Showing papers on "Iterative reconstruction published in 1981"
TL;DR: It is shown that some well-known iterative methods of image reconstruction fall into the class of algorithms under consideration, and are thus covered by the convergence theory, and a novel application to truly three-dimensional image reconstruction is described.
276 citations
TL;DR: In this correspondence, an operator is derived that finds the best oriented plane at each point in the image, which complements other approaches that are either interactive or heuristic extensions of 2-D techniques.
Abstract: Modern scanning techniques, such as computed tomography, have begun to produce true three-dimensional imagery of internal structures. The first stage in finding structure in these images, like that for standard two-dimensional images, is to evaluate a local edge operator over the image. If an edge segment in two dimensions is modeled as an oriented unit line segment that separates unit squares (i.e., pixels) of different intensities, then a three-dimensional edge segment is an oriented unit plane that separates unit volumes (i.e., voxels) of different intensities. In this correspondence we derive an operator that finds the best oriented plane at each point in the image. This operator, which is based directly on the 3-D problem, complements other approaches that are either interactive or heuristic extensions of 2-D techniques.
272 citations
TL;DR: An exact interpolation scheme is proposed which, in practice, can be approached with arbitrary accuracy using well-conditioned algorithms and demonstrates the feasibility of direct FT reconstruction of CT data.
Abstract: Direct Fourier transform (FT) reconstruction of images in computerized tomography (CT) is not widely used because of the difficulty of precisely interpolating from polar to Cartesian samples. In this paper, an exact interpolation scheme is proposed which, in practice, can be approached with arbitrary accuracy using well-conditioned algorithms. Several features of the direct FT method are discussed. A method that allows angular band limiting of the data before processing -to avoid angular aliasing artifacts in the reconstructed image-is discussed and experimentally verified. The experimental results demonstrate the feasibility of direct FT reconstruction of CT data.
200 citations
TL;DR: In this article, a reconstruction algorithm for TOF-positron computed tomography (PCT) based on the back-projection with 1-dimensional weight and 2-dimensional filtering is presented.
Abstract: In positron CT, the path difference of annhilation pair gamma rays can be measured by time-of-flight (TOF) difference of pair gamma rays. This TOF information gives us rough position information along a projection line and will reduce noise propagation in the reconstruction process. A reconstruction algorithm for TOF-positron computed tomography (PCT) based on the back-projection with 1-dimensional weight and 2-dimensional filtering is presented. Also a formula to evaluate the variance of the reconstructed image and the optimal back-projection function are presented. The advantage of TOF-PCT over conventional PCT was investigated in view of noise figure. An example of such noise figure evaluations for CsF and liquid Xenon scintillators is given.
170 citations
TL;DR: In this paper, a back projection of filtered projection (BKFIL) reconstruction algorithm is presented that is applicable to single-photon emission computed tomography (ECT) in the presence of a constant attenuating medium such as the brain.
Abstract: A back projection of filtered projection (BKFIL) reconstruction algorithm is presented that is applicable to single-photon emission computed tomography (ECT) in the presence of a constant attenuating medium such as the brain. The filters used in transmission computed tomography (TCT)-comprised of a ramp multiplied by window functions?are modified so that the single-photon ECT filter is a function of the constant attenuation coefficient. The filters give good reconstruction results with sufficient angular and lateral sampling. With continuous samples the BKFIL algorithm has a point spread function that is the Hankel transform of the window function. The resolution and statistical properties of the filters are demonstrated by various simulations which assume an ideal detector response. Statistical formulas for the reconstructed image show that the square of the percent-root-mean-square (percent-rms) uncertainty of the reconstruction is inversely proportional to the total measured counts. The results indicate that constant attenuation can be compensated for by using an attenuation-dependent filter that reconstructs the transverse section reliably. Computer time requirements are two times that of conventional TCT or positron ECT and there is no increase in memory requirements.
158 citations
TL;DR: In this article, a system consisting of a laser beam array generator, an optical image recorder, and software for controlling the required operations is presented for 3D reconstruction of objects with complex surface shapes.
