Simultaneous Iterative Reconstruction Technique Algorithm Research Articles

SIRT methods for the iterative solution of sparse OPT data reconstruction

Optical projection tomography (OPT) is an advanced three-dimensional (3D) imaging technology, which uses the filtered backprojection (FBP) algorithm to recover the 3D volume with sufficient number of projections. As to in vivo imaging, it is urgent to reduce the number of projections because the acquisition time could be minimized. However, reconstructing from undersampled OPT data can lead to artifacts and the decline in image quality. The simultaneous iterative reconstruction technique (SIRT) is introduced to remove artifacts and improve the image quality. The image qualities reconstructed from FBP and SIRT separately are compared, and the structural similarity and peak signal-to-noise ratio are calculated. Through simulated phantoms and OPT data of in vivo zebrafish embryo, SIRT consistently outperforms FBP in terms of reduced artifacts and enhanced image contrast especially when the projection numbers are reduced. SIRT method can provide high-quality reconstruction with 50 or fewer projections, thereby significantly reducing the minimum acquisition time and light dose while maintaining reconstruction quality. Through optimization and GPU acceleration, the SIRT algorithm can converge faster so as to reduce the image processing time. To our knowledge, this is the first time one SIRT algorithm is used for reconstruction of sparse OPT data. The experimental results show that SIRT algorithm outperform FBP especially when the number of projections is reduced. In addition, SIRT performs better in the preservation of vascular signal, which is significant for the monitoring of angiogenesis.

Mapping conduits in two-dimensional heterogeneous karst aquifers using hydraulic tomography

Hydraulic tomography (HT) is a well-established approach to yield the spatial distribution of hydraulic conductivity of an aquifer. This work explores the potential of HT for the characterization of the distribution and connectivity of conduits in a two-dimensional sandbox and its corresponding synthetic aquifer. Two inversion techniques were implemented and compared: the geostatistics-based inversion which uses the simultaneous successive linear estimator (SimSLE) algorithm to conduct stochastic inversions on the transient hydraulic heads, and the travel time-based inversion which employs the simultaneous iterative reconstruction technique (SIRT) algorithm on the hydraulic travel times for tomography reconstructions. Four artificial karst conduits of different geometries were placed in an aquifer of layer with different hydraulic conductivities. We conducted 6 pumping tests at 6 different locations, and the resultant pressure responses were recorded at 42 observation points in both the sandbox and the corresponding synthetic aquifer. The measured data were then used for the inversion of hydraulic diffusivity using the SimSLE and SIRT algorithms. Our results show that both algorithms were able to approximately identify the embedded karst conduits and yield similar hydraulic diffusivity distribution. Statistically, the travel time-based inversion re-constructed high-contrast diffusivities which clearly differentiate the karst structures from the surrounding matrix. The geostatistics-based SimSLE algorithm yields a better agreement on the positions and the shapes of the embedded karst structures, compared to those obtained by the travel time-based SIRT algorithm. Uncertainties and limitations of our results are also discussed in this work, followed by recommendations on hydraulic tests in karst aquifers.

Temperature Distribution Reconstruction Method for Acoustic Tomography Based on Compressed Sensing.

Acoustic tomography (AT) is one of a few non-contact measurement techniques that can present information about the temperature distribution. Its successful application greatly depends on the performance of the reconstruction algorithm. In this paper, a temperature distribution reconstruction method based on compressed sensing (CS) is proposed. Firstly, a measurement matrix of an AT system in a CS framework is established. Secondly, a sparse basis is selected based on the mutual coherence between the measurement matrix and sparse basis. Thirdly, an improvement of the orthogonal matching pursuit (OMP) algorithm, called the IMOMP algorithm, is proposed for pursuing efficiency in recovering sparse signals. Reconstruction experiments of Gaussian sparse signals showed that IMOMP was better than OMP in both success ratio and running time, and the selection method of sparse basis was effective. Finally, a temperature distribution reconstruction algorithm based on compressed sensing, that is, the CS-IMOMP algorithm, is proposed. Simulation and experiment results show that, compared with the least square algorithm and the Simultaneous Iterative Reconstruction Technique algorithm, the CS-IMOMP algorithm has smaller reconstruction errors and provides more accurate information about the temperature distribution.

