Algebraic Reconstruction Research Articles

Algebraic reconstruction and postprocessing in one-step diffuse optical tomography

The photon average trajectory method is considered, which is used as an approximate method of diffuse optical tomography and is based on the solution of the Radon-like trajectory integral equation. A system of linear algebraic equations describing a discrete model of object reconstruction is once inverted by using a modified multiplicative algebraic technique. The blurring of diffusion tomograms is eliminated by using space-varying restoration and methods of nonlinear colour interpretation of data. The optical models of the breast tissue in the form of rectangular scattering objects with circular absorbing inhomogeneities are reconstructed within the framework of the numerical experiment from optical projections simulated for time-domain measurement technique. It is shown that the quality of diffusion tomograms reconstructed by this method is close to that of tomograms reconstructed by using Newton-like multistep algorithms, while the computational time is much shorter.

Diffraction Contrast Tomography - A Synchrotron Radiation Technique for Mapping Polycrystalline Microstructures in 3D

In this paper the authors describe a technique based on synchrotron x-ray diffraction which has been used to produce full 3D grain maps (both grain shapes and orientations) in annealed aluminium alloy and stainless steel samples containing around 500 grains. The procedure is termed diffraction contrast tomography (DCT), reflecting its similarities with conventional absorption contrast tomography. It is an extension of the 3D X-ray diffraction microscopy (3DXRD) concept, and has been developed in collaboration with its inventors. The specimen is illuminated using a monochromatic synchrotron x-ray beam, and grains imaged using the extinction contrast that appears in the transmitted beam when grains are aligned in the diffraction condition during rotation of the sample. The beams of radiation diffracted by the grains are captured simultaneously on the same detector as the direct beam image. The combination of diffraction and extinction information aids the grain indexing operation, in which pairs of diffraction and extinction images are assigned to grain sets. 3D grain shapes are determined by algebraic reconstruction from the limited number of extinction projections, while crystallographic orientation is found from the diffraction geometry. The non-destructive nature of the technique allows for in-situ studies of mapped samples. Research is in progress to extend the technique to allow the determination of the elastic strain and stress tensors on a grain-by-grain basis.

Algebraic B-Spline Curve Reconstruction Based on Signed Distance Field

Algebraic B-Spline Curve Reconstruction Based on Signed Distance Field

A comparison of reconstruction algorithms for C-arm mammography tomosynthesis

Digital tomosynthesis is an imaging technique to produce a tomographic image from a series of angular digital images in a manner similar to conventional focal plane tomography. Unlike film focal plane tomography, the acquisition of the data in a C-arm geometry causes the image receptor to be positioned at various angles to the reconstruction tomogram. The digital nature of the data allows for input images to be combined into the desired plane with the flexibility of generating tomograms of many separate planes from a single set of input data. Angular datasets were obtained of a low contrast detectability (LCD) phantom and cadaver breast utilizing a Lorad stereotactic biopsy unit with a coupled source and digital detector in a C-arm configuration. Datasets of 9 and 41 low-dose projections were collected over a 30 degrees angular range. Tomographic images were reconstructed using a Backprojection (BP) algorithm, an Iterative Subtraction (IS) algorithm that allows the partial subtraction of out-of-focus planes, and an Algebraic Reconstruction (AR) algorithm. These were compared with single view digital radiographs. The methods' effectiveness at enhancing visibility of an obscured LCD phantom was quantified in terms of the Signal to Noise Ratio (SNR), and Signal to Background Ratio (SBR), all normalized to the metric value for the single projection image. The methods' effectiveness at removing ghosting artifacts in a cadaver breast was quantified in terms of the Artifact Spread Function (ASF). The technology proved effective at partially removing out of focus structures and enhancing SNR and SBR. The normalized SNR was highest at 4.85 for the obscured LCD phantom, using nine projections and IS algorithm. The normalized SBR was highest at 23.2 for the obscured LCD phantom, using 41 projections and an AR algorithm. The highest normalized metric values occurred with the obscured phantom. This supports the assertion that the greatest value of tomosynthesis is in imaging fibroglandular breasts. The ASF performance was best with the AR technique and nine projections.