Abstract: It is pointed out that the generic utility of a robot in a factory/assembly environment could be substantially enhanced by providing a vision capability to the robot. A standard videocamera for robot vision provides a two-dimensional image which contains insufficient information for a detailed three-dimensional reconstruction of an object. Approaches which supply the additional information needed for the three-dimensional mapping of objects with complex surface shapes are briefly considered and a description is presented of a laser-based system which can provide three-dimensional vision to a robot. The system consists of a laser beam array generator, an optical image recorder, and software for controlling the required operations. The projection of a laser beam array onto a surface produces a dot pattern image which is viewed from one or more suitable perspectives. Attention is given to the mathematical method employed, the space coding technique, the approaches used for obtaining the transformation parameters, the optics for laser beam array generation, the hardware for beam array coding, and aspects of image acquisition.
156 citations
TL;DR: Several new digital reconstruction techniques for coded aperture imaging are developed which are especially applicable to uniformly redundant arrays (URAs), and it is shown that another new digital technique, periodic decoding, is much faster.
Abstract: Several new digital reconstruction techniques for coded aperture imaging are developed which are especially applicable to uniformly redundant arrays (URAs). The techniques provide improved resolution without upsetting the artifact-free nature of URAs. Two new techniques are described; one which allows self-supporting URAs and one which avoids (or at least mitigates) a blur which has been associated with previous correlation analyses. Each of the methods and their resolution improvements are demonstrated with reconstructions of a laser-driven compression. Particular emphasis has been placed on the special sampling required of the encoded picture and the decoding function if artifacts are to be avoided. For large URAs, it is shown that another new digital technique, periodic decoding, is much faster. Periodic decoding does produce artifacts, but they usually are negligible.
155 citations
TL;DR: The approach described here provides a rationale for combined source-channel coding which provides improved quality image reconstruction without sacrificing transmission bandwidth and is shown to result in a relatively robust design which is reasonably insensitive to channel errors and yet provides performance approaching theoretical performance limits.
Abstract: An approach is described for exploiting the tradeoffs between source and channel coding in the context of image transmission. The source encoder employs two-dimensional (2-D) block transform coding using the discrete cosine transform (DCT). This technique has proven to be an efficient and readily implementable source coding technique in the absence of channel errors. In the presence of channel errors, however, the performance degrades rapidly, requiring some form of error-control protection if high quality image reconstruction is to be achieved. This channel coding can be extremely wasteful of channel bandwidth if not applied judiciously. The approach described here provides a rationale for combined source-channel coding which provides improved quality image reconstruction without sacrificing transmission bandwidth. This approach is shown to result in a relatively robust design which is reasonably insensitive to channel errors and yet provides performance approaching theoretical performance limits. Analytical results are provided for assumed 2-D autoregressive image models, while simulation results are provided for real-world images.
138 citations
TL;DR: A very efficient back-projection algorithm which results in large time savings when implemented in machine code and a minor modification to this algorithm which converts it to a re- projection procedure with comparable efficiency is described.
Abstract: While the computation time for reconstructing images in C.T. is not a problem in commercial systems, there are many experimental and developmental applications where resources are limited and image reconstruction places a heavy burden on the computer system. This paper describes a very efficient back-projection algorithm which results in large time savings when implemented in machine code. Also described is a minor modification to this algorithm which converts it to a re-projection procedure with comparable efficiency.
137 citations
TL;DR: The spectral artifact problem in X-ray computed tomography (CI) is well known and many techniques have been suggested to correct for this problem, including linearization methods, iterative methods, and dual spectrum methods.
Abstract: The spectral artifact problem in X-ray computed tomography (CI) is well known. Many techniques have been suggested to correct for this problem, including linearization methods, iterative methods, and dual spectrum methods.
134 citations
TL;DR: In two-dimensional image reconstruction from line integrals using maximum likelihood, Bayesian, or minimum variance algorithms, the x-y plane on which the object estimate is defined is decomposed into nonoverlapping regions, or "pixels".
