Two-dimensional Image Reconstruction Research Articles

A parallel way of data decomposition approach for ANN based image reconstruction in e-MRI on a multi-core computer system

Abstract This paper presents the performance of sequential data decomposition and parallel data decomposition strategies applied on a Back-Propagation Artificial Neural Network (BP-ANN) algorithm. The application system is developed for reconstruction of two-dimensional spatial images from continuous wave electron magnetic resonance imaging (CW-EMRI) tomography data, on a multi-core computer. The BP-ANN learns the relationship between the ‘ideal’ images that are reconstructed using filtered back projection (FBP) technique and the corresponding projection data from various temporal data of in vivo objects. In an earlier work, it has been reported that as the exemplar sizes are too large, the training time is too long and image PSNR (Peak Signal to Noise Ratio) values are too low. Hence, in the present work, we propose that the exemplar datasets are decomposed into subsets. Using these subsets, artificial sub neural nets (subnets) are constructed and training is carried out on a multi-core system. Consequently, the sequential approach of the proposed method yields better PSNR images. However, it consumes more training time. But when the parallel approach is applied the computational training time becomes reduced. The parallel approach of BP-ANN is able to simplify reconstruction tasks and is seen improving both in accuracy and efficiency. The performance results are tabulated for different exemplar subset sizes, different subnet sizes and the number of multi-core processors. The parallel approach is further explored for image reconstruction from ‘noisy’ and ‘limited-angle’ datasets.

Improvement of Forward-Backward Pursuit Algorithm Based on Weak Selection

Forward-backward pursuit (FBP) algorithm is a novel two-stage greedy approach. However once its forward and backward steps were determined during iteration, it would make computing time increased and affected the reconstruction efficiency. This paper presents a algorithm called forward-backward pursuit algorithm based on weak selection (SWFBP) by introducing threshold strategy into FBP algorithm, and in view of that in the first few iterations, most of the atoms which are selected are right, so this part of atoms are directly incorporated into support set instead of using backward strategy to reduce them. Flexible forward and backward steps accelerate the speed of atom selecting and improve the reconstruction accuracy. We compared SWFBP and FBP algorithm via one-dimensional signal and two-dimensional image reconstruction experiments. The simulation results demonstrate that compared with FBP, SWFBP algorithm has superior performance, including higher PSNR, faster computing speed and lower recovery time.

Ultrawideband Noise Radar Tomography: Principles, Simulation, and Experimental Validation

The paper introduces the principles, simulation results, and hardware implementation of ultrawideband (UWB) noise radar for obtaining tomographic images of various scenarios of rotating cylindrical objects using independent and identically distributed UWB noise waveforms. A UWB noise radar was designed to transmit multiple UWB random noise waveforms over the 3–5 GHz frequency range and to measure the backward scattering data for the validation of the theoretical analysis and numerical simulation results. The reconstructed tomographic images of the rotating cylindrical objects based on experimental results are seen to be in good agreement with the simulation results, which demonstrates the capability of UWB noise radar for complete two-dimensional tomographic image reconstruction of various shaped metallic and dielectric target objects.

Compressed Sensing Based on Trust Region Method

Developed in recent years, compressed sensing (CS) has saved considerable data storage and time in signal acquisition and processing, drawing the attention of many scholars in various fields. At present, a key issue is the design of an effective CS reconstruction algorithm. Unlike the commonly used CS convex optimization approaches, which require determining the direction first and later using the linear search to attain the optimal displacement, the trust region method introduced into the CS model in this paper solves a quadratic convex optimization problem in the varied circular area. The simulated reconstruction of two-dimensional images is performed via MATLAB. Meanwhile, comparative analysis is executed using different CS reconstruction methods, such as the greedy algorithms (orthogonal matching pursuit, sparse adaptive matching pursuit) and convex optimization algorithms (basis pursuit, conjugate gradient). The experimental results are summarized and analyzed, demonstrating that the proposed CS trust region method may recover the images more accurately than state-of-the-art schemes.

