through Cross-Section Imaging at Frequency 0.5 GHz to 1.5 GHz

The growing significance of cancerous tissue including brain tumour requires a fast and efficient technology detection. The most current technologies being applied for brain imaging system are Computed Tomography (CT) scan and Magnetic Resonance Imaging (MRI). Whilst these two detection applications are very well established, both systems are expensive, time and space consuming, and raise safety issues to patients due to the radiation and strong magnetic effects. This research aims to assess the feasibility and potential performance of microwave tomography (MWT) for brain imaging with a particular focus on brain tumour detection. The study was conducted using Finite Element Model software, COMSOL Multiphysics to develop a 2D modelling of an antenna array and measure the scattered electric field by solving forward problem. MATLAB software will be used as an inverse problem solver to reconstruct 2D images of the tumour by using Linear Back Projection (LBP) algorithm.

Application of deep learning and compressed sensing for reconstruction of images

Compressed sensing (CS) is a technique in signal processing which reconstructs any given signal at a rate less than that of Nyquist’s’ rate given that the signal is sparse and incoherent in nature. The main focus of CS is to find a random matrix which reconstructs the original signal using as few samples as possible. In recent years there has been a lot of interest in using CS to reconstruct 2D images. Several machine learning and deep learning algorithms have been proposed for finding the random matrix. However, using deep learning techniques to generate the random matrix is still an emerging concept. There are several papers exploring the concepts of deep learning with compressed sensing for images and have produced promising results. The results obtained in these papers warrant a comparison to analyze their performances against more traditional methods to determine the best approach to reconstruct images. These results are also compared with the popular JPEG and JPEG2000 codecs. This paper focuses on surveying deep learning algorithms for reconstruction of images using CS. The comparison reveals that deep learning algorithms perform significantly better than traditional methods and perform well when compared to any image compression codec like JPEG. Possible methods to improve the existing algorithms have been suggested.

Microwave Imaging of Voids in Oil Palm Trunk Applying UWB Antenna and Robust Time-Reversal Algorithm

The oil palm trees in Southeast Asia face a great challenge due to voids within tree trunks. Besides, both plantations and the palm oil industry suffered considerable losses due to ineffective inspection of defective trees. Several techniques such as ultrasound, X-ray, capacitive volume, gamma computed tomography, and microwave tomography were applied to detect and control the decay of a trunk. However, all the techniques showed substantial drawbacks (such as limited resolution, tedious processing time, and use of bulky equipment with limited mobility) except for microwave tomography which overtook the other techniques by using a method that distinguishes the dielectric properties of healthy and diseased trunks. This work proposes ultra-wide-band (UWB) signal transmission and reception using antenna sensor arrays that record reflections from affected regions in the trunk. Various factors have been considered, such as different cylindrical arrays of 4, 8, 12, and 16 antennas; different positions of hollows; a heterogeneous trunk; multiple targets; and larger trunk samples (16–30 cm). To validate the system’s capabilities, two cylindrical wood samples with different diameters of 100 mm and 140 mm and with one hollow and three hollows within are 3D-printed, investigated, and then measured. The authors recommended a robust time-reversal algorithm (RTR) to reconstruct 2D images that successfully identified and localized cavities with the smallest diameter of 3.5 mm. Furthermore, reconstructed images of measured data verified a practical and reliable oil palm trunk imaging and sensing system with a high structural similarity index and resolution.

A Compressed Sensing Approach for Multiple Obstacle Localisation Using Sonar Sensors in Air.

Methods for autonomous navigation systems using sonars in air traditionally use the time-of-flight technique for obstacle detection and environment mapping. However, this technique suffers from constructive and destructive interference of ultrasonic reflections from multiple obstacles in the environment, requiring several acquisitions for proper mapping. This paper presents a novel approach for obstacle detection and localisation using inverse problems and compressed sensing concepts. Experiments were conducted with multiple obstacles present in a controlled environment using a hardware platform with four transducers, which was specially designed for sending, receiving and acquiring raw ultrasonic signals. A comparison between the performance of compressed sensing using Orthogonal Matching Pursuit and two traditional image reconstruction methods was conducted. The reconstructed 2D images representing the cross-section of the sensed environment were quantitatively assessed, showing promising results for robotic mapping tasks using compressed sensing.

Synthetic Aperture Sonar (SAS) without Navigation: Scan Registration as Basis for Near Field Synthetic Imaging in 2D.