Abstract: In two-dimensional image reconstruction from line integrals using maximum likelihood, Bayesian, or minimum variance algorithms, the x-y plane on which the object estimate is defined is decomposed into nonoverlapping regions, or "pixels." This decomposition of an otherwise continuous structure results in significant errors, or model noise, which can exceed the effects of the fundamental measurement noise.
TL;DR: In this article, a TOF-assisted PET device is proposed to estimate the difference between the time of flight (TOF) of the annihilation photons between their inception and their detection.
Abstract: In positron emission tomography (PET), the annihilation radiation is usually detected as a coincidence occurrence that localizes the position of the annihilation event to a straight line joining the detectors. The measure of the difference between the time of flight (TOF) of the annihilation photons between their inception and their detection permits the localization of the position of the annihilation event along the coincidence line. The incorporation of TOF information into the PET reconstruction process improves the signal-to-noise ratio in the image obtained. The utilization of scintillation detectors utilizing cesium fluoride scintillators, fast photomultiplier tubes, and fast timing circuits allows sub-nanosecond coincidence timing resolution needed for the effective use of TOF in PET. Mathematical considerations and pilot experiments show that with state-of-the-art electronic components and through the application of proper reconstruction algorithms, the combination of TOF and PET positional data improves severalfold the signal-to-noise ratio with respect to conventional PET image reconstruction at the cost of increasing the amount of data to be processed. The construction of a TOF-assisted PET device is within the capability of state-of-the-art technology.
TL;DR: It is shown how this estimate can be used to alter the measured projections in such a way that the image of the heart region can be significantly improved.
Abstract: Using a stroboscopic procedure based on electrocardiographic gating, "stationary" images of the beating heart can be obtained from X-ray computed tomography body scanners. However, due to the limited amount of time over which the heart motion is periodic, only a small number of projections (X-ray views) per phase of the heart cycle can be measured. It is suggested here how to obtain satisfactory image quality when only a limited number of projections per phase are available. The procedure involves recognizing that the material surrounding the heart is stationary, and so can be estimated using a large number of projections. It is shown how this estimate can be used to alter the measured projections in such a way that the image of the heart region can be significantly improved.
TL;DR: The results of computer simulations show clearly how the process of forcing the image to conform to a priori object data reduces artifacts arising from limited data available in the Fourier domain.
Abstract: An iterative technique is proposed for improving the quality of reconstructions from projections when the number of projections is small or the angular range of projections is limited. The technique consists of transforming repeatedly between image and transform spaces and applying a priori object information at each iteration. The approach is a generalization of the Gerchberg-Papoulis algorithm, a technique for extrapolating in the Fourier domain by imposing a space-limiting constraint on the object in the spatial domain. A priori object data that may be applied, in addition to truncating the image beyond the known boundaries of the object, include limiting the maximum range of variation of the physical parameter being imaged. The results of computer simulations show clearly how the process of forcing the image to conform to a priori object data reduces artifacts arising from limited data available in the Fourier domain.
TL;DR: In this paper, a general convergence proof for a general class of iterative signal reconstruction algorithms is presented, which relies on the concept of a nonexpansive mapping in both the time and frequency domains.
Abstract: Iterative algorithms for signal reconstruction from partial time- and frequency-domain knowledge have proven useful in a number of application areas. In this paper, a general convergence proof, applicable to a general class of such iterative reconstruction algorithms, is presented. The proof relies on the concept of a nonexpansive mapping in both the time and frequency domains. Two examples studied in detail are time-limited extrapolation (equivalently, band-limited extrapolation) and phase-only signal reconstruction. The proof of convergence for the phase-only iteration is a new result obtained by this method of proof. The generality of the approach allows the incorporation of nonlinear constraints such as time- (or space-) domain positivity or minimum and maximum value constraints. Finally, the underrelaxed form of these iterations is also shown to converge even when the solution is not guaranteed to be unique.
TL;DR: In this article, the singular value decomposition (SVD) pseudoinversion method has been applied to image reconstruction from projections and two SVD pseudo-inversion methods are discussed in the search for optimum restoration; one uses Wiener filtering and the other uses truncated inverse filtering.
