A MatLAB Based Virtual Phantom for 2D Electrical Impedance Tomography (MatVP2DEIT): Studying the Medical Electrical Impedance Tomography Reconstruction in Computer

Electrical Impedance Tomography (EIT) is a computerized medical imaging technique which reconstructs the electrical impedance images of a domain under test from the boundary voltage-current data measured by an EIT electronic instrumentation using an image reconstruction algorithm. Being a computed tomography technique, EIT injects a constant current to the patient's body through the surface electrodes surrounding the domain to be imaged (Omega) and tries to calculate the spatial distribution of electrical conductivity or resistivity of the closed conducting domain using the potentials developed at the domain boundary (partial derivative Omega). Practical phantoms are essentially required to study, test and calibrate a medical EIT system for certifying the system before applying it on patients for diagnostic imaging. Therefore, the EIT phantoms are essentially required to generate boundary data for studying and assessing the instrumentation and inverse solvers a in EIT. For proper assessment of an inverse solver of a 2D EIT system, a perfect 2D practical phantom is required. As the practical phantoms are the assemblies of the objects with 3D geometries, the developing of a practical 2D-phantom is a great challenge and therefore, the boundary data generated from the practical phantoms with 3D geometry are found inappropriate for assessing a 2D inverse solver. Furthermore, the boundary data errors contributed by the instrumentation are also difficult to separate from the errors developed by the 3D phantoms. Hence, the errorless boundary data are found essential to assess the inverse solver in 2D EIT. In this direction, a MatLAB-based Virtual Phantom for 2D EIT (MatVP2DEIT) is developed to generate accurate boundary data for assessing the 2D-EIT inverse solvers and the image reconstruction accuracy. MatVP2DEIT is a MatLAB-based computer program which simulates a phantom in computer and generates the boundary potential data as the outputs by using the combinations of different phantom parameters as the inputs to the program. Phantom diameter, inhomogeneity geometry (shape, size and position), number of inhomogeneities, applied current magnitude, background resistivity, inhomogeneity resistivity all are set as the phantom variables which are provided as the input parameters to the MatVP2DEIT for simulating different phantom configurations. A constant current injection is simulated at the phantom boundary with different current injection protocols and boundary potential data are calculated. Boundary data sets are generated with different phantom configurations obtained with the different combinations of the phantom variables and the resistivity images are reconstructed using EIDORS. Boundary data of the virtual phantoms, containing inhomogeneities with complex geometries, are also generated for different current injection patterns using MatVP2DEIT and the resistivity imaging is studied. The effect of regularization method on the image reconstruction is also studied with the data generated by MatVP2DEIT. Resistivity images are evaluated by studying the resistivity parameters and contrast parameters estimated from the elemental resistivity profiles of the reconstructed phantom domain. Results show that the MatVP2DEIT generates accurate boundary data for different types of single or multiple objects which are efficient and accurate enough to reconstruct the resistivity images in EIDORS. The spatial resolution studies show that, the resistivity imaging conducted with the boundary data generated by MatVP2DEIT with 2048 elements, can reconstruct two circular inhomogeneities placed with a minimum distance (boundary to boundary) of 2 mm. It is also observed that, in MatVP2DEIT with 2048 elements, the boundary data generated for a phantom with a circular inhomogeneity of a diameter less than 7% of that of the phantom domain can produce resistivity images in EIDORS with a 1968 element mesh. Results also show that the MatVP2DEIT accurately generates the boundary data for neighbouring, opposite reference and trigonometric current patterns which are very suitable for resistivity reconstruction studies. MatVP2DEIT generated data are also found suitable for studying the effect of the different regularization methods on reconstruction process. Comparing the reconstructed image with an original geometry made in MatVP2DEIT, it would be easier to study the resistivity imaging procedures as well as the inverse solver performance. Using the proposed MatVP2DEIT software with modified domains, the cross sectional anatomy of a number of body parts can be simulated in PC and the impedance image reconstruction of human anatomy can be studied.

Improving tangential resolution with a modified delay-and-sum reconstruction algorithm in photoacoustic and thermoacoustic tomography

Spatial resolution in photoacoustic and thermoacoustic tomography is ultrasound transducer (detector) bandwidth limited. For a circular scanning geometry the axial (radial) resolution is not affected by the detector aperture, but the tangential (lateral) resolution is highly dependent on the aperture size, and it is also spatially varying (depending on the location relative to the scanning center). Several approaches have been reported to counter this problem by physically attaching a negative acoustic lens in front of the nonfocused transducer or by using virtual point detectors. Here, we have implemented a modified delay-and-sum reconstruction method, which takes into account the large aperture of the detector, leading to more than fivefold improvement in the tangential resolution in photoacoustic (and thermoacoustic) tomography. Three different types of numerical phantoms were used to validate our reconstruction method. It is also shown that we were able to preserve the shape of the reconstructed objects with the modified algorithm. (C) 2014 Optical Society of America

Reconstruction from incomplete data in cone-beam tomography

A method for reconstruction of an object f(x) x=(x,y,z) from a limited set of cone-beam projection data has been developed. This method uses a modified form of convolution back-projection and projection onto convex sets (POCS) for handling the limited (or incomplete) data problem. In cone-beam tomography, one needs to have a complete geometry to completely reconstruct the original three-dimensional object. While complete geometries do exist, they are of little use in practical implementations. The most common trajectory used in practical scanners is circular, which is incomplete. It is, however, possible to recover some of the information of the original signal f(x) based on a priori knowledge of the nature of f(x). If this knowledge can be posed in a convex set framework, then POCS can be utilized. In this report, we utilize this a priori knowledge as convex set constraints to reconstruct f(x) using POCS. While we demonstrate the effectiveness of our algorithm for circular trajectories, it is essentially geometry independent and will be useful in any limited-view cone-beam reconstruction.