Sonars are essential for underwater sensing as they can operate over extended ranges and in poor visibility conditions. The use of a synthetic aperture is a popular approach to increase the resolution of sonars, i.e., the sonar with its N transducers is positioned at k places to generate a virtual sensor with transducers. The state of the art for synthetic aperture sonar (SAS) is strongly coupled to constraints, especially with respect to the trajectory of the placements and the need for good navigation data. In this article, we introduce an approach to SAS using registration of scans from single arrays, i.e., at individual poses of arbitrary trajectories, hence avoiding the need for navigation data of conventional SAS systems. The approach is introduced here for the near field using the coherent phase information of sonar scans. A Delay and Sum (D&S) beamformer (BF) is used, which directly operates on pixel/voxel form on a Cartesian grid supporting the registration. It is shown that this pixel/voxel-based registration and the coherent processing of several scans forming a synthetic aperture yields substantial improvements of the image resolution. The experimental evaluation is done with an advanced simulation tool generating realistic 2D sonar array data, i.e., with simulations of a linear 1D antenna reconstructing 2D images. For the image registration of the raw sonar scans, a robust implementation of a spectral method is presented. Furthermore, analyses with respect to the trajectories of the sensor locations are provided to remedy possible grating lobes due to the gaping positions of the transmitter devices.

Three-dimensional imaging through scattering media using a single pixel detector.

Imaging objects hidden by turbid media, such as smoke, fog, or biological tissues, is a challenge for scientists. Compressive ghost imaging and a photometric stereo approach are employed to estimate the 3D shape of an object behind a scattering medium. A sequence of speckle patterns is projected onto the object. Four images with different shadings are accurately reconstructed from the object behind a diffuser. The 3D shape is obtained by applying the photometric stereo to the reconstructed 2D images. This technique is robust against scattering, even for 3D imaging in opaque media with multiple scattering, and it is not sensitive to changes in the scattering media or displacement of the medium. Also, it has the benefits of compressive ghost imaging strategy, such as hyperspectral or polarimetric imaging with sub-Nyquist sampling. As a proof for this concept, the 3D shape of a target behind a diffuser was experimentally retrieved, and the results were compared with the original 3D shape and the 3D shape reconstructed in the absence of the diffuser. The accuracy of the reconstructed 3D shapes was maintained in the presence of the diffuser plate in various thicknesses and orientations.

Image reconstruction from undersampled confocal microscopy data using multiresolution based maximum entropy regularization

We consider the problem of reconstructing 2D images from randomly under-sampled confocal microscopy samples. The well known and widely celebrated total variation regularization, which is the ℓ1 norm of derivatives, turns out to be unsuitable for this problem; it is unable to handle both noise and under-sampling together. This issue is linked with the notion of phase transition phenomenon observed in compressive sensing research, which is essentially the break-down of total variation methods, when sampling density gets lower than certain threshold. The severity of this breakdown is determined by the so-called mutual incoherence between the derivative operators and measurement operator. In our problem, the mutual incoherence is low, and hence the total variation regularization gives serious artifacts in the presence of noise even when the sampling density is not very low. There has been very few attempts in developing regularization methods that perform better than total variation regularization for this problem. We develop a multi-resolution based regularization method that is adaptive to image structure. In our approach, the desired reconstruction is formulated as a series of coarse-to-fine multi-resolution reconstructions; for reconstruction at each level, the regularization is constructed to be adaptive to the image structure, where the information for adaption is obtained from the reconstruction obtained at coarser resolution level. This adaptation is achieved by using maximum entropy principle, where the required adaptive regularization is determined as the maximizer of entropy subject to the information extracted from the coarse reconstruction as constraints. We also utilize the directionally adaptive second order derivatives for constructing the regularization with directions guided by the given coarse reconstruction, which leads to an improved suppression of artifacts. We demonstrate the superiority of the proposed regularization method over existing ones using several reconstruction examples.