Abstract: The singular value decomposition (SVD) pseudoinversion method has been applied to image reconstruction from projections. In this paper, two SVD pseudoinversion methods are discussed in the search for optimum restoration; one uses Wiener filtering and the other uses truncated inverse filtering. These methods partly overcome the ill-conditioned nature of reconstruction problems by trading off between noise and signal quality. Using computer simulation, the present SVD method was compared with the conventional Fourier convolution method. Results are presented together with some limitations peculiar to the application of this method for image reconstruction and restoration.
TL;DR: The method takes into account attenuation of gamma rays inside the source and makes use of an iterative technique, based on the difference between the projection data obtained from the sources and computed projections, called reprojections, from successive reconstructions of the sources.
Abstract: A method of computing tomographic images from single photon radionuclide emission data is presented. The method takes into account attenuation of gamma rays inside the source and makes use of an iterative technique, based on the difference between the projection data obtained from the source and computed projections, called reprojections, from successive reconstructions of the sources. The method has been tested both by computer simulations and reconstruction of plastic phantoms imaged with 99mTc radionuclides. Substantial improvement in reconstruction accuracy over algorithms uncorrected for internal attenuation is demonstrated. Since the technique is iterative, it can be used with a variety of reconstruction algorithms or combined with other first approximation techniques of attenuation correction.
TL;DR: In this paper, a simple two-stage reconstruction method is described for obtaining such images efficiently with isotropic resolution, and examples are presented to demonstrate the validity and usefulness of this mode.
Abstract: Nuclear magnetic resonance (NMR) zeugmatographic imaging may become a safe and versatile alternative to medical imaging techniques that employ ionising and ultrasonic radiation. Most of the techniques that have been described for obtaining NMR images use single point, line, or plane scans to give a single slice, or reconstruct only a two-dimensional projection, and are relatively inefficient, complex, or difficult to scale up for use on the human body. There are a number of advantages to scanning simultaneously an approximately spherical volume to obtain a true three-dimensional image. A simple two-stage reconstruction method is described for obtaining such images efficiently with isotropic resolution, and examples are presented to demonstrate the validity and usefulness of this mode. The feasibility of high-resolution imaging on large objects is also discussed.
TL;DR: The techniques include gray scale modification, frame averaging, low-pass filtering in the intensity and density domains, and application of the short space spectral subtraction image restoration technique in the density domain.
Abstract: In this paper, several techniques to reduce speckle noise (more generally signal independent multiplicative noise) in images are studied. The techniques include gray scale modification, frame averaging, low-pass filtering in the intensity and density domains, and application of the short space spectral subtraction image restoration technique in the density domain. Some discussions on the theoretical basis of the techniques studied are given and their performances are illustrated by way of examples.
TL;DR: An iterative algorithm for tomographic reconstruction of refractive-index fields from measured values of path integrals along rays which have been bent by refraction is presented.
Abstract: An iterative algorithm for tomographic reconstruction of refractive-index fields from measured values of path integrals along rays which have been bent by refraction is presented The behavior of the algorithm is studied by applying it to path length data obtained by computer simulation of experiments in which holographic or Mach-Zehnder interferograms of the field are recorded for several different viewing directions A special form of the algorithm is also used to measure concentration profiles in the boundary layer formed at the cathode of an electrolytic cell containing ZnCl2 The Appendix contains a discussion of series expansion techniques for reconstructing object fields from measured values of line integrals through the field
TL;DR: The mathematical generalization of image restoration by recursive methods furnished by D. C. Youla is used to show that arbitrary L2 images can be reconstructed from two projections without any a priori assumption regarding the mathematical properties of the object, such as space- limitedness or band-limitedness.
