Numerical Image Reconstruction Research Articles

Fixed-time neural networks with time-invariant and time-varying coefficients for mixed variational inequalities

This paper develops several fixed-time neural networks for solving mixed variational inequalities (MVIs). The proposed networks are highly efficient and with fixed-time convergence. First, based on the conventional forward-backward-forward neural network (FNN) and sliding mode control technique, a time-invariant fixed-time FNN (FxTFNN) is designed. Next, the Euclidean norm of FNN is introduced into FxTFNN to design the modified FxTFNN (MFxTFNN). It is shown that the proposed FxTFNN and MFxTFNN have fixed-time convergence properties and their settling-time functions are independent of the initial values. The proposed FxTFNN and MFxTFNN can be used to solve the Lasso problem and apply sparse signal reconstruction and image reconstruction. In addition, by introducing time-varying coefficients based on FxTFNN and MFxTFNN, time-varying FxTFNN (TFxTFNN) and time-varying MFxTFNN (TMFxTFNN) are developed. Finally, experimental results of numerical example, signal reconstruction, and image reconstruction are used to verify the effectiveness and superiority of the proposed neural networks.

Automated phase unwrapping in digital holography with deep learning.

Digital holography can provide quantitative phase images related to the morphology and content of biological samples. After the numerical image reconstruction, the phase values are limited between -π and π; thus, discontinuity may occur due to the modulo 2π operation. We propose a new deep learning model that can automatically reconstruct unwrapped focused-phase images by combining digital holography and a Pix2Pix generative adversarial network (GAN) for image-to-image translation. Compared with numerical phase unwrapping methods, the proposed GAN model overcomes the difficulty of accurate phase unwrapping due to abrupt phase changes and can perform phase unwrapping at a twice faster rate. We show that the proposed model can generalize well to different types of cell images and has high performance compared to recent U-net models. The proposed method can be useful in observing the morphology and movement of biological cells in real-time applications.

A Novel Iterative MLEM Image Reconstruction Algorithm Based on Beltrami Filter: Application to ECT Images.

The implementation of emission-computed tomography (ECT), including positron emission tomography and single-photon emission-computed tomography, has been an important research topic in recent years and is of significant and practical importance. However, the slow rate of convergence and the computational complexity have severely impeded the efficient implementation of iterative reconstruction. By combining the maximum-likelihood expectation maximization (MLEM) iteratively along with the Beltrami filter, this paper proposes a new approach to reformulate the MLEM algorithm. Beltrami filtering is applied to an image obtained using the MLEM algorithm for each iteration. The role of Beltrami filtering is to remove mainly out-of-focus slice blurs, which are artifacts present in most existing images. To improve the quality of an image reconstructed using MLEM, the Beltrami filter employs similar structures, which in turn reduce the number of errors in the reconstructed image. Numerical image reconstruction tomography experiments have demonstrated the performance capability of the proposed algorithm in terms of an increase in signal-to-noise ratio (SNR) and the recovery of fine details that can be hidden in the data. The SNR and visual inspections of the reconstructed images are significantly improved compared to those of a standard MLEM. We conclude that the proposed algorithm provides an edge-preserving image reconstruction and substantially suppress noise and edge artifacts.

Multi-Modality Imaging: A Software Fusion and Image-Guided Therapy Perspective

With the introduction of computers in medical imaging, which were popularized with the presentation of Hounsfield’s ground-breaking work in 1971, numerical image reconstruction and analysis of medical images became a vital part of medical imaging research. While mathematical aspects of reconstruction dominated research in the beginning, a growing body of literature attests to the progress made over the past 30 years in image fusion. This article describes the historical development of non-deformable software-based image co-registration and it’s role in the context of hybrid imaging and provides an outlook on future developments.

Quantitative evaluation of functional Near Infrared Spectroscopy measurements with different source-detector separations using Monte Carlo simulation

Quantitative evaluation of functional Near Infrared Spectroscopy measurements with different source-detector separations using Monte Carlo simulation

Slowing dynamics of a supersonic beam, simulation and experiments

In this paper we present numerical and experimental methods aimed to study the evolution in space and time of a slowed supersonic beam. These generic methods are applicable to a variety of beams and decelerating techniques. The present implemented experimental set up is based upon Zeeman slowing of a metastable atom beam. The detection uses a channel-electron multiplier and a delay-line detector allowing time-of-flight analysis and numerical image reconstruction. In particular a depopulation effect at the centre of the beam is evidenced. In view of quantifying the slowing process, Monte Carlo calculations based on rate-equations are detailed.