3D topography and tomography of multilayered freeform optical surfaces using large-range measurement swept-source low-coherence interferometry

Multilayered freeform optical surfaces are frequently used in various types of light-emitting diodes (LEDs) as encapsulant, light extraction, beam shaping and diffusing elements. We demonstrate optical metrology and sectioning of these types of optical surfaces by using a swept-source low-coherence interferometric (SS-LCI) system. This work reports the extended range of measurement of multilayered surfaces with high resolution. To validate the detection and measurement capability of SS-LCI, experiments are conducted on different LEDs having multilayered surfaces, e.g. step-sized, conical- shaped, dome-shaped red, green, blue and aspheric surfaces. 3D topographic and tomographic images of the aforementioned objects are obtained through various 2D X-Z scans of the sample beam with 12 μm axial resolution. The instantaneous spectral linewidth of the swept source leads to large range of depth/height measurement (penetration depth ~12 mm) without any ambiguity problem. In addition, the acquisition speed of the system for scanning a large sample area (16 × 16 × 12 mm) is very high due to the fast wavelength sweeping speed of the micro-electromechanical system- vertical-cavity surface-emitting laser swept source. The measured 3D topography and tomography of freeform optical surfaces is further used to formulate their approximate profile and measure the distance between multilayered surfaces. Furthermore, the reconstructed 2D images corresponding to various freeform surfaces are converted into binary images by setting a certain threshold value and then is higher-order polynomial fitted to obtain profiles of the objects.

Multifield measurement of magnetic fluctuation-induced particle flux in a high-temperature toroidal plasma

Magnetic fluctuation-induced particle transport is explored in the high-temperature, high-beta interior of the Madison symmetric torus (MST) reversed-field pinch by performing a multifield measurement of the correlated product of magnetic and density fluctuations associated with global resistive tearing modes. Local density fluctuations are obtained by inverting the line-integrated interferometry data after resolving the mode helicity through correlation techniques. The local magnetic and current density fluctuations are then reconstructed using a parameterized fit of Faraday-effect polarimetry measurements. Reconstructed 2D images of density and current density perturbations in a poloidal cross section exhibit significantly different spatial structure. Combined with their relative phase, the magnetic-fluctuation-induced particle transport flux and its spatial distribution are resolved. The convective magnetic fluctuation-induced particle flux profile is measured for both standard and high-performance plasmas in MST with tokamak-like confinement, showing large reduction in the flux during improved confinement.

A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography

Synchrotron source propagation-based X-ray phase contrast computed tomography is increasingly used in pre-clinical imaging. However, it typically requires a large number of projections, and subsequently a large radiation dose, to produce high quality images. To improve the applicability of this imaging technique, reconstruction algorithms that can reduce the radiation dose and acquisition time without degrading image quality are needed. The proposed research focused on using a novel combination of Douglas–Rachford splitting and randomized Kaczmarz algorithms to solve large-scale total variation based optimization in a compressed sensing framework to reconstruct 2D images from a reduced number of projections. Visual assessment and quantitative performance evaluations of a synthetic abdomen phantom and real reconstructed image of an ex-vivo slice of canine prostate tissue demonstrate that the proposed algorithm is competitive in reconstruction process compared with other well-known algorithms. An additional potential benefit of reducing the number of projections would be reduction of time for motion artifact to occur if the sample moves during image acquisition. Use of this reconstruction algorithm to reduce the required number of projections in synchrotron source propagation-based X-ray phase contrast computed tomography is an effective form of dose reduction that may pave the way for imaging of in-vivo samples.

Assessment of a fast generated analytical matrix for rotating slat collimation iterative reconstruction: a possible method to optimize the collimation profile

In SPECT imaging, improvement or deterioration of performance is mostly due to collimator design. Classical SPECT systems mainly use parallel hole or pinhole collimators. Rotating slat collimators (RSC) can be an interesting alternative to optimize the tradeoff between detection efficiency and spatial resolution. The present study was conducted using a RSC system for small animal imaging called CLiR. The CLiR system was used in planar mode only. In a previous study, planar 2D projections were reconstructed using the well-known filtered backprojection algorithm (FBP). In this paper, we investigated the use of the statistical reconstruction algorithm maximum likelihood expectation maximization (MLEM) to reconstruct 2D images with the CLiR system using a probability matrix calculated using an analytic approach. The primary objective was to propose a method to quickly generate a light system matrix, which facilitates its handling and storage, while providing accurate and reliable performance. Two other matrices were calculated using GATE Monte Carlo simulations to investigate the performance obtained using the matrix calculated analytically. The first matrix calculated using GATE took all the physics processes into account, where the second did not consider for the scattering, as the analytical matrix did not take this physics process into account either. 2D images were reconstructed using FBP and MLEM with the three different probability matrices. Both simulated and experimental data were used. A comparative study of these images was conducted using different metrics: the modulation transfert function, the signal-to-noise ratio and quantification measurement. All the results demonstrated the suitability of using a probability matrix calculated analytically. It provided similar results in terms of spatial resolution (about 0.6 mm with differences <5%), signal-to-noise ratio (differences <10%), or quality of image.