Abstract: The mathematical generalization of image restoration by recursive methods furnished by D. C. Youla [ IEEE Trans. Circuits Syst.CAS 25, 695– 702 ( 1978)] is used to show that arbitrary L2 (i.e., square-integrable) images can be reconstructed from two projections without any a priori assumption regarding the mathematical properties of the object, such as space-limitedness or band-limitedness. Recursive algorithms are given to restore images from (1) extended segments and low-pass spectra and (2) short segments and high-pass spectra. Using the alternating projection theorem, we prove monotonic convergence (in the norm) to the original image.
TL;DR: In this paper, the authors have shown that a significant improvement in image quality results from such an approach and that coincidence resolving times of less than 500 psec FWHM are easily achievable with cesium fluoride (CsF) detectors.
Abstract: Recent advances in PET designs have shown that a gain in signal-to-noise ratio can be expected by incorporating time-of-flight data in positron emission tomography over the conventional PET mode. It has also been shown that cesium fluoride (CsF) offers the potential of faster timing and high detection efficiency which would be required for a clinical scanner utilizing time-of-flight information. Our research with CsF and the results of a feasibility study of time-off-light positron emission tomography reconstruction have shown that, indeed, a significant improvement in image quality results from such an approach and that coincidence resolving times of less than 500 psec FWHM are easily achievable with CsF detectors. However, the design of fast tomographic systems with multiple detectors which maintain this fast coincidence timing poses a challenging technical problem. The solution to this problem requires a departure from the conventional mode of PET designs to a fast on-line microprocessor based system which is capable of compressing and correcting the data for timing differences, normalization and image function. Such a system is described in this paper and its advantages and disadvantages are discussed.
TL;DR: In this article, a method for image reconstruction that processes the data in polar rather than rectangular coordinates and does not require backprojection is described, based on the decomposition of the object and its shadow (set of projections) into circular harmonics, or radial modulators of angular Fourier components.
Abstract: A method is described for image reconstruction that processes the data in polar rather than rectangular coordinates and does not require backprojection. It is based on the decomposition of the object and its shadow (set of projections) into circular harmonics, or radial modulators of angular Fourier components. Inverse filters are derived that enable the radial modulators of the object to be reconstructed from those of the shadow. An optical system for reconstruction using the method is proposed.
TL;DR: The description of a fully hardware- and software-interfaced CT-directed stereotactic surgical system is presented and examples of images reconstructed with a high spatial resolution algorithm are illustrated.
Abstract: The three-dimensional data obtained by computed tomographic (CT) scanning offer an advantage in using this imaging technique for stereotactic surgical procedures. This requires interfacing of CT image data with a stereotactic guide. In the performance of functional procedures where the surgical target must be identified from brain landmarks, such as the anterior and posterior commissures, an image reconstruction technique that presents in an image high spatial resolution structural information must be used. The description of a fully hardware- and software-interfaced CT-directed stereotactic surgical system is presented. The logic of operation and examples of images reconstructed with a high spatial resolution algorithm are illustrated. The experimentally determined measurement of an electrode tip localization with this system is within 1 pixel or +/- 0.5 mm in any direction.
Journal Article•
TL;DR: Seven-pinhole tomography is a practical three-dimensional imaging system that has been demonstrated to be useful in the emission cardiology setting and was shown to reduce imaging time and increase sensitivity without loss in specificity when compared with standard parallel-hole-collimated imaging.
Abstract: A single-photon emission tomography system was developed and studied. Based upon a seven-pinhole-collimated Anger camera, interfaced to a digital minicomputer, this imaging configuration yielded seven independent, nonoverlapping projection images of the radioactivity in a commonly viewed volume. The computer was used to implement an iterative algorithm that processed these projections to yield a three-dimensional reconstruction of the source distribution. The algorithm provides a nonlinear first approximation to the reconstruction, then uses a single iteration technique to reduce errors resulting from that approximation. Point spread functions (PSF) at various distances from the collimator face, and point-source sensitivity (PSS) at a location in the middle of the reconstruction volume were determined. The system was used for thallium-201 imaging, where it was shown to reduce imaging time and increase sensitivity without loss in specificity when compared with standard parallel-hole-collimated imaging. Seven-pinhole tomography is a practical three-dimensional imaging system that has been demonstrated to be useful in the emission cardiology setting.