Fractional-order total variation combined with sparsifying transforms for compressive sensing sparse image reconstruction

The total variation (TV) model has been considered to be one of the most successful and representative model for compressive sensing (CS) sparse image reconstruction due to its advantage of preserving image edges. However, TV regularized term often favors piecewise constant solution and therefore it fails to preserve the details and textures. To overcome this defect and reconstruct the fine details, this paper proposes a two-dimensional CS sparse image reconstruction model by introducing the fractional-order TV (FrTV) regularization constraint into CS optimization problem. Furthermore, in order to achieve sparser representation flexibly, a combination of discrete wavelet transform and curvelet transform ℓ1-norm regularization is also incorporated into the cost function and a method for estimating the regularization parameter that trades off the two terms in the cost function is proposed. By using a smooth approximation of the ℓ1-norm, a gradient projection algorithm is derived to solve the combined FrTV and sparsifying transforms constrained minimization problem effectively. Compared with several state-of-the-art reconstruction algorithms, the proposed algorithm is more efficient and robust, not only yielding higher peak-signal-to-noise ratio, but also reconstructing the fine details and textures more efficiently.

Fast two-dimensional super-resolution image reconstruction algorithm for ultra-high emitter density

Single-molecule localization microscopy achieves sub-diffraction-limit resolution by localizing a sparse subset of stochastically activated emitters in each frame. Its temporal resolution is limited by the maximal emitter density that can be handled by the image reconstruction algorithms. Multiple algorithms have been developed to accurately locate the emitters even when they have significant overlaps. Currently, compressive-sensing-based algorithm (CSSTORM) achieves the highest emitter density. However, CSSTORM is extremely computationally expensive, which limits its practical application. Here, we develop a new algorithm (MempSTORM) based on two-dimensional spectrum analysis. With the same localization accuracy and recall rate, MempSTORM is 100 times faster than CSSTORM with ℓ(1)-homotopy. In addition, MempSTORM can be implemented on a GPU for parallelism, which can further increase its computational speed and make it possible for online super-resolution reconstruction of high-density emitters.

Aliasing Artefact Suppression in Compressed Sensing MRI for Random Phase-Encode Undersampling.

Random phase-encode undersampling of Cartesian k-space trajectories is widely implemented in compressed sensing (CS) MRI. However, its one-dimensional (1-D) randomness inherently introduces large coherent aliasing artefacts along the undersampled direction in the reconstruction and, thus, degrades the image quality. This paper proposes a novel reconstruction scheme to reduce the 1-D undersampling-induced aliasing artefacts. The proposed reconstruction progress is separated into two steps in our new algorithm. In step one, we transfer the original two-dimensional (2-D) image reconstruction into a parallel 1-D signal reconstruction procedure, which takes advantage of the superior incoherence property in the phase direction. In step two, using the new k-space data obtained from the 1-D reconstructions, we implement a follow-up 2-D CS reconstruction to produce a better solution, which exploits the inherent correlations between the adjacent lines of 1-D reconstructed signals. We evaluated the performance on various cases of typical MR images, including cardiac cine, brain, foot, and angiogram at the reduction factor up to 10 and compared the results with the conventional CS method. Experiments using the proposed method demonstrated faithful reconstruction of the MR images. Compared with conventional method, the new method achieves more accurate reconstruction results with 2-5 dB gain in peak SNR and higher structural similarity index. The proposed method improves image quality of the reconstructions and suppresses the coherent artefacts introduced by the random phase-encode undersampling.

Data consistency conditions for truncated fanbeam and parallel projections.