A Numerical Study on Travel Time Based Hydraulic Tomography Using the SIRT Algorithm with Cimmino Iteration

Travel time based hydraulic tomography is a technique for reconstructing the spatial distribution of aquifer hydraulic properties (e.g., hydraulic diffusivity). Simultaneous Iterative Reconstruction Technique (SIRT) is a widely used algorithm for travel time related inversions. Due to the drawbacks of SIRT implementation in practice, a modified SIRT with Cimmino iteration (SIRT-Cimmino) is proposed in this study. The incremental correction is adjusted, and an iteration-dependent relaxation parameter is introduced. These two modifications enable an appropriate speed of convergence, and the stability of the inversion process. Furthermore, a new result selection rule is suggested to determine the optimal iteration step and its corresponding result. SIRT-Cimmino and SIRT are implemented and verified by using two numerical aquifer models with different predefined (“true”) diffusivity distributions, where high diffusivity zones are embedded in a homogenous low diffusivity field. Visual comparison of the reconstructions shows that the reconstruction based on SIRT-Cimmino demonstrates the aquifer’s hydraulic features better than the conventional SIRT algorithm. Root mean square errors and correlation coefficients are also used to quantitatively evaluate the performance of the inversion. The reconstructions based on SIRT-Cimmino are found to preserve the connectivity of the high diffusivity zones and to provide a higher structural similarity to the “true” distribution.

Computed Laminography of CFRP Using an X-Ray Cone-Beam and Robotic Sample Manipulator Systems

Carbon fiber-reinforced polymers (CFRPs) are of interest to the aerospace sector for meeting future CO2 emission targets due to their weight reduction potential. However, the detection of structural and matrix defects is crucial for determining the performance and suitability of CFRPs in current and future generations of aircraft. Computed laminography (CL), a well-established nondestructive testing method, is well suited to the scanning of CFRP components with large aspect ratios, for which the conventional computed tomography (CT) is less suitable. Utilizing an existing Nikon Metrology custom build X-ray CT scanner, two lift-in lift-out robotic sample manipulator systems are used to extend the capability of the system and allow the exploration of atypical scanning geometries. Implementing raster and limited angle trajectories, reconstructions using the ASTRA Tomography Toolbox and the Simultaneous Iterative Reconstruction Technique algorithm are able to show structural defects in CFRPs, despite the reduced information inherent with CL systems. This paper reports on the system design and initial experiments that demonstrate benefits and drawbacks of different design options and scanning trajectory choices.

OA158] Noise equivalent number of quanta (NEQ): A tool for choosing the optimal reconstruction algorithm in computed tomography (CT)

Purpose Evaluate optimal reconstruction algorithm and voxel size for a breast CT system using NEQ. Methods CT scans of a wire phantom and a homogeneous cylindrical sample have been performed using a tomographic acquisition system for breast-CT with synchrotron radiation. By setting a monochromatic beam of 38 KeV , the images have been acquired using a CdTe photon-counting detector with a pixel size of 60 μ m. The optimal CT reconstruction algorithm has been investigated comparing the Filtered Back Projection (FBP), the Simultaneous Algebraic Reconstruction Technique (SART) and the Simultaneous Iterative Reconstruction Technique (SIRT). CT images have been reconstructed using two voxel sizes ( V 60 = 60 3 μ m3 and V 120 = 120 3 μ m3). The spatial resolution and the noise have been evaluated on CT reconstructions respectively trough the modulation transfer function (MTF) and the normalized noise power spectrum (NNPS). MTF has been evaluated with the thin wire method and the NNPS has been measured on the CT reconstructions of the homogeneous sample. The NEQ is defined as the ratio between the squared MTF and the NNPS. It is a measure of the signal to noise ratio in frequency domain and has been used to compare the performances of the considered reconstruction algorithms. Results For both used voxel sizes, compared to SART and FBP algorithms, SIRT algorithm shows highest values of NEQ for all accessible frequencies. Apart from the reconstruction algorithm, compared to V 60 , V 120 lead to better NEQ values for frequencies below 3.3 mm - 1 thus, for this system, details with diameter lower than 300 μ m are better resolved by the smallest voxel size available. Conclusions Summarizing information about spatial resolution and noise, NEQ is an extremely comprehensive metric which contains all the key issues for the global image quality assessment. For a given CT system, the comparison between NEQ curves measured on CT reconstructions provides a general method for choosing the best reconstruction algorithm and the voxel size to be used for achieving optimal performances in terms of spatial resolution and noise.

A methodology for finding the optimal iteration number of the SIRT algorithm for quantitative Electron Tomography

The SIRT (Simultaneous Iterative Reconstruction Technique) algorithm is commonly used in Electron Tomography to calculate the original volume of the sample from noisy images, but the results provided by this iterative procedure are strongly dependent on the specific implementation of the algorithm, as well as on the number of iterations employed for the reconstruction. In this work, a methodology for selecting the iteration number of the SIRT reconstruction that provides the most accurate segmentation is proposed. The methodology is based on the statistical analysis of the intensity profiles at the edge of the objects in the reconstructed volume. A phantom which resembles a a carbon black aggregate has been created to validate the methodology and the SIRT implementations of two free software packages (TOMOJ and TOMO3D) have been used.