2D image of local density and magnetic fluctuations from line-integrated interferometry-polarimetry measurements.

Combined polarimetry-interferometry capability permits simultaneous measurement of line-integrated density and Faraday effect with fast time response (∼1 μs) and high sensitivity. Faraday effect fluctuations with phase shift of order 0.05° associated with global tearing modes are resolved with an uncertainty ∼0.01°. For physics investigations, local density fluctuations are obtained by inverting the line-integrated interferometry data. The local magnetic and current density fluctuations are then reconstructed using a parameterized fit of the polarimetry data. Reconstructed 2D images of density and magnetic field fluctuations in a poloidal cross section exhibit significantly different spatial structure. Combined with their relative phase, the magnetic-fluctuation-induced particle transport flux and its spatial distribution are resolved.

Two-View Digital Breast Tomosynthesis Screening with Synthetically Reconstructed Projection Images: Comparison with Digital Breast Tomosynthesis with Full-Field Digital Mammographic Images

To compare the performance of two versions of reconstructed two-dimensional (2D) images in combination with digital breast tomosynthesis (DBT) versus the performance of standard full-field digital mammography (FFDM) plus DBT. This trial had ethical committee approval, and all participants gave written informed consent. Examinations (n = 24 901) in women between the ages of 50 and 69 years (mean age, 59.2 years) were interpreted prospectively as part of a screening trial that included independent interpretations of FFDM plus DBT and reconstructed 2D images plus DBT. Reconstructed 2D images do not require radiation exposure. Using analyses for binary data that accounted for correlated interpretations and were adjusted for reader-specific volume, two versions (initial and current) of reconstructed 2D images used during trial periods 1 (from November 22, 2010, to December 21, 2011; 12 631 women) and 2 (from January 20, 2012, to December 19, 2012; 12 270 women) were compared in terms of cancer detection and false-positive rates with the corresponding FFDM plus DBT interpretations. Cancer detection rates were 8.0, 7.4, 7.8, and 7.7 per 1000 screening examinations for FFDM plus DBT in period 1, initial reconstructed 2D images plus DBT in period 1, FFDM plus DBT in period 2, and current reconstructed 2D images plus DBT in period 2, respectively. False-positive scores were 5.3%, 4.6%, 4.6%, and 4.5%, respectively. Corresponding reader-adjusted paired comparisons of false-positive scores revealed significant differences for period 1 (P = .012) but not for period 2 (ratio = 0.99; 95% confidence interval: 0.88, 1.11; P = .85). The combination of current reconstructed 2D images and DBT performed comparably to FFDM plus DBT and is adequate for routine clinical use when interpreting screening mammograms.

Skeleton and level set for channel construction and flow simulation

This paper aims to introduce a unified code for fluid flow modeling in complex channels reconstructed from imagery. Given a binary image of a cross-section or projection of planar connected channels with circular cross-sections, we wish to: (1) reconstruct a three-dimensional model of the boundary of the geometry, (2) establish boundary condition of the flow field, and (3) compute a fluid simulation based on a Cartesian grid. Our solution has the following advantages. First, we use the same mathematical tools throughout the process i.e. a level set function and a skeleton to describe the geometry. The skeleton of the geometry is essential in the imagery part to transform the 2D geometry into a 3D geometry but is also essential in the fluid flow part to construct a velocity field of reference for boundary conditions in the mechanical fluid flow model. Then, the integration of the geometry into the fluid mechanic code is simplified thanks to a Cartesian grid taking into account the geometry through the level set function. Finally, this work leads to a stand-alone code capable of simulating 3D flows in geometry reconstructed 2D images. We show its usefulness in applications to medical imagery (namely angiography) and bifluid flows in microchannels.