TL;DR: A precise data acquisition mechanism to realize a sharp pencil beam, use of an optimum x-ray band to achieve high contrast, deconvolution processing to restore blurred projections, and the iterative revision method to compensate for physically unavailable data are incorporated into the system.
Abstract: A high-resolution high-contrast x-ray tomography system for imaging the structure of submillimeter-sized objects is constructed. A precise data acquisition mechanism to realize a sharp pencil beam, use of an optimum x-ray band to achieve high contrast, deconvolution processing to restore blurred projections, and the iterative revision method to compensate for physically unavailable data are incorporated into the system. Basic experimental results obtained for an optical fiber used as a test object show that the system has ~20- μm spatial resolution and good adsorption coefficient discrimination.
TL;DR: A rigorous theoretical analysis of the echo-planar imaging technique is presented, as a result of which a general reconstruction algorithm, applicable to any form of periodic gradient modulation, is derived.
TL;DR: In this article, the authors apply the Fourier-Radon transform to the case of far field inverse scattering and show that the Bojarski and the Kennaugh identities constitute a Fourier Radon transform pair.
Abstract: In a wide variety of electromagnetic profile reconstruction or shape imaging techniques, a need often arises to deduce the three-, two-, or one-dimensional distribution of different physical quantities from their projections, e.g., in radio-astronomy, structural biology, roentgenology, geophysics, and also in electromagnetic imaging. Investigation of such problems in various specialized areas resulted in the establishment of the new interdisciplinary subject known as "reconstruction from projections." The underlying theory, which was first rigorously formulated by Radon, will become of increasing importance to radar target mapping, wave-imaging, and related electromagnetic inverse problems; therefore, a tutorial exposition is timely and well suited for this issue. Major emphasis will be placed on showing how Ludwig's theorems on support, determinacy, and self-consistency can be used favorably to analyze the data-limited reconstruction cases. The derived theorems will be applied to the specific case of physical optics far field inverse scattering, clearly proving that the Bojarski and the Kennaugh identities constitute a Fourier-Radon transform pair.
TL;DR: Physical principles underlying the application of the techniques of computed tomography to quantitative imaging of the ultrasonic attenuation within soft tissue specimens are explored and a new technique is described to compensate for the frequency dependence of the transmitter directivity pattern in the computation of the slope.
Abstract: Physical principles underlying the application of the techniques of computed tomography to quantitative imaging of the ultrasonic attenuation within soft tissue specimens are explored. From a phenomenological model of the propagation of ultrasound through inhomogeneous media, appropriate methods are reviewed that provide attenuation measurements consistent with the imaging equations of computed tomography. Specifically, the use of a phase-insensitive acoustoelectric receiving transducer is demonstrated to eliminate phase cancellation errors. Attenuation reconstructions based on the slope of the attenuation coefficient as a function of frequency are shown to reduce image artifacts arising from reflection and refraction. A new technique is described to compensate for the frequency dependence of the transmitter directivity pattern in the computation of the slope. Reconstructed images of excised hearts are used to illustrate these techniques. The use of ultrasonic computed tomography to identify tissue pathology in vitro is demonstrated using myocardial infarction in the dog as a model. Results of attenuation and time-of-flight reconstructions are compared, with both methods demonstrated to be capable of differentiating normal myocardium from infarct. The consequences of anisotropy, i.e., the dependence of the attenuation on the direction of ultrasonic propagation, are discussed in the context of computed tomographic imaging.
TL;DR: The convergence of the additive and linear ART algorithm with relaxation is proved in a new way and under weaker assumptions on the sequence of the relaation parameters than in earlier works.
Abstract: The convergence of the additive and linear ART algorithm with relaxation is proved in a new way and under weaker assumptions on the sequence of the relaation parameters than in earlier works. These algorithms are iterative methods for the reconstruction of digitized pictures from one-dimesional views. A second proof using elementary matrix algebra shows the geometric convergence of the linear ART algorithm with relaxation.