In image reconstruction from projections, data consistency conditions (DCCs) are mathematical relationships that express the overlap of information between ideal projections. DCCs have been incorporated in image reconstruction procedures for positron emission tomography, single photon emission computed tomography, and x-ray computed tomography (CT). Building on published fanbeam DCCs for nontruncated projections along a line, the authors recently announced new DCCs that can be applied to truncated parallel projections in classical (two-dimensional) image reconstruction. These DCCs take the form of polynomial expressions for a weighted backprojection of the projections. The purpose of this work was to present the new DCCs for truncated parallel projections, to extend these conditions to truncated fanbeam projections on a circular trajectory, to verify the conditions with numerical examples, and to present a model of how DCCs could be applied with a toy problem in patient motion estimation with truncated projections. A mathematical derivation of the new parallel DCCs was performed by substituting the underlying imaging equation into the mathematical expression for the weighted backprojection and demonstrating the resulting polynomial form. This DCC result was extended to fanbeam projections by a substitution of parallel to fanbeam variables. Ideal fanbeam projections of a simple mathematical phantom were simulated and the DCCs for these projections were evaluated by fitting polynomials to the weighted backprojection. For the motion estimation problem, a parametrized motion was simulated using a dynamic version of the mathematical phantom, and both noiseless and noisy fanbeam projections were simulated for a full circular trajectory. The fanbeam DCCs were applied to extract the motion parameters, which allowed the motion contamination to be removed from the projections. A reconstruction was performed from the corrected projections. The mathematical derivation revealed the anticipated polynomial behavior. The conversion to fanbeam variables led to a straight-forward weighted fanbeam backprojection which yielded the same function and therefore the same polynomial behavior as occurred in the parallel case. Plots of the numerically calculated DCCs showed polynomial behavior visually indistinguishable from the fitted polynomials. For the motion estimation problem, the motion parameters were satisfactorily recovered and ten times more accurately for the noise-free case. The reconstructed images showed that only a faint trace of the motion blur was still visible after correction from the noisy motion-contaminated projections. New DCCs have been established for fanbeam and parallel projections, and these conditions have been validated using numerical experiments with truncated projections. It has been shown how these DCCs could be applied to extract parameters of unwanted physical effects in tomographic imaging, even with truncated projections.

Two-dimensional Projection and Image Reconstruction

Two-dimensional Projection and Image Reconstruction

Quantitative Assessment of the Human Retinal Microvasculature With or Without Vascular Comorbidity

To determine whether morbidity and mortality in patients with cardiovascular comorbidities, but no known ocular disease, is related to demonstrable quantitative changes in the retinal microvasculature. Eleven eyes from 8 donors with cardiovascular comorbidities as a diseased group were compared with 16 eyes from 14 donors free from vascular disease as a control group. All eyes had no known ocular disease. The retina was perfusion-fixed and labeled for endothelial f-actin using micro-cannulation techniques. The retinal microvasculature 3 mm superior to the optic disc was imaged with confocal scanning laser microscopy. Quantitative measurements of capillary diameter and density were obtained using two-dimensional image reconstructions. Pathological vascular changes in other regions of the retinal vasculature found in the diseased group were identified and reconstructed in two or three dimensions. Capillary densities were significantly different between each capillary network in the diseased group. There was a significant decrease in density between both the nerve fiber layer and retinal ganglion cell layer of the diseased group when compared with those layers in the control eyes. There were pathological vascular changes including microaneurysms and tortuous, dilated venules identified in the diseased group. Cardiovascular comorbidities may be associated with changes to the capillary density within the human retinal microvasculature, before the manifestation of known ocular diseases. These differences in capillary density may have important correlations with neuronal function and facilitates the basis of understanding pathogenic mechanisms in retinal vascular disease.

