ULTRASONIC TOMOGRAPHY IN COMPOSITE MATERIALS

12 - Direct image reconstruction in electrical tomography and its applications

The authors studied certain characteristics of the expectation-maximization (EM) algorithm for image reconstruction in positron emission tomography (PET). They have attempted to speed up the algorithm by performing some time-consuming computation only once, at the initiation stage. They have studied the resulting memory size, disk space, and CPU requirements versus the number of pixels in the reconstructed image and the number of gamma -ray detectors in the tomograph. The convergence and image quality have been studied as a function of the number of iterations performed. Preliminary results are presented. >

While high resolution, regularly gridded observations are generally preferred in remote sensing, actual observations are often not evenly sampled and have lower-than-desired resolution. Hence, there is an interest in resolution enhancement and image reconstruction. This paper discusses a general theory and techniques for image reconstruction and creating enhanced resolution images from irregularly sampled data. Using irregular sampling theory, we consider how the frequency content in aperture function-attenuated sidelobes can be recovered from oversampled data using reconstruction techniques, thus taking advantage of the high frequency content of measurements made with nonideal aperture filters. We show that with minor modification, the algebraic reconstruction technique (ART) is functionally equivalent to Grochenig's (1992) irregular sampling reconstruction algorithm. Using simple Monte Carlo simulations, we compare and contrast the performance of additive ART, multiplicative ART, and the scatterometer image reconstruction (SIR) (a derivative of multiplicative ART) algorithms with and without noise. The reconstruction theory and techniques have applications with a variety of sensors and can enable enhanced resolution image production from many nonimaging sensors. The technique is illustrated with ERS-2 and SeaWinds scatterometer data.

Image reconstruction in electrical impedance tomography using the sensitivity theorem is generally based on the assumption that the initial conductivity distribution of the body being imaged is uniform. The technique of image reconstruction using this method is described and reconstructed images are presented. Improvements in image quality and accuracy are demonstrated when accurate a priori `anatomical' information, in the form of a model of the distribution of conductivity within the region to be imaged, is used to construct the sensitivity matrix. In practice correct a priori information is not available, for example the conductivity values within the various anatomical regions will not be known. An iterative algorithm is presented which allows the conductivity parameters of the a priori model to be determined during reconstruction. Keywords: electrical impedance tomography, image reconstruction, a priori information

BackgroundAfter the release of compressed sensing (CS) theory, reconstruction algorithms from sparse and incomplete data have shown great improvements in diminishing artifacts of missing data. Following this progress, both local and non-local regularization induced iterative reconstructions have been actively used in limited view angle imaging problems.MethodsIn this study, a 3D iterative image reconstruction method (ART + TV)NLM was introduced by combining local total variation (TV) with non-local means (NLM) filter. In the first step, TV minimization was applied to the image obtained by algebraic reconstruction technique (ART) for background noise removal with preserving edges. In the second step, NLM is used in order to suppress the out of focus slice blur which is the most existent image artifact in tomosynthesis imaging. NLM exploits the similar structures to increase the smoothness in the image reconstructed by ART + TV.ResultsA tomosynthesis system and a 3D phantom were designed to perform simulations to show the superior performance of our proposed (ART + TV)NLM over ART and widely used ART + TV methods. Visual inspections show a significant improvement in image quality compared to ART and ART + TV.ConclusionsRMSE, Structure SIMilarity (SSIM) value and SNR of a specific layer of interest (LOI) showed that by proper selection of NLM parameters, significant improvements can be achieved in terms of convergence rate and image quality.

Resolution in ART: An experimental investigation of the resolving power of an algebraic picture reconstruction technique

Fluorescence diffuse optical tomography (fDOT) is a noninvasive imaging technique that makes it possible to quantify the spatial distribution of fluorescent tracers in small animals. fDOT image reconstruction is commonly performed by means of iterative methods such as the algebraic reconstruction technique (ART). The useful results yielded by more advanced l1-regularized techniques for signal recovery and image reconstruction, together with the recent publication of Split Bregman (SB) procedure, led us to propose a new approach to the fDOT inverse problem, namely, ART-SB. This method alternates a cost-efficient reconstruction step (ART iteration) with a denoising filtering step based on minimization of total variation of the image using the SB method, which can be solved efficiently and quickly. We applied this method to simulated and experimental fDOT data and found that ART-SB provides substantial benefits over conventional ART.