Reconstructing non-ideal-bordered field by simple self-correlative algebraic reconstruction technique

A new algorithm for iterative reconstruction is suggested. It is named simple self-correlative algebraic reconstruction technique (SSART). With numerical simulation experiments, SSART was applied in reconstructing a non-ideal-bordered field in order to test its reconstructive effect. For contrast, three current representative algebraic reconstruction(ARTs) including basic ART, simultaneous ART (SART) and modified SART (MSART) were simulated simultaneously. The calculated results and reconstructive accuracy are discussed with three kinds of error indexes, namely mean-square error (MSE), absolute value error (AVE) and peak error (PE). As the results, the indexes of reconstructive accuracy are much improved by the proposed SSART. The MSE and PE have been decreased by 63.6% on the order of magnitude 10−4 and 88.9% on the order of magnitude 0–2, respectively, compared to that of ART. It is concluded that SSART is one of the most super iterative reconstructing techniques.

Noisy temperature field reconstruction by wavelet-expansion in OCT measurement

A wavelet-expansion approach to reconstruct the noisy temperature field in optical computerized tomography (OCT) measurement is described. The reconstruction quality and computational efficiency of this method has been compared with some of the series expansion approach [algebraic reconstruction (ART), simultaneous algebraic reconstruction (SART) and multiplicative algebraic reconstruction (MART)]. Through computer numerical simulation, the affection of the measure errors to the reconstruction result has been studied and a sensitive equation of reconstruction error was established.

Algebraic 2D PET image reconstruction using depth-of-interaction information

Recently a high-performance PET scanner, which measures depth-of-interaction (DOI) information, is being developed for molecular imaging. DOI measurement of multi-layered thin crystals can improve spatial resolution and scanner sensitivity simultaneously. In this paper, we apply an algebraic image reconstruction method to 2-dimensional (2D) DOI-PET scanners using accurate system modeling, in order to evaluate the effects of using DOI information on PET image quality. Algebraic image reconstruction methods have been successfully used to improve PET image quality, compared with the conventional filtered backprojection method. The proposed method is applied to simulated data for a small 2D DOI-PET scanner. The results show that accurate system modeling improves spatial resolution without noise emphasis, and that DOI information improves uniformity of spatial resolution.

Shape recovery from equal thickness contours

A unique imaging modality based on equal thickness contours (ETC) has introduced a new opportunity for 3D shape reconstruction from multiple views. These ETC can be generated through an interference between transmitted and diffracted beams. We present a computational framework for representing each view of an object in terms of its object thickness and then integrating these representations into a 3D surface by algebraic reconstruction. In this framework, the object thickness is first derived from ideal contours and then extended to real data. For real data, the object thickness is inferred by grouping curve segments that correspond to points of second derivative maxima. At each step of the process, we use some form of regularization to ensure closeness to the original features as well as neighborhood continuity. We apply our approach to images of a submicron crystal structure obtained through a holographic process.

Use of High-Performance Computing Algorithms in Combination With Parallel Computing for Tomography

The electron microscope is essential for resolving complex biological structures, such as mitochondria, which are too small to be viewed in detail with the light microscope. In contrast to a conventional instrument, the High-Voltage Electron Microscope (HVEM) located at the National Center for Microscopy and Imaging Research (NCMIR) can obtain images from relatively thick specimens that contain substantial three-dimensional structure. Though a single image acquired with the HVEM represents a projection through the specimen, tomographic methods can be applied to a set of images acquired from different orientations to derive a three-dimensional representation of its biological structure. Tomography requires extensive computation and considerable processing time on conventional workstations in order to reconstruct the typically large HVEM volumes from the tilt series.In order to expedite tomographic processing, we have implemented both the commonly used singleaxis tilt, R-weighted backprojection algorithm and two iterative reconstruction methods, algebraic reconstruction (ART) and simultaneous iterative reconstruction (SIRT) on the massively parallel Intel Paragon at the San Diego Supercompter Center.