A projection-based approach to diffraction tomography on curved boundaries

An approach to diffraction tomography is investigated for two-dimensional image reconstruction of objects surrounded by an arbitrarily-shaped curve of sources and receivers. Based on the integral theorem of Helmholtz and Kirchhoff, the approach relies upon a valid choice of the Green’s functions for selected conditions along the (possibly-irregular) boundary. This allows field projections from the receivers to an arbitrary external location. When performed over all source locations, it will be shown that the field caused by a hypothetical source at this external location is also known along the boundary. This field can then be projected to new external points that may serve as a virtual receiver. Under such a reformation, data may be put in a form suitable for image construction by synthetic aperture methods. Foundations of the approach are shown, followed by a mapping technique optimized for the approach. Examples formed from synthetic data are provided.

Two-dimensional image reconstruction with spectrally-randomized ultrasound signals

An ultrasound imaging method using unfocused frequency-randomized transmissions and image reconstruction from data received by a single element is experimentally demonstrated. The elements of an ultrasound imaging array are randomly assigned different frequencies and driven by a multicycle sinusoidal burst. The resulting acoustic field is spectrally unique and target localization is possible based on the a priori knowledge of this field. A 64-element phased array driven by arbitrary waveform generators is used in the experiments. Transmission frequencies range from 2.00 to 2.64 MHz with 10 kHz resolution. One element of the array is reserved for receiving backscattered signals and an image is reconstructed from the signals received by this single element. Reconstruction is based on cross-correlation of the received data with transmitted bursts to obtain radial elliptical projections. Multiple projections are obtained from single received data, which are back-projected to obtain an image. Successful target localization is made possible through multiple frequency-randomized acquisitions. The performance of the method is measured using images of a single point target. These images are quantified and analyzed in terms of their point spread function (PSF) and SNR. Optimum imaging parameters, such as the number of acquisitions, transmit burst length, and number of possible receivers, are obtained through further analysis of SNR. Images obtained with the frequency-randomized transmission method compared well with the performance measurements of a typical B-mode acquisition. It is demonstrated that the frequency-randomized method provides images superior to B-mode images in terms of PSF. The two-point discrimination threshold is measured to be 2 mm in the lateral and azimuth directions.

Two-Dimensional Medical Image 3D Visualization System’s Realization

With the development of virtual reality application in the medical field, two-dimensional medical image of the three-dimensional visualization technology made possible. Surgery gets into minimally invasive operation microscopy Era, and gradually becomes a new research hotspot. This paper studies the realization of two-dimensional medical im-age 3D reconstruction visualization system method, and the overall process and management module. Using the main technology of VTK (The Visualization Toolkit) to achieve a two-dimensional medical image three-dimensional visua-lization system, which can help the physician to obtain help clinical diagnosis Information and play an important role in treatment, accurate positioning in diseased tissue and tumor early diagnosis.

Sparse Signal Reconstruction via ECME Hard Thresholding

We propose a probabilistic model for sparse signal reconstruction and develop several novel algorithms for computing the maximum likelihood (ML) parameter estimates under this model. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown deterministic sparse signal component and a zero-mean white Gaussian component with an unknown variance. Our reconstruction schemes are based on an expectation-conditional maximization either (ECME) iteration that aims at maximizing the likelihood function with respect to the unknown parameters for a given signal sparsity level. Compared with the existing iterative hard thresholding (IHT) method, the ECME algorithm contains an additional multiplicative term and guarantees monotonic convergence for a wide range of sensing (regression) matrices. We propose a double overrelaxation (DORE) thresholding scheme for accelerating the ECME iteration. We prove that, under certain mild conditions, the ECME and DORE iterations converge to local maxima of the likelihood function. The ECME and DORE iterations can be implemented exactly in small-scale applications and for the important class of large-scale sensing operators with orthonormal rows used e.g., partial fast Fourier transform (FFT). If the signal sparsity level is unknown, we introduce an unconstrained sparsity selection (USS) criterion and a tuning-free automatic double overrelaxation (ADORE) thresholding method that employs USS to estimate the sparsity level. We compare the proposed and existing sparse signal reconstruction methods via one-dimensional simulation and two-dimensional image reconstruction experiments using simulated and real X-ray CT data.