Improving ultrasonic measurement of diaphragmatic excursion after cardiac surgery using the anatomical M-mode: a randomized crossover study

Motion-mode (MM) echography allows precise measurement of diaphragmatic excursion when the ultrasound beam is parallel to the diaphragmatic displacement. However, proper alignment is difficult to obtain in patients after cardiac surgery; thus, measurements might be inaccurate. A new imaging modality named the anatomical motion-mode (AMM) allows free placement of the cursor through the numerical image reconstruction and perfect alignment with the diaphragmatic motion. Our goal was to compare MM and AMM measurements of diaphragmatic excursion in cardiac surgical patients. Cardiac surgical patients were studied after extubation. The excursions of the right and left hemidiaphragms were measured by two operators, an expert and a trainee, using MM and AMM successively, according to a blinded, randomized, crossover sequence. Values were averaged over three consecutive respiratory cycles. The angle between the MM and AMM cursors was quantified for each measurement. Fifty patients were studied. The mean (±SD) angle between the MM and AMM cursors was 37°±16°. The diaphragmatic excursion as measured by experts was 1.8±0.7cm using MM and 1.5±0.5cm using AMM (p<0.001). Overall, the diaphragmatic excursion as estimated by MM was larger than the value obtained with AMM in 75% of the measurements. Bland-Altman analysis showed tighter limits of agreement between experts and trainees with AMM [bias: 0.0cm; 95% confidence interval (CI): 0.8cm] than with MM (bias: 0.0cm; 95% CI: 1.4cm). MM overestimates diaphragmatic excursion in comparison to AMM in cardiac surgical patients. Using MM may lead to a lack of recognition of diaphragmatic dysfunction.

ELECTRICAL RESISTANCE IMAGING OF TWO-PHASE FLOW WITH A MESH GROUPING TECHNIQUE BASED ON PARTICLE SWARM OPTIMIZATION

An electrical resistance tomography (ERT) technique combining the particle swarm optimization (PSO) algorithm with the Gauss-Newton method is applied to the visualization of two-phase flows. In the ERT, the electrical conductivity distribution, namely the conductivity values of pixels (numerical meshes) comprising the domain in the context of a numerical image reconstruction algorithm, is estimated with the known injected currents through the electrodes attached on the domain boundary and the measured potentials on those electrodes. In spite of many favorable characteristics of ERT such as no radiation, low cost, and high temporal resolution compared to other tomography techniques, one of the major drawbacks of ERT is low spatial resolution due to the inherent ill-posedness of conventional image reconstruction algorithms. In fact, the number of known data is much less than that of the unknowns (meshes). Recalling that binary mixtures like two-phase flows consist of only two substances with distinct electrical conductivities, this work adopts the PSO algorithm for mesh grouping to reduce the number of unknowns. In order to verify the enhanced performance of the proposed method, several numerical tests are performed. The comparison between the proposed algorithm and conventional Gauss-Newton method shows significant improvements in the quality of reconstructed images.

NEAR FIELD IMAGE RECONSTRUCTION ALGORITHM FOR PASSIVE MILLIMETER-WAVE IMAGER BHU-2D-U

A passive millimeter-wave imager BHU-2D-U based on synthetic aperture interferometric radiometer (SAIR) technique has been developed by Beihang University. The imager is designed for detecting concealed weapons on human body and operated under the near-field condition of the antenna array, thus the conventional Fourier imaging theory does not apply. In this paper, an accurate numerical image reconstruction algorithm using regularization theory is proposed. By means of adding a prior information of desired brightness temperature image, the influences of measurement noise and focusing error on the reconstructed image have been reduced. Numerical simulations and experiments on BHU-2D-U have been performed to verify the superiorities of the proposed algorithm over the corrected Fourier method and the Moore-Penrose pseudo inverse method. The results demonstrate that the proposed method is an advantageous imaging algorithm for near-field millimeter-wave SAIR.

Local Convergence of an EM-like Image Reconstruction Method for Diffuse Optical Tomography

In this paper, an EM-like image reconstruction iterative formula specifically developed for stable external sources is rewritten as a map towards a fixed point iteration. Local convergence of the image reconstruction method is then proved. Finally a three-dimensional numerical image reconstruction example is presented. Mathematics subject classification: 78A70; 78M50; 93B15.