Image reconstruction with laterally truncated projections in helical cone-beam CT: Linear prediction based projection completion techniques

Lateral or transaxial truncation of cone-beam data can occur either due to the field of view limitation of the scanning apparatus or iregion-of-interest tomography. In this paper, we Suggest two new methods to handle lateral truncation in helical scan CT. It is seen that reconstruction with laterally truncated projection data, assuming it to be complete, gives severe artifacts which even penetrates into the field of view. A row-by-row data completion approach using linear prediction is introduced for helical scan truncated data. An extension of this technique known as windowed linear prediction approach is introduced. Efficacy of the two techniques are shown using simulation with standard phantoms. A quantitative image quality measure of the resulting reconstructed images are used to evaluate the performance of the proposed methods against an extension of a standard existing technique.

Tree-ring based hydroclimate reconstruction over northern Vietnam from Fokienia hodginsii: eighteenth century mega-drought and tropical Pacific influence

We present here the first statistically calibrated and verified tree-ring reconstruction of climate from continental Southeast Asia.The reconstructed variable is March-May (MAM) Palmer Drought Severity Index (PDSI) based on ring widths from 22 trees (42 radial cores) of rare and long-lived conifer, Fokienia hodginsii (Po Mu as locally called) from northern Vietnam. This is the first published tree ring chronology from Vietnam as well as the first for this species. Spanning 535 years, this is the longest cross-dated tree-ring series yet produced from continental Southeast Asia. Response analysis revealed that the annual growth of Fokienia at this site was mostly governed by soil moisture in the pre-monsoon season. The reconstruction passed the calibration-verification tests commonly used in dendroclimatology, and revealed two prominent periods of drought in the mid-eighteenth and late-nineteenth enturies. The former lasted nearly 30 years and was concurrent with a similar drought over northwestern Thailand inferred from teak rings, suggesting a ``mega-drought'' extending across Indochina in the eighteenth century. Both of our reconstructed droughts are consistent with the periods of warm sea surface temperature (SST)anomalies in the tropical Pacific. Spatial correlation analyses with global SST indicated that ENSO-like anomalies might play a role in modulating droughts over the region, with El Nio (warm) phases resulting in reduced rainfall. However, significant correlation was also seen with SST over the Indian Ocean and the north Pacific,suggesting that ENSO is not the only factor affecting the climate of the area. Spectral analyses revealed significant peaks in the range of 53.9-78.8 years as well as in the ENSO-variability range of 2.0 to 3.2 years.

Iterative solution of a class of linear equations with application to reconstruction of three-dimensional object arrays

An iterative algorithm baaed on probabilistic estimation is described for obtaining the minimum-norm solution of a very large, consistent, linear system of equations AX = g where A is an (m times n) matrix with non-negative elements, x and g are respectively (n times 1) and (m times 1) vectors with positive components.

Launch Envelope Optimization of Virtual Sliding Target Guidance Scheme

This paper presents an optimization of the performance of a recently proposed virtual sliding target (VST) guidance scheme in terms of maximization of its launch envelope for three- dimensional (3-D) engagements. The objective is to obtain the launch envelope of the missile using the VST guidance scheme for different lateral launch angles with respect to the line of sight (LOS) and demonstrate its superiority over kinematics-based guidance laws like proportional navigation (PN). The VST scheme uses PN as its basic guidance scheme and exploits the relation between the atmospheric properties, missile aerodynamic characteristics, and the optimal trajectory of the missile. The missile trajectory is shaped by controlling the instantaneous position and the speed of a virtual target which the missile pursues during the midcourse phase. In the proposed method it is shown that an appropriate value of initial position for the virtual target in 3-D, combined with optimized virtual target parameters, can significantly improve the launch envelope performance. The paper presents the formulation of the optimization problem, obtains the approximate models used to make the optimization problem more tractable, and finally presents the optimized performance of the missile in terms of launch envelope and shows significant improvement over kinematic-based guidance laws. The paper also proposes modification to the basic VST scheme. Some simulations using the full-fledged six degrees-of-freedom (6-DOF) models are also presented to validate the models and technique used.

