Showing papers on "Iterative reconstruction published in 1979"
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01 Jan 1979TL;DR: A systematic introduction to the concepts and techniques of computer image processing and recognition is presented in this paper, where the authors give an overview of such topics as image formation and perception; computer representation of images; image enhancement and restoration; reconstruction from projections; digital television, encoding, and data compression; scene understanding; scene matching and recognition; and processing techniques for linear systems.
Abstract: A systematic introduction to the concepts and techniques of computer image processing and recognition is presented. Consideration is given to such topics as image formation and perception; computer representation of images; image enhancement and restoration; reconstruction from projections; digital television, encoding, and data compression; scene understanding; scene matching and recognition; and processing techniques for linear systems.
617 citations
TL;DR: It is shown that the retrieval ambiguity represents a lesser problem in the two-dimensional case compared to the well-known problem of image reconstruction from its spectrum modulus.
345 citations
TL;DR: In this paper, the authors presented a technique for overcoming the problem of tissue absorption in emission tomography by solving a linear partial-differential equation that links the derivatives of the spectrum with respect to absorption and spatial frequencies.
Abstract: This paper presents a technique for overcoming the problem of tissue absorption in emission tomography. Given a set of equispaced projections in the interval (0, 2π), it is possible to derive an exact formula for recovering the spectrum of the image. The formula is obtained by solving a linear partial-differential equation that links the derivatives of the spectrum with respect to absorption and spatial frequencies. Examples of the application of the technique to synthetic and real data are given.
229 citations
01 Jan 1979
159 citations
TL;DR: In this paper, a backprojection method for reconstructing cross-sectional images of ultrasonic reflectivity from scattering measurements is presented, and the point spread function (PSF) for each case is derived and is shown to depend on the shape of the acoustic pulse used.
159 citations
TL;DR: In this article, a cyclic subgradient projection (CSP) method was proposed to calculate simultaneously attenuation and activity concentration coefficients, and some experimental results in its favor are presented.
Abstract: In order to obtain truly quantitative reconstruction of gamma-emitter concentration in Emission Computerized Tomography (ECT) the attenuation within the region of interest has to be accounted for. In this report we propose to calculate simultaneously attenuation and activity concentration coefficients. Starting from the system of non-linear equations which describes the model of single photon gamma-ray emission in a discretized form we show how to reduce it to a mixed convex-concave feasibility problem and apply to it our method of Cyclic Subgradient Projections (CSP). This approach is discussed and some experimental results in its favor are presented.
151 citations
TL;DR: A combined source-channel coding approach is described for the encoding, transmission and remote reconstruction of image data, resulting in a relatively robust design which is reasonably insensitive to channel errors and yet provides performance approaching the rate-distortion bound.
Abstract: A combined source-channel coding approach is described for the encoding, transmission and remote reconstruction of image data. The source encoder employs two-dimensional (2-D) differential pulse code modulation (DPCM). This is a relatively efficient encoding scheme in the absence of channel errors. In the presence of channel errors, however, the performance degrades rapidly. By providing error control protection to those encoded bits which contribute most significantly to image reconstruction, it is possible to minimize this degradation without sacrificing transmission bandwidth. The result is a relatively robust design which is reasonably insensitive to channel errors and yet provides performance approaching the rate-distortion bound. Analytical results are provided for assumed 2-D autoregressive image models while simulation results are described for real-world images.
147 citations
01 Jan 1979
TL;DR: In this article, the problem of reconstruction of structures from data collected based on transmitted or emitted radiation is addressed, and a wide range of areas, such as X-ray CT, emission tomography, photon migration imaging, electron microscopic reconstruction, etc.
Abstract: This article covers the problem of reconstruction of structures from data collected based on transmitted or emitted radiation. The problem occurs in a wide range of areas, such as X-ray CT, emission tomography, photon migration imaging, electron microscopic reconstruction, etc. The article addresses the design, implementation, evaluation, and application of computer algorithms for solving the reconstruction problem in various biomedical areas and emphasizes the essential role of computers, which is due to the fact that the underlying biomedical problems result in mathematical problems in which the number of unknowns is in the millions.
125 citations
TL;DR: This work presents procedures for preprocessing incomplete projections so that images can be reconstructed from them using the convolution/back projection method.