An accelerated threshold‐based back‐projection algorithm for Compton camera image reconstruction

Compton camera imaging (CCI) systems are currently under investigation for radiotherapy dose reconstruction and verification. The ability of such a system to provide real-time images during dose delivery will be limited by the computational speed of the image reconstruction algorithm. In this work, the authors present a fast and simple method by which to generate an initial back-projected image from acquired CCI data, suitable for use in a filtered back-projection algorithm or as a starting point for iterative reconstruction algorithms, and compare its performance to the current state of the art. Each detector event in a CCI system describes a conical surface that includes the true point of origin of the detected photon. Numerical image reconstruction algorithms require, as a first step, the back-projection of each of these conical surfaces into an image space. The algorithm presented here first generates a solution matrix for each slice of the image space by solving the intersection of the conical surface with the image plane. Each element of the solution matrix is proportional to the distance of the corresponding voxel from the true intersection curve. A threshold function was developed to extract those pixels sufficiently close to the true intersection to generate a binary intersection curve. This process is repeated for each image plane for each CCI detector event, resulting in a three-dimensional back-projection image. The performance of this algorithm was tested against a marching algorithm known for speed and accuracy. The threshold-based algorithm was found to be approximately four times faster than the current state of the art with minimal deficit to image quality, arising from the fact that a generically applicable threshold function cannot provide perfect results in all situations. The algorithm fails to extract a complete intersection curve in image slices near the detector surface for detector event cones having axes nearly parallel to the image plane. This effect decreases the sum of the image, thereby also affecting the mean, standard deviation, and SNR of the image. All back-projected events associated with a simulated point source intersected the voxel containing the source and the FWHM of the back-projected image was similar to that obtained from the marching method. The slight deficit to image quality observed with the threshold-based back-projection algorithm described here is outweighed by the 75% reduction in computation time. The implementation of this method requires the development of an optimum threshold function, which determines the overall accuracy of the method. This makes the algorithm well-suited to applications involving the reconstruction of many large images, where the time invested in threshold development is offset by the decreased image reconstruction time. Implemented in a parallel-computing environment, the threshold-based algorithm has the potential to provide real-time dose verification for radiation therapy.

The influence of CT image noise on proton range calculation in radiotherapy planning**Presented at the 51st Annual Meeting of the American Association of Physicists in Medicine, Anaheim, CA, July 26–30, 2009.

The purpose of this note is to evaluate the relationship between the stochastic errors in CT numbers and the standard deviation of the computed proton beam range in radiotherapy planning. The stochastic voxel-to-voxel variation in CT numbers called ‘noise,’ may be due to signal registration, processing and numerical image reconstruction technique. Noise in CT images may cause a deviation in the computed proton range from the physical proton range, even assuming that the error due to CT number-stopping power calibration is removed. To obtain the probability density function (PDF) of the computed proton range, we have used the continuing slowing down approximation (CSDA) and the uncorrelated white Gaussian noise along the proton path. The model of white noise was accepted because for the slice-based fan-beam CT scanner; the power-spectrum properties apply only to the axial (x, y) domain and the noise is uncorrelated in the z domain. However, the possible influence of the noise power spectrum on the standard deviation of the range should be investigated in the future. A random number generator was utilized for noise simulation and this procedure was iteratively repeated to obtain convergence of range PDF, which approached a Gaussian distribution. We showed that the standard deviation of the range, σ, increases linearly with the initial proton energy, computational grid size and standard deviation of the voxel values. The 95% confidence interval width of the range PDF, which is defined as 4σ, may reach 0.6 cm for the initial proton energy of 200 MeV, computational grid 0.25 cm and 5% standard deviation of CT voxel values. Our results show that the range uncertainty due to random errors in CT numbers may be significant and comparable to the uncertainties due to calibration of CT numbers.

Spatial Phase-Shifting Digital Holography for Three-Dimensional Particle Tracking Velocimetry

This paper presents a holographic technique for three-dimensional particle tracking. The complex amplitude on an image sensor is measured with two pairs of spatially phase-shifted digital holograms captured in a short time interval using a phase-shifting technique. Pairs of digital holograms are used to track small tracer particles in three-dimensional space and the phase-adjusted complex amplitude is employed in numerical image reconstruction to accurately detect the particles. The performance of the method is evaluated by numerical simulation. In order to demonstrate the feasibility of the method for real flow measurement, it is applied to the velocity measurement of tracer particles in a small water channel along which a high voltage is applied. The resulting components of the velocity vector in three-dimensional space are compared to those obtained using a conventional single-shot phase-shifting technique.