Performance Analysis of Reconstruction Techniques for Frequency-Domain Optical-Coherence Tomography

We address the issue of noise robustness of reconstruction techniques for frequency-domain optical-coherence tomography (FDOCT). We consider three reconstruction techniques: Fourier, iterative phase recovery, and cepstral techniques. We characterize the reconstructions in terms of their statistical bias and variance and obtain approximate analytical expressions under the assumption of small noise. We also perform Monte Carlo analyses and show that the experimental results are in agreement with the theoretical predictions. It turns out that the iterative and cepstral techniques yield reconstructions with a smaller bias than the Fourier method. The three techniques, however, have identical variance profiles, and their consistency increases linearly as a function of the signal-to-noise ratio.

Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances. (C) 2010 Optical Society of America

Image reconstruction by inhomogeneous diffusion for positron emission tomography

In positron emission tomography (PET), image reconstruction is a demanding problem. Since, PET image reconstruction is an ill-posed inverse problem, new methodologies need to be developed. Although previous studies show that incorporation of spatial and median priors improves the image quality, the image artifacts such as over-smoothing and streaking are evident in the reconstructed image. In this work, we use a simple, yet powerful technique to tackle the PET image reconstruction problem. Proposed technique is based on the integration of Bayesian approach with that of finite impulse response (FIR) filter. A FIR filter is designed whose coefficients are determined based on the surface diffusion model. The resulting reconstructed image is iteratively filtered and fed back to obtain the new estimate. Experiments are performed on a simulated PET system. The results show that the proposed approach is better than recently proposed MRP algorithm in terms of image quality and normalized mean square error.

Dynamic programming based optimum non-uniform samples for speech reconstruction and coding

Non-uniform sampling of a signal is formulated as an optimization problem which minimizes the reconstruction signal error. Dynamic programming (DP) has been used to solve this problem efficiently for a finite duration signal. Further, the optimum samples are quantized to realize a speech coder. The quantizer and the DP based optimum search for non-uniform samples (DP-NUS) can be combined in a closed-loop manner, which provides distinct advantage over the open-loop formulation. The DP-NUS formulation provides a useful control over the trade-off between bitrate and performance (reconstruction error). It is shown that 5-10 dB SNR improvement is possible using DP-NUS compared to extrema sampling approach. In addition, the close-loop DP-NUS gives a 4-5 dB improvement in reconstruction error.

Composite MR image reconstruction and unaliasing for general trajectories using neural networks

In rapid parallel magnetic resonance imaging, the problem of image reconstruction is challenging. Here, a novel image reconstruction technique for data acquired along any general trajectory in neural network framework, called ``Composite Reconstruction And Unaliasing using Neural Networks'' (CRAUNN), is proposed. CRAUNN is based on the observation that the nature of aliasing remains unchanged whether the undersampled acquisition contains only low frequencies or includes high frequencies too. Here, the transformation needed to reconstruct the alias-free image from the aliased coil images is learnt, using acquisitions consisting of densely sampled low frequencies. Neural networks are made use of as machine learning tools to learn the transformation, in order to obtain the desired alias-free image for actual acquisitions containing sparsely sampled low as well as high frequencies. CRAUNN operates in the image domain and does not require explicit coil sensitivity estimation. It is also independent of the sampling trajectory used, and could be applied to arbitrary trajectories as well. As a pilot trial, the technique is first applied to Cartesian trajectory-sampled data. Experiments performed using radial and spiral trajectories on real and synthetic data, illustrate the performance of the method. The reconstruction errors depend on the acceleration factor as well as the sampling trajectory. It is found that higher acceleration factors can be obtained when radial trajectories are used. Comparisons against existing techniques are presented. CRAUNN has been found to perform on par with the state-of-the-art techniques. Acceleration factors of up to 4, 6 and 4 are achieved in Cartesian, radial and spiral cases, respectively. (C) 2010 Elsevier Inc. All rights reserved.

On the Nash-Williams′ Lemma in Graph Reconstruction Theory

A generalization of Nash-Williams′ lemma is proved for the Structure of m-uniform null (m − k)-designs. It is then applied to various graph reconstruction problems. A short combinatorial proof of the edge reconstructibility of digraphs having regular underlying undirected graphs (e.g., tournaments) is given. A type of Nash-Williams′ lemma is conjectured for the vertex reconstruction problem.

Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units

Diffuse optical tomographic image reconstruction uses advanced numerical models that are computationally costly to be implemented in the real time. The graphics processing units (GPUs) offer desktop massive parallelization that can accelerate these computations. An open-source GPU-accelerated linear algebra library package is used to compute the most intensive matrix-matrix calculations and matrix decompositions that are used in solving the system of linear equations. These open-source functions were integrated into the existing frequency-domain diffuse optical image reconstruction algorithms to evaluate the acceleration capability of the GPUs (NVIDIA Tesla C 1060) with increasing reconstruction problem sizes. These studies indicate that single precision computations are sufficient for diffuse optical tomographic image reconstruction. The acceleration per iteration can be up to 40, using GPUs compared to traditional CPUs in case of three-dimensional reconstruction, where the reconstruction problem is more underdetermined, making the GPUs more attractive in the clinical settings. The current limitation of these GPUs in the available onboard memory (4 GB) that restricts the reconstruction of a large set of optical parameters, more than 13, 377. (C) 2010 Society of Photo-Optical Instrumentation Engineers. DOI: 10.1117/1.3506216]