Preconditioning of projected SIRT algorithm for electromagnetic tomography

For Electromagnetic Tomography (EMT) Techniques, image reconstruction is one of the crucial steps, which directly affects the quality of reconstruction and real-time performance of the EMT system. Following analyzing a pre-iterative method for SIRT (simultaneous iterative reconstruction technique) algorithm, a preconditioning for the projected SIRT is proposed to accelerate the image reconstruction speed and alleviate the ill-posed nature of the EMT inverse problem. Experimental tests confirm that the quality of the reconstructed images using the preconditioning algorithm is enhanced with only a small number of iterations required.

Derivation of site‐specific relationships between hydraulic parameters and p‐wave velocities based on hydraulic and seismic tomography

In this study, hydraulic and seismic tomographic measurements were used to derive a site‐specific relationship between the geophysical parameter p‐wave velocity and the hydraulic parameters, diffusivity and specific storage. Our field study includes diffusivity tomograms derived from hydraulic travel time tomography, specific storage tomograms, derived from hydraulic attenuation tomography, and p‐wave velocity tomograms, derived from seismic tomography. The tomographic inversion was performed in all three cases with the Simultaneous Iterative Reconstruction Technique algorithm, using a ray tracing technique with curved trajectories. The experimental set up was designed such that the p‐wave velocity tomogram overlaps the hydraulic tomograms by half. The experiments were performed at a well‐characterized sand and gravel aquifer, located in the Leine River valley near Göttingen, Germany. Access to the shallow subsurface was provided by direct‐push technology. The high spatial resolution of hydraulic and seismic tomography was exploited to derive representative site‐specific relationships between the hydraulic and geophysical parameters, based on the area where geophysical and hydraulic tests were performed. The transformation of the p‐wave velocities into hydraulic properties was undertaken using a k‐means cluster analysis. Results demonstrate that the combination of hydraulic and geophysical tomographic data is a promising approach to improve hydrogeophysical site characterization.

Convergence rate calculation of simultaneous iterative reconstruction technique algorithm for diffuse optical tomography image reconstruction: A feasibility study

Diffuse optical tomography (DOT) is an emerging technique for functional biological imaging. The imaging quality of DOT depends on the imaging reconstruction algorithm. The SIRT has been widely used for DOT image reconstruction but there is no criterion to truncate based on any kind of residual parameter. The iteration loops will always be decided by experimental rule. This work presents the CR calculation that can be great help for SIRT optimization. In this paper, four inhomogeneities with various shapes of absorption distributions are simulated as imaging targets. The images are reconstructed and analyzed based on the simultaneous iterative reconstruction technique (SIRT) method. For optimization between time consumption and imaging accuracy in reconstruction process, the numbers of iteration loop needed to be optimized with a criterion in algorithm, that is, the root mean square error (RMSE) should be minimized in limited iterations. For clinical applications of DOT, the RMSE cannot be obtained because the measured targets are unknown. Thus, the correlations between the RMSE and the convergence rate (CR) in SIRT algorithm are analyzed in this paper. From the simulation results, the parameter CR reveals the related RMSE value of reconstructed images. The CR calculation offers an optimized criterion of iteration process in SIRT algorithm for DOT imaging. Based on the result, the SIRT can be modified with CR calculation for self-optimization. CR reveals an indicator of SIRT image reconstruction in clinical DOT measurement. Based on the comparison result between RMSE and CR, a threshold value of CR (CRT) can offer an optimized number of iteration steps for DOT image reconstruction. This paper shows the feasibility study by utilizing CR criterion for SIRT in simulation and the clinical application of DOT measurement relies on further investigation.

A Combined Reconstruction Algorithm for Limited-View Multi-Element Photoacoustic Imaging

We present a photoacoustic imaging system with a linear transducer array scanning in limited-view fields and develop a combined reconstruction algorithm, which is a combination of the limited-field filtered back projection (LFBP) algorithm and the simultaneous iterative reconstruction technique (SIRT) algorithm, to reconstruct the optical absorption distribution. In this algorithm, the LFBP algorithm is exploited to reconstruct the original photoacoustic image, and then the SIRT algorithm is used to improve the quality of the final reconstructed photoacoustic image. Numerical simulations with calculated incomplete data validate the reliability of this algorithm and the reconstructed experimental results further demonstrate that the combined reconstruction algorithm effectively reduces the artifacts and blurs and yields better quality of reconstruction image than that with the LFBP algorithm.