Abstract: Conventional approaches to computed tomography involve scanning the entire cross section and producing an image whose spatial and density resolution is uniform over its entire area. If the extent of each scan is restricted to the width of the lesion being investigated, then the x-ray dose is reduced, but a set of incomplete "truncated" projections is measured. Conversely, projections are "hollow" when their inner parts cannot be measured, e.g., when there is a metallic object within the body cross section. We present procedures for preprocessing incomplete projections so that images can be reconstructed from them using the convolution/back projection method.
112 citations
TL;DR: A new image reconstruction technique for computed tomography using projection data obtained by a smaller angle rotation less than 180 degrees around the object to estimate missing region in the Fourier transformed domain by extrapolation employing analytic continuity.
Abstract: A new image reconstruction technique for computed tomography is described. Projection data obtained by a smaller angle rotation less than 180 degrees around the object are used to make the image. The main feature of the method is the estimation of missing region in the Fourier transformed domain by extrapolation employing analytic continuity. Numerical simulations were carried out using computer generated pattern data. The results show strong effects of the content of noisy component on the reconstructed image. The method might be, however, practically applied to some real fields for medical diagnosis.
86 citations
TL;DR: It is shown analytically that the secondary‐image level is reduced and remains unchanged when the receiver angular aperture (aperture relative to distance) is limited and kept constant during the whole observation time.
Abstract: Ultrafast cardiac‐valve ultrasonic tomography requires parallel multichannel processing of received echoes. In parallel processing the level of secondary ’’ghost’’ images due to spatial undersampling is much higher than in slower series processors which use a selective field insonification. The paper describes a 20‐channel moving‐focus parallel‐processing analog electronic system, which is realized in our laboratory. It is shown analytically that the secondary‐image level is reduced and remains unchanged when the receiver angular aperture (aperture relative to distance) is limited and kept constant during the whole observation time.
TL;DR: In this paper, an analytical expression for the point spread function (PSF) generated by the backprojection process has been derived for several different choices of the acoustic pulse: a narrowband pulse, wideband pulse and two analytically derived optimum pulses which provided the best sidelobe response and a mainlobe width equal to approximately 0.4λ c, where λ c is the wavelength corresponding to the upper cutoff frequency of the pulse.
TL;DR: A new iterative method is proposed for finding the optimal Bayesian estimate of an unknown image from its projection data (experimentally obtained integrals of its grayness over thin strips) and its performance is illustrated.
Abstract: A new iterative method is proposed for finding the optimal Bayesian estimate of an unknown image from its projection data (experimentally obtained integrals of its grayness over thin strips). Convergence of the method is proved and its performance is illustrated. The method compares favorably with previously proposed procedures.
TL;DR: In this paper, a convolutional formula is obtained for the direct reconstruction of a three-dimensional structure function from cone-beam projection measurements, where the cone apex is assumed to move on a circle to generate the two-dimensional projected images.
Abstract: A convolutional formula is obtained for the direct reconstruction of a three-dimensional structure function from cone-beam projection measurements. The cone apex is assumed to move on a circle to generate the two-dimensional projected images. The derivation starts from the three-dimensional form of the Radon inversion formula. A transformation of variables is applied to adapt this formula to the cone-beam projection geometry.
TL;DR: In typical liquid surface acoustical holography systems, a small tank (minitank) contains the imaging fluid, which relates the acoustic particle velocity at the liquid surface to the velocity potential in the incident acoustic field, which causes the transfer function to become oscillatory at even small angles of incidence.
Abstract: In typical liquid surface acoustical holography systems, a small tank (minitank) contains the imaging fluid. A thin membrane separates the imaging fluid from the main tank in which the acoustic object is immersed. It is usually assumed that this membrane is acoustically transparent. The inertial reactance of the membrane can be of the order of the characteristic impedances of the adjacent fluids. When this occurs, the membrane is not transparent, and the transmission and reflection coefficients at the membrane will be complex; the transmission coefficient decreases in magnitude and the reflection coefficient increases. These coefficients appear in the expression for the minitank transfer function, which relates the acoustic particle velocity at the liquid surface to the velocity potential in the incident acoustic field. The transfer function exhibits oscillatory behavior at large minitank depths and moderate angles of incidence due to multiple internal reflections and interference effects. When membrane inertia is signifiManuscript received February 22, 1979. This work was supported by the Office of Naval Research as part of NRL Problem 84F01-25. 20375. The author is with the Naval Research Laboratory, Washington, D.C. CLARK, JR. cant, the minitank becomes a more efficient waveguide; interference effects become more pronounced and occur at shallow depths. Using identical fluids causes the transfer function to become oscillatory at even small angles of incidence. The best fidelity is obtained at shallow depths over moderate angles of incidence; the magnitude and phase of the transfer function are approximately constant then.