High-throughput analysis of mouse embryos by magnetic resonance imaging.

Genetic studies in the mouse are crucial for uncovering new genes and signaling pathways associated with development. The identification of murine models with developmental malformations in high-throughput mutagenesis screens is made difficult because, after mid-embryogenesis, the embryo is opaque. Traditional phenotyping methods such as histological sectioning are labor intensive and destructive. We have developed and optimized a novel method for high-throughput multiembryo magnetic resonance imaging (MRI). Here we present our method for processing 32 mouse embryos for analysis by MRI. We describe the MR system, imaging software, and the reconstruction of two-dimensional (2D) and three-dimensional (3D) images. We also discuss the applications of this technique, highlight its advantages, and point out some disadvantages. Using this approach, we can identify developmental malformations in mutant embryos at high spatial resolution (voxel size 25.4 × 25.4 × 24.4 µm). This technique can be easily used for mouse mutagenesis screens and thus provides an important tool for identifying new mouse models for human diseases.

2D Microwave Image Reconstruction of Breast Cancer Detector Using a Simplex Method and Method of Moments

This paper presents a tumor detection system for breast cancer that utilizes two-dimensional (2D) image reconstruction with microwave tomographic imaging. The breast cancer detection system under development consists of 16 transmit/receive antennas, and the microwave tomography system operates at 900 MHz. To solve a 2D inverse scattering problem, the method of moments (MoM) is employed for forward problem solving, and the simplex method employed as an optimization algorithm. The results of the reconstructed image show that the method accurately shows the position of a breast tumor.

Doppler encoded excitation pattern tomographic optical microscopy

Most far-field optical imaging systems rely on lenses and spatially resolved detection to probe distinct locations on the object. We describe and demonstrate a high-speed wide-field approach to imaging that instead measures the complex spatial Fourier transform of the object by detecting its spatially integrated response to dynamic acousto-optically synthesized structured illumination. Tomographic filtered backprojection is applied to reconstruct the object in two or three dimensions. This technique decouples depth of field and working distance from resolution, in contrast to conventional imaging, and can be used to image biological and synthetic structures in fluoresced or scattered light employing coherent or broadband illumination. We discuss the electronically programmable transfer function of the optical system and its implications for imaging dynamic processes. We also explore wide-field fluorescence imaging in scattering media by coherence gating. Finally, we present two-dimensional high-resolution tomographic image reconstructions in both scattered and fluoresced light demonstrating a thousandfold improvement in the depth of field compared to conventional lens-based microscopy.

Poster Board Number: 56: Morphologic Evaluation and Characteristic Classification of Facial Asymmetry Using 3D-CT

Statement of the Problem: Despite improvements in the diagnosis and surgical treatment of orthognathic patients, a more accurate approach to understanding characteristics of facial asymmetry is needed. However, until now, a systemic classification method for patients with facial asymmetry has not existed, and the common use of two-dimensional images for analysis has many limitations. However, reconstruction of two-dimensional images into three-dimensional images decreases magnification and distortion errors, making it possible to determine quantitative measurements for anatomical structures.

Two-Dimensional Lorentz Force Image Reconstruction for Magnetoacoustic Tomography with Magnetic Induction

Magnetoacoustic tomography with magnetic induction has shown potential applications in imaging the electrical impedance for biological tissues. We present a novel methodology for the inverse problem solution of the 2-D Lorentz force distribution reconstruction based on the acoustic straight line propagation theory. The magnetic induction and acoustic generation as well as acoustic detection are theoretically provided as explicit formulae and also validated by the numerical simulations for a multilayered cylindrical phantom model. The reconstructed 2-D Lorentz force distribution reveals not only the conductivity configuration in terms of shape and size but also the amplitude value of the Lorentz force in the examined layer. This study provides a basis for further study of conductivity distribution reconstruction of MAT-MI in medical imaging.

On the v-line radon transform and its imaging applications.

Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results.