Mantle shear structure beneath the Americas and surrounding oceans

Maps of lateral variation in shear velocity within the mantle beneath North and South America, their surrounding oceans, and parts of Africa and Eurasia are produced from inversion of travel times of horizontally polarized shear body waves. The data consist of S and ScS waves as well as multibounce phases SS, SSS and SSSS. Waves that bottom within the upper mantle are modeled using synthetic seismograms in order to estimate travel times for each of the multiple arrivals caused by velocity discontinuities near 400 and 660 km depth. The model consists of blocks with uniform slowness anomalies relative to a one‐dimensional starting model and extends from the surface to the core‐mantle boundary. The blocks have horizontal dimensions of roughly 275 by 275 km and vary in the vertical dimension from 75 to 150 km. The data are inverted using a simultaneous iterative reconstruction technique algorithm. The upper 400 km of the model is dominated by lateral variations that correspond to surface tectonic environments. Three shields on three separate continents have higher than average velocities down to between 320 and 400 km depth. Young tectonically active regions are very slow in the upper 250 km. The transition zone from 400 to 660 km depth is the most poorly resolved region. High velocity beneath western South America in the transition zone is probably associated with subducting slab. The transition zone velocity beneath the western and central part of North America also appears to be slightly faster than average. The lower mantle is dominated by large‐scale sheets of higher than average velocity and more equidimensional regions of slow velocity. From South America to Siberia, sheet‐like high‐velocity anomalies are observed from 750 km depth to the core‐mantle boundary. Another lower mantle high‐velocity anomaly is seen beneath southern Eurasia. The high‐velocity lower mantle anomalies seem to be associated with subduction during the last 150 Ma. Comparing the location of past subduction with the location of lower mantle anomalies, the identification of lower mantle anomalies with old subducted slabs suggests slow sinking of slabs in the lower mantle (about 1 to 2 cm/yr). If this interpretation is correct then high velocity in the deepest mantle off the west coast of South America through the western United States requires significant subduction from 120 to 150 Ma a few thousand kilometers off the coast of the Americas. The slowest deep region found in this study is at the base of the mantle beneath the eastern Atlantic Ocean and may be associated with hotspots in that region. Other hotspots do not appear to be associated with slow lower mantle velocity.

TOMOGRAPHIC INVERSION OF NORMALIZED DATA: DOUBLE‐TRACE TOMOGRAPHY ALGORITHMS1

AbstractTomography is widely used in geophysics as a technique for imaging geological structures by means of data that are line integrals of physical characteristics. In some transmission measurements, due to various kinds of normalization, the measured data are related to two (the current and the reference) raypaths and can be expressed as a function of differences between line integrals. This is the case, for example, in seismo‐acoustic emission measurements, when (since the exact start time is unknown) only the differences between traveltimes (differences between line integrals of the slowness) can be determined. Similarly the use of normalized Fourier amplitudes results in data dependent upon the difference between line integrals of the absorption coefficient (computed along the actual and the reference raypaths).In order to invert these data the ordinary tomography algorithms should be modified. Some generalizations are presented for series expansion tomography methods in order to make them applicable to reconstruction problems in which the input data are differences between two line integrals. The conjugate gradient and the simultaneous iterative reconstruction technique (SIRT) methods were adapted and tested. It is shown that the modified tomography algorithms are stable and sufficiently accurate for practical use. In the reconstruction of noise‐free difference data, the conjugate gradient algorithm is found to be faster and more accurate while, in the case of noisy difference data, the modified SIRT algorithm is more stable and insensitive to noise.

Methods of least squares and SIRT in reconstruction

In this paper we show that a particular version of the Simultaneous Iterative Reconstruction Technique (SIRT) proposed by Gilbert in 1972 strongly resembles the Richardson least-squares algorithm. By adopting the adjustable parameters of the general Richardson algorithm, we have been able to produce generalized SIRT algorithms with improved convergence. A particular generalization of the SIRT algorithm, GSIRT, has an adjustable parameter σ and the starting picture ρ 0 as input. A value 1 2 for σ and a weighted back-projection for ρ 0 produce a stable algorithm. We call the SIRT-like algorithms for the solution of the weighted leastsquares problems LSIRT and present two such algorithms, LSIRT1 and LSIRT2, which have definite computational advantages over SIRT and GSIRT. We have tested these methods on mathematically simulated phantoms and find that the new SIRT methods converge faster than Gilbert's SIRT but are more sensitive to noise present in the data. However, the faster convergence rates allow termination before the noise contribution degrades the reconstructed image excessively.