TL;DR: In this paper, a generalized method for the reconstruction of a region of interest within a slice in the presence of beam hardening is introduced, which is based on variable sampling of the projection data and a post-reconstruction correction scheme.
Abstract: A generalized method for the reconstruction of a region of interest within a slice in the presence of beam hardening is introduced. The method, limited field of reconstruction (LFV), is based on variable sampling of the projection data and a post-reconstruction correction scheme. An initial reconstruction of the whole slice is performed using the coarsely sampled projections. The low resolution reconstructed image is used to estimate the bone and tissue thicknesses along each ray. The bone and tissue lengths obtained from the first low resolution image are then used in subtracting the contribution of the external region from the region of interest and to correct for beam hardening. The finely sampled corrected projections are used in reconstructing a high resolution image of the region of interest without artifacts from the external region and beam hardening. Computer simulation results are presented and applicability of the present correction method to practical scanners is discussed.
TL;DR: In this paper, the effects of the angular range of data taking in reconstructions in planar positron cameras using the deconvolution method was investigated. But the results were not applied to other transmission and emission imaging devices.
Abstract: The effects of the angular range of data taking in reconstructions in planar positron cameras using the deconvolution method is investigated. It is found that in the absence of any a priori information there are undetermined components in the reconstruction if the field of view of the positron camera is limited. However, all of the undetermined components are recovered if the fact that the object extent is finite is utilized. The results obtained can be applied to other transmission and emission imaging devices.
TL;DR: The feasibility and potential of a DSR system has been demonstrated by studies using a currently operational single source prototype assembly, the SSDSR, from which full three-dimensional dynamic reconstructions of the thorax and its contents have been obtained.
Abstract: High temporal resolution, full three-dimensional imaging of the heart and circulation is required for accurate basic physiological studies of the structural-to-functional relationships of these organ systems, and for improved diagnostic evaluation and treatment of patients with cardiovascular disorders. A new generation, fully electronic and very rapid whole-body computed tomography system called the Dynamic Spatial Reconstructor (DSR) will provide stop-action (0.01 sec), rapidly sequential (60-per-second), synchronous volume (240 simultaneous transaxial sections) reconstructions and display of the full anatomic extent of the heart throughout successive cardiac cycles, and will permit visualization of the three-dimensional vascular anatomy and circulatory functions in all regions of the body of patients with cardiovascular and other pathological disabilities. The feasibility and potential of a DSR system has been demonstrated by studies using a currently operational single source prototype assembly, the SSDSR, from which full three-dimensional dynamic reconstructions of the thorax and its contents have been obtained.
TL;DR: In this article, the authors presented a convolve-and-backproject (C&B) algorithm for both parallel and divergent ray geometries for image reconstruction in two and three dimensions.
Abstract: The solutions to the image reconstruction problem, in two and three dimensions, for both parallel and divergent ray geometries, are presented within a general linear reconstruction framework. It is shown that, with suitable parameterizations, each of these solutions reduces to a "convolve-and-backproject" algorithm. The exact solution to the three-dimensional divergent ray geometry problem is a new result and is treated in detail. This problem arises when the sensors are located around the object region in three-dimensional space, and the measurement rays diverge (i.e., fan out) from the individual sources. An approximation to the exact solution has been made in order to derive convenient and practical convolving functions for this geometry.
TL;DR: In this article, the line integrals of densities and optical, ultraviolet, and X-ray emission were derived and analyzed for the special cases with source functions possessing helical symmetry, ranging from DNA to MHD.
Abstract: Several plasma diagnostics techniques measure the line integrals of quantities such as densities and optical, ultraviolet, and X-ray emission. Some approaches for reconstructing the local quantities from their line integrals, based on methods utilized in computerized tomography, electron microscopy, holographic interferometry, and radio astronomy, are derived and presented. Results for the special cases with source functions possessing helical symmetry-ranging from DNA to MHD-are emphasized.
TL;DR: An iterative algorithm for direct three-dimensional reconstruction from cone-beam projection data is presented, based on the maximum entropy criterion and uses an efficient parametrization of the cone- beam projection geometry.