Three-dimensional differential absorption x-ray cone-beam microtomography using balanced filters and algebraic reconstruction

A new x-ray tomographic method to image a particular element is proposed and described. This method uses an x-ray tube spectrum and a pair of balanced filters with absorption edges just above and just below the edge of the desired element. The proposed system consists of a microfocus x-ray tube as an x-ray source and a 2-D detector array to collect projection data. The main advantage of this system over traditional differential tomography using two monoenergetic sources is its easy application to fan-beam or cone-beam geometry without reducing too much its intensity. ART is used to reconstruct the 3-D images from the simulated projection data generated by a Monte Carlo program. Computer experiments demonstrate the feasibility of selective imaging in cone-beam geometry.

The development of cross hole seismic techniques and case studies

This paper outlines the development of a cross hole seismic tomography package by The Broken Hill Proprietary Co. Ltd. (BHP), as a tool for mineral exploration and mine planning. The methodology of cross hole seismic tomography, field procedures, instrumentation, processing software, and field trials are described.Explosives are principally used as the source of seismic energy. A repetitive source, based on rapid hydrogen-oxygen combustion, has also been developed. Signals are detected by geophone-based detector strings, and recorded by a data acquisition system developed by BHP. Tomographic imaging is conducted by the Algebraic Reconstruction, Back Projection and Simultaneous Iterative Reconstruction techniques.Surveys have been conducted in a number of different geological environments, and include: lead-zinc, iron ore and manganese exploration leases and mines to locate mineralisation and overburden interfaces; underground coal mines to locate regions of mining induced stress; and open cut and underground coal mines to locate coal and overburden contacts. The results of these surveys are discussed.

Image Resampling on a Cylindrical Sector Grid

A cylindrical sector image grid with equal area pixels for representing tomographic images is described which offers computational advantages for some algebraic and stochastic reconstruction strategies. An evaluation of techniques for resampling from the cylindrical representation to the standard square pixel representation is included. The resampling techniques of nearest-neighbors, bilinear, cubic B spline, two high resolution cubic spline, and overlap weighting are evaluated by their noise propagation, resolution recovery, noise power spectra, and visual appearance.

Superresolution ultrasonic imaging system using focused beam illumination and algebraic reconstruction

A superresolution ultrasonic imaging system is proposed that uses focused beam illumination of a region of interest and matrix correspondence of the detected hologram signal to its modeled wave field. The method described povides an image of the interior of the minimum point discernible with conventional focused beam imaging methods, that is, a superresolution image. The principle, construction, experimental results, and discussions of the superresolution systems are given. The results indicate approximately five times greater resolution than that available with conventional methods.

On the reconstruction of boolean algebras from their automorphism groups

A Boolean algebraB is called faithful, if for every direct summandB 1 ofB: ifB 1 is rigid, (that is, it does not have any automorphisms other than the identity), then there isB 2 such thatB≅B 1×B 1×B 1×B 2. LetB be a complete Boolean algebra, thenB can be uniquely represented asB≅B R×B D×B D×B F, whereB R,B D,B F are pairwise totally different, (that is, no two of them have non-zero isomorphic direct summands),B R,B D are rigid andB F is faithful. Aut(B) denotes the automorphism group ofB.

Super-resolution acoustical passive imaging system using algebraic reconstruction

To obtain the fine structures of a wave field on a noise emitting object, a new super-resolution passive imaging system is constructed. The wave field detected by a hemispherically arranged microphone array corresponds directly to the wave field on the object by exploiting a priori information about the object’s physical structures. Thus resolution of one-tenth of a wavelength is realized. The principle, concrete construction, proposal of proper sound source models, and discussions on the effects of the measuring and additive noises are given, as well as several observed results.