Image reconstruction for ultrasonic transmission tomography (UTT) is a complex problem. Due to the limited diffusion angle of ultrasonic transducers, few useful data are received from the opposite transducers so the image reconstruction problem is ill-posed. The traditional logic backprojection (LBP) algorithm cannot sufficiently deal with the sparse characteristic of measurement data. In this article, transducers with a large diffusion angle are designed to collect more information. A sparse preimaged orthogonal matching pursuit (SP-OMP) algorithm is presented for UTT image sparse reconstruction. The performance of the proposed algorithm is experimentally evaluated by a UTT system versus classical algorithms such as LBP, algebra reconstruction technique (ART), simultaneous iteration reconstruction (Sirt), Tikhonov, and L1-regularization. The quality parameters such as mean square error (MSE), position error (PE), size error (SE), relative error (RE), and correlation coefficient (CC) are surveyed which indicated that the SP-OMP algorithm could provide higher quality images than those provided by the conventional image reconstruction algorithms.

A comparison of regularization operators for noisy gamma-ray tomographic reconstruction

Tomography is a method for reconstructing an image of some object cross-section using emitted electromagnetics waves. Some techniques frequently applied for tomography covers backprojection, Algebraic Reconstruction Technique (ART), and backpropagation. In this paper, frequency selection and image reconstruction techniques for tomography are investigated using parallel-beam projection at microwave frequency. The use of some microwave frequencies of 1.5GHz, 3GHz, and 4.5GHz is intended to determine the characteristics and effect of selected frequency in producing the reconstructed image. A perforated wood is used as a target which is represented by a wood of tree trunk for object measurement. Here, the filtered backprojection and backpropagation techniques are implemented for reconstructing the image of measured object. From the result, it shows that the reconstructed image using backpropagation technique at the frequency of 3GHz has better image quality compared to the ones using filtered backprojection technique.

Fluorescence diffuse optical tomography (FDOT) based on the total light approach is developed. The continuous wave light is used for excitation in this system. The reconstruction algorithm is based on the total light approach that reconstructs the absorption coefficients increased by the fluorophore. Additionally we propose noise reduction using the algebraic reconstruction technique (ART) incorporating the truncated singular value decomposition (TSVD). Numerical and phantom experiments show that the developed system successfully reconstructs the fluorophore concentration in the biological media, and the ART with TSVD alleviates the influence of noises. In vivo experiment demonstrated that the developed FDOT system localized the fluorescent agent which was concentrated in the cancer transplanted into a kidney in a mouse.

The accuracy of the system model in an iterative reconstruction algorithm greatly affects the quality of reconstructed positron emission tomography (PET) images. For efficient computation in reconstruction, the system model in PET can be factored into a product of a geometric projection matrix and sinogram blurring matrix, where the former is often computed based on analytical calculation, and the latter is estimated using Monte Carlo simulations. Direct measurement of a sinogram blurring matrix is difficult in practice because of the requirement of a collimated source. In this work, we propose a method to estimate the 2D blurring kernels from uncollimated point source measurements. Since the resulting sinogram blurring matrix stems from actual measurements, it can take into account the physical effects in the photon detection process that are difficult or impossible to model in a Monte Carlo (MC) simulation, and hence provide a more accurate system model. Another advantage of the proposed method over MC simulation is that it can easily be applied to data that have undergone a transformation to reduce the data size (e.g., Fourier rebinning). Point source measurements were acquired with high count statistics in a relatively fine grid inside the microPET II scanner using a high-precision 2D motion stage. A monotonically convergent iterative algorithm has been derived to estimate the detector blurring matrix from the point source measurements. The algorithm takes advantage of the rotational symmetry of the PET scanner and explicitly models the detector block structure. The resulting sinogram blurring matrix is incorporated into a maximum a posteriori (MAP) image reconstruction algorithm. The proposed method has been validated using a 3 × 3 line phantom, an ultra-micro resolution phantom and a 22Na point source superimposed on a warm background. The results of the proposed method show improvements in both resolution and contrast ratio when compared with the MAP reconstruction with a MC-based sinogram blurring matrix, and one without a detector response model. The reconstruction time is unaffected by the new method since the blurring component takes a relatively small part of the overall reconstruction time. The proposed method can be applied to other PET scanners for human and animal imaging.