A Level Set based Regularization Framework for EIT Image Reconstruction

Electrical Impedance Tomography (EIT) reconstructs the conductivity distribution within a medium from electrical stimulation and measurements at the medium surface. Level set based reconstruction method (LSRM) has gained attention during the last decade as an effective solution to address the need of reconstructing structures with limited amount of available data. The classical LSRM is based on the quadratic formulations (L2 norms); however, the L2 norms are not robust to outliers and spatial noise. The L1 norm is a more solid alternative to produce high robustness against outliers and noise. The L1 norm is minimized by Primal dual-interior point method (PDIPM). In this paper, we derive a novel level set (LS) based regularization framework for using the L1 norm independently on the data and the regularization term of an inverse problem. The proposed LS based regularization method, called LS based PDIPM (LS-PDIPM), applies the PDIPM to minimize the L1 norms. We use the LS-PDIPM to reconstruct 2D images from EIT simulated data. The proposed LS-PDIPM with the L1 norms provides sharper and less noisy images, when comparing with the L2 norm based regularization method.

Acoustic dipole radiation based electrical impedance contrast imaging approach of magnetoacoustic tomography with magnetic induction

Different from the theory of acoustic monopole spherical radiation, the acoustic dipole radiation based theory introduces the radiation pattern of Lorentz force induced dipole sources to describe the principle of magnetoacoustic tomography with magnetic induction (MAT-MI). Although two-dimensional (2D) simulations have been studied for cylindrical phantom models, layer effects of the dipole sources within the entire object along the z direction still need to be investigated to evaluate the performance of MAT-MI for different geometric specifications. The purpose of this work is further verifying the validity and generality of acoustic dipole radiation based theory for MAT-MI with two new models in different shapes, dimensions, and conductivities. Based on the theory of acoustic dipole radiation, the principles of MAT-MI were analyzed with derived analytic formulae. 2D and 3D numerical studies for two new models of aluminum foil and cooked egg were conducted to simulate acoustic pressures and corresponding waveforms, and 2D images of the scanned layers were reconstructed with the simplified back projection algorithm for the waveforms collected around the models. The spatial resolution for conductivity boundary differentiation was also analyzed with different foil thickness. For comparison, two experimental measurements were conducted for a cylindrical aluminum foil phantom and a shell-peeled cooked egg. The collected waveforms and the reconstructed images of the scanned layers were achieved to verify the validation of the acoustic dipole radiation based theory for MAT-MI. Despite the difference between the 2D and 3D simulated pressures, good consistence of the collected waveforms proves that wave clusters are generated by the abrupt pressure changes with bipolar vibration phases, representing the opposite polarities of the conductivity changes along the measurement direction. The configuration of the scanned layer can be reconstructed in terms of shape and size, and the conductivity boundaries are displayed in stripes with different contrast and bipolar intensities. Layer effects are demonstrated to have little influence on the collected waveforms and the reconstructed images of the scanned layers for the two new models. The experimental results have good agreements with numerical simulations, and the reconstructed 2D images provide conductivity configurations in the scanned layers of the aluminum foil and the egg models. It can be concluded that the acoustic pressure of MAT-MI is produced by the divergence of the induced Lorentz force, and the collected waveforms comprise wave clusters with bipolar vibration phases and different amplitudes, providing the information of conductivity boundaries in the scanned layer. With the simplified back projection algorithm for diffraction sources, collected waveforms can be used to reconstruct 2D conductivity contrast image and the conductivity configuration in the scanned layer can be obtained in terms of shape and size in stripes with the spatial resolution of the acoustic wavelength. The favorable results further verify the validity and generality of the acoustic dipole radiation based theory and suggest the feasibility of MAT-MI as an effective electrical impedance contrast imaging approach for medical imaging.

Sampling and processing for compressive holography [Invited

Compressive holography applies sparsity priors to data acquired by digital holography to infer a small number of object features or basis vectors from a slightly larger number of discrete measurements. Compressive holography may be applied to reconstruct three-dimensional (3D) images from two-dimensional (2D) measurements or to reconstruct 2D images from sparse apertures. This paper is a tutorial covering practical compressive holography procedures, including field propagation, reference filtering, and inverse problems in compressive holography. We present as examples 3D tomography from a 2D hologram, 2D image reconstruction from a sparse aperture, and diffuse object estimation from diverse speckle realizations.

Reconstructing 2D images with natural neighbour interpolation

In this paper, we explore image reconstruction by natural neighbour interpolation from irregularly spaced samples. We sample the image irregularly with techniques based on the Laplacian or the derivative in the direction of the gradient. Local coordinates based on the Voronoi diagram are used in natural neighbour interpolation to quantify the “neighbourliness” of data sites. Then we use natural neighbour interpolation in order to reconstruct the image. The main result is that the image quality is always very good in the case of the sampling techniques based on the Laplacian.