TL;DR: The streak-like pattern in the image noise due to the anisotropic nature of the noise cross-correlation function is discussed and how these nonlinear phenomena affect noise filtering and tissue characterization using statistical parameters is discussed.
Abstract: The variance of the image noise in computed X-ray transmission tomography (CT) due to quantum noise is in a first approximation a nonlinear function of X-ray attenuation. Beam hardening in CT is also a nonlinear function of attenuation. We present a theoretical study of both phenomena. Computer simulations and numerical results show that both nonlinear dependencies have quite similar effects on image quality. We also show how the two-dimensional distribution of the noise variance in a CT image is a weighted superposition of images obtained by backprojecting integer powers of the noiseless projection data corresponding to the scanned object. The streak-like pattern in the image noise due to the anisotropic nature of the noise cross-correlation function is discussed. We also discuss how these nonlinear phenomena affect noise filtering and tissue characterization using statistical parameters.
28 Dec 1979
TL;DR: In this article, an optimal restoration filter based on maximizing the a posteriori probability density (MAP) is developed for photon resolved low light level image signals detected by a counting array.
Abstract: A model for photon resolved low light level image signals detected by a counting array is developed. Those signals are impaired by signal dependent Poisson noise and linear blurring. An optimal restoration filter based on maximizing the a posteriori probability density (MAP) is developed. A suboptimal overlap-save sectioning method using a Newton-Raphson iterative procedure is used for the solution of the high dimensionality nonlinear estimation equations for any type of space-variant and invariant linear blur. An accurate image model with a nonstationary mean and stationary variance is used to provide a priori information for the MAP restoration filter. Finally, a comparison between the MAP filter and a linear space-invariant minimum mean-square error (LMMSE) filter is made.
TL;DR: A theory of imaging for detector systems with a very limited number of projections has been developed in this paper, where the relationships between a matrix which determines the system, its eigenvectors and eigenvalues, and the physical characteristics of the detector system are analyzed in order to assist in the most effective design of an instrument.
Abstract: A theory of imaging for detector systems with a very limited number of projections has been developed. The relationships between a matrix which determines the system, its eigenvectors and eigenvalues, and the physical characteristics of the detector system are analyzed in order to assist in the most effective design of an instrument. It is shown that reconstruction methods for complete data sets are essentially an extension of the methods developed for incomplete sets. The concept of mathematical sweeping to replace mechanical detector motion in incomplete detector systems is demonstrated.
TL;DR: In this paper, a twin-cone scanning geometry and a reconstruction method are proposed capable of multislice reconstructing using wide cone angles, and the reconstruction method is shown to be more robust than the one proposed in this paper.
Abstract: A twin-cone scanning geometry and a reconstruction method are proposed capable of multislice-reconstructing using wide cone angles
28 Dec 1979
TL;DR: In this article, an iterative computer method that can be used to solve a number of problems in optics is discussed, including synthesis of a Fourier transform pair having desirable properties in both domains, and reconstruction of an object when only partial information is available in any one domain.
Abstract: This paper discusses an iterative computer method that can be used to solve a number of problems in optics. This method can be applied to two types of problems: (1) synthesis of a Fourier transform pair having desirable properties in both domains, and (2) reconstruction of an object when only partial information is available in any one domain. Illustrating the first type of problem, the method is applied to spectrum shaping for computer-generated holograms to reduce quantization noise. A problem of the second type is the reconstruction of astronomical objects from stellar speckle interferometer data. The solution of the latter problem will allow a great increase in resolution over what is ordinarily obtainable through a large telescope limited by atmospheric turbulence. Experimental results are shown. Other applications are mentioned briefly.
TL;DR: The algorithm uses the fast Fourier transform to diagonalize and decouple the system of equations which results from the application of the least-squares criterion and is accurate and stable, and is perhaps an order of magnitude faster than the best iterative method.
Abstract: This paper describes a fast direct algorithm for obtaining least-squares phase estimates from arrays of noisy phase differences. The algorithm uses the fast Fourier transform to diagonalize and decouple the system of equations which results from the application of the least-squares criterion. It is accurate and stable, and is perhaps an order of magnitude faster than the best iterative method. The effectiveness of the algorithm has been demonstrated by using it in connection with the Knox–Thompson speckle-imaging procedure to restore an optical object perturbed by simulated atmospheric turbulence. Representative results are discussed in the paper.