Numerical modelling and image reconstruction in diffuse optical tomography

The development of diffuse optical tomography as a functional imaging modality has relied largely on the use of model-based image reconstruction. The recovery of optical parameters from boundary measurements of light propagation within tissue is inherently a difficult one, because the problem is nonlinear, ill-posed and ill-conditioned. Additionally, although the measured near-infrared signals of light transmission through tissue provide high imaging contrast, the reconstructed images suffer from poor spatial resolution due to the diffuse propagation of light in biological tissue. The application of model-based image reconstruction is reviewed in this paper, together with a numerical modelling approach to light propagation in tissue as well as generalized image reconstruction using boundary data. A comprehensive review and details of the basis for using spatial and structural prior information are also discussed, whereby the use of spectral and dual-modality systems can improve contrast and spatial resolution.

Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction

Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package.

Three-dimensional remote sensing by optical scanning holography

A technique is presented by which holograms can be recorded when an object or scene is scanned with an optically heterodyned Fresnel zone pattern. The experimental setup, based on optical scanning holography, is described and experimental results are presented. We apply the scanning holography technique to three-dimensional reflective objects for the first time to our knowledge and address the unique requirements for such a system. We discuss holographic recording and numerical image reconstruction using a system point-spread function (PSF) approach. We demonstrate numerical image reconstruction of experimentally recorded holograms by two techniques: deconvolution with a simulated PSF and an experimentally acquired PSF.

A new theoretical approach to x-ray diffraction tomography

A new theoretical approach to x-ray diffraction tomography isproposed. Numerical simulations and image reconstruction are presented,which utilize a discrete implementation of the new formalism. A uniqueaspect of the present method is the inclusion of a position-sensitivedetector and an analyser crystal to detect small-angle coherent scatteringfrom a specimen. This arrangement excludes background and multiplescattering, thereby allowing maps of the differential coherent scatteringcross section, and the linear attenuation coefficient, to be reconstructedfrom diffracted data only.

An analytical SMASH procedure (ASP) for sensitivity-encoded MRI.

The simultaneous acquisition of spatial harmonics (SMASH) method of imaging with detector arrays can reduce the number of phase-encoding steps, and MRI scan time several-fold. The original approach utilized numerical gradient-descent fitting with the coil sensitivity profiles to create a set of composite spatial harmonics to replace the phase-encoding steps. Here, an analytical approach for generating the harmonics is presented. A transform is derived to project the harmonics onto a set of sensitivity profiles. A sequence of Fourier, Hilbert, and inverse Fourier transform is then applied to analytically eliminate spatially dependent phase errors from the different coils while fully preserving the spatial-encoding. By combining the transform and phase correction, the original numerical image reconstruction method can be replaced by an analytical SMASH procedure (ASP). The approach also allows simulation of SMASH imaging, revealing a criterion for the ratio of the detector sensitivity profile width to the detector spacing that produces optimal harmonic generation. When detector geometry is suboptimal, a group of quasi-harmonics arises, which can be corrected and restored to pure harmonics. The simulation also reveals high-order harmonic modulation effects, and a demodulation procedure is presented that enables application of ASP to a large numbers of detectors. The method is demonstrated on a phantom and humans using a standard 4-channel phased-array MRI system.

Parallel Image Reconstruction in Real-Time Ultrasound Process Tomography for Two-phased Flow Measurements

This paper investigates different parallel-processing architectures as a means of achieving real-time ultrasound tomographic imaging capability. The real-time numerical image reconstruction is implemented by a parallel processor network and DSP controlled data acquisition electronics. The parallel imaging technique developed for the present work has been shown to be capable of achieving the necessary real-time image generation rate (100 frames per second on a 100 × 100 image array for software image reconstruction) and an average update frequency of 30 frames per second when acquiring data from the hardware. The parallel image processing algorithm which combines geometric and algorithmic parallelism aiming at optimizing the parallel efficiency of the processors of the array has been implemented and verified. The experimental imaging results generated by the parallel imaging system are presented and the dynamic performance of the parallel system are discussed.

Holographic Interference Electron Microscopy by Numerical Reconstruction Method

Holographic interference electron microscopy has recently been put to practical use with a field-emission electron microscope. In this microscopy, the optical image reconstruction method are usually used, but many practical difficulties such as optical adjustment are always accompanied. On the other hand, the numerical image reconstruction method has many advantages. In this paper, therefore, holographic interference electron microscopy are tried by using a numerically reconstructed image.In the first step, an off-axis Fresnel electron hologram (Fig.1) was formed in a 100 kV thermionic-emission electron microscope equipped with an electron biprism. MgO smoke particles were used as a specimen. A reconstructed image is given by the convolution of amplitude transmittance of an electron hologram with propagation function from a hologram plane to an image reconstruction plane. In the second step for the numerical reconstruction, the hologram was enlarged and printed on a photographic paper.