Objectives Global navigation satellite system(GNSS) tomography, characterized by reconstructing the three-dimensional distribution of the atmospheric water vapor, has proved its capacity for studying the extreme weather events. The ill-conditioned problem resulting from the GNSS acquisition geometry is the critical issue of the GNSS tomography system. Algebraic reconstruction techniques, with the advantages of simple iteration and fast convergence, has been widely applied to the tropospheric tomography. However, the error allocation principle based on the intersection length of GNSS rays with each ray-voxel affects the accuracy of tomographic results. An improved adaptive algebraic reconstruction techniques are proposed to address this problem. Methods In view of the unreasonable error allocation in the traditional algorithm, we suggest a new error allocation principle based on the variation of water vapor density(WVD) in voxels for the adaptive algorithms, in which the product of the intersection length and WVD is considered as a new principle to redistribute the difference between the GNSS slant water vapor(SWV)and the reconstructed SWV. Besides, the weight matrix model of elevation angles is introduced to the improved algorithm to optimize the tomographic results. Results The new algorithms are tested by measured data from Xuzhou continuously operating reference stations(CORS) network and radiosonde during July2016. Experimental results reveal that the WVD derived from the adaptive algorithms performs better than that of the general algorithms in root mean squared error(RMSE), standard deviation(STD) and mean absolute error(MAE), and the RMSE is decreased by 25.91%, 15.81%, and 24.64% for adaptive algebraic reconstruction technique(AART), adaptive multiplicative algebraic reconstruction technique(AMART)and adaptive simultaneous iterative reconstruction technique(ASIRT) respectively. Under the conditions of light rain, moderate rain and heavy rain, the adaptive algorithms retrieve better water vapor profile than the traditional ones. Conclusions Overall, the water vapor profile derived from the adaptive algorithms agrees with the radiosonde distribution better than the traditional algorithms, which reveals the advantage of the proposed method on optimizing the tomography solutions.

In order to study properties of the maximum-likelihood-estimator (MLE) algorithm for image reconstruction in positron-emission tomography (PET), the algorithm is applied to data obtained by the ECAT-III tomograph from a brain phantom. The procedure for subtracting accidental coincidences from the data stream generated by this physical phantom is such that the resultant data are not Poisson distributed. This makes the present investigation different from other investigations based on computer-simulated phantoms. It is shown that the MLE algorithm is robust enough to yield comparatively good images, especially when the phantom is in the periphery of the field of view, even though the underlying assumption of the algorithm is violated. A stopping rule derived earlier and allowing the user to stop the iterative process before the images begin to deteriorate is tested. Since the rule is based on the Poisson assumption, it does not work well with the presently available data, although it is successful with computer-simulated Poisson data. >

Several algorithms for image reconstruction in positron emission tomography (PET) have been described in the medical and statistical literature. We study a continuous idealization of the PET reconstruction problem, considered as an example of bivariate density estimation based on indirect observations. Given a large sample of indirect observations, we consider the size of the equivalent sample of observations, whose original exact positions would allow equally accurate estimation of the image of interest. Both for indirect and for direct observations, we establish exact minimax rates of convergence of estimation, for all possible estimators, over suitable smoothness classes of functions. A key technical device is a modulus of continuity appropriate to global function estimation. For indirect data and (in practice unobservable) direct data, the rates for mean integrated square error are $n^{-p/(p + 2)}$ and $(n/\\log n)^{-p/(p + 1)}$, respectively, for densities in a class corresponding to bounded square-integrable $p$th derivatives. We obtain numerical values for equivalent sample sizes for minimax linear estimators using a slightly modified error criterion. Modifications of the model to incorporate attenuation and the third dimension effect do not affect the minimax rates. The approach of the paper is applicable to a wide class of linear inverse problems.