Showing papers on "Iterative reconstruction published in 1980"

Image reconstruction from projections

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.

Iterative Method Applied To Image Reconstruction And To Computer-Generated Holograms

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.

Iterative Ray Tracing between Boreholes for Underground Image Reconstruction

Abstract: A computerized method is described for calculating an image of the refractive index distribution in a plane bounded by two underground boreholes. The scanning geometry is assumed to be limited to probing from borehole to borehole, with rays at numerous depths and angles to effectively cover the cross section between holes. A geometrical optics model is assumed for the transmission data. We stress situations where significant bending of electromagnetic or seismic rays occurs. Image reconstruction involves an iterated sequence of numerical ray tracing and linear system inversion. A similar approach, discussed in the literature, sometimes fails to converge. We report here our refinements of this method, including use of a smoothness constraint.

Performance Analysis of Three Camera Configurations for Single Photon Emission Computed Tomography

Abstract: The performance of three camera-based detector configurations for single photon emission computed tomography (SPECT) have been compared for system sensitivity and spatial resolution in the reconstructed images. These configurations are the flat detector with parallel channel collimation, the flat detector with focused channel collimation, and the fan-curved detector with focused channel collimation. The analysis was done by simulation of the projection data collection process in the collimator-detector assembly and subsequent image reconstruction for each configuration. Generally the results indicate that both the system sensitivity and image spatial resolution can be simultaneously improved by using largearea detectors with focused collimators. Except for short focal length cases, differences in performance between the two focused configurations are minimal.. Although the depth-dependence of collimator spatial resolution introduces point spread function (psf) shape anisotropy along the radius, varying both in the radial and azimuthal crirections, it does not significantly degrade reconstructed image quality.

Zeugmatography by Reconstruction from Projections

Abstract: Nuclear magnetic resonance (NMR) zeugmatographic imaging may be accomplished in a number of ways Reconstruction from projections offers several advantages when compared with those techniques that depend upon transient perturbations of the NMR response The generation of either two- or three-dimensional images is possible, and the effects of differences in relaxation times and spectroscopic properties may be incorporated into the experiment Complete three-dimensional reconstruction is an especially efficient imaging method, and some examples of such images are shown

Iterative image restoration for linearly degraded images. I. Basis

Abstract: An image-restoration method applying the iterative method to solve simultaneous linear equations is described. The advantages of this method are that the memory capacity to be used is minimal, the computation time is very short, and the man-machine interaction in the course of processing is easily effected. Owing to these advantages, this method seems to be superior from a practical viewpoint to other recently proposed linear-algebraic approaches for image restoration. The mathematical basis of this iterative image-restoration method is described and the suitability of this method is presented. The characteristics of this method are clarified through analysis in frequency space. Nonlinear constraints can also be introduced in this method, which restrain occurrence of erratic results caused by noise amplification. Experimental results using a minicomputer-base digital image-processing system demonstrate that the method is very effective and applicable in practice.

A study of fourier space methods for “limited angle” image reconstruction *

Abstract: The problem of recovering a function f(x 1,x 2) from a limited number of its one-dimensional projections is an ill-conditioned inverse problem arising in areas which include radio astronomy, electron microscopy, and X-ray tomography. The ill-conditioning of the problem is related to the availability of data only for angles 0 ⩽θ ⩽ α < π. In this paper we make a detailed study of small scale models of the practical implementation of some Fourier methods for the reconstruction of f(x 1 x 2). We concentrate on explaining the source of the ill-conditioning, as well as trying to give a qualitative connection between the amount of “angular data” a and the degree of well-posedness of the problem. Our study leads one naturally to the study of the detailed structure of the spectral properties of a certain selfadjoint positive definite operator, similar to the one encountered in the study of prolate spheroidal functions by Sepian, Pollak, and Landau. A careful look at these spectral properties as a function of the p...

Three-dimensional reconstruction from planar projections

Abstract: The technique of direct three-dimensional reconstruction from planar projections is analyzed from a linear system viewpoint. It is found that unfiltered back projection and summation of the one-dimensional planar projections gives a point-spread function that behaves like 1/r in three-dimensional space. Thus an analogy between this reconstruction problem and the familiar electrostatic problem is set up. To correct the 1/r blurring, a Laplacian operation on the unfiltered summation image is required. Another method for reconstruction is to perform a second derivative operation on the one-dimensional planar projection set before the back projection. For spherically symmetric objects, this algorithm reduces to the Vest–Steel formula. The advantages of this reconstruction scheme as compard with reconstruction from line projections are also discussed.

Techniques For Speckle Noise Removal

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.

Reconstruction of a reflectivity field from line integrals over circular paths

Abstract: When a broadband acoustic pulse is emitted from an omnidirectional source into a two‐dimensional reflecting medium and the resultant backscattered echoes are recorded as a function of time at a point coinciding with the source, measurements of line integrals of the acoustic reflectivity are obtained over concentric arcs centered at the source point. Sufficient line‐integral data can be generated in this fashion, by translating the omnidirectional source–receiver point over a suitable aperture, to reconstruct the unknown reflectivity function. A closed‐form solution to this image reconstruction problem is derived, and on the basis of this solution, computer reconstructions of a point reflecting object from simulated echo data are presented. Finally, the closed‐form reconstruction formula is shown to be expressible as the sum of two terms, where the first term corresponds to a simple delay‐and‐sum operation applied to the echo data recorded over the aperture; the second term is new and represents a correcti...

An Integral-Transport Method for Compton-Scatter Correction in Emission Computed Tomography

Abstract: A systematic method has been devised for elimination of Compton-scatter for medical ?-ray images by three dimensional emission tomography. The approach is based upon the collision-expansion formalism which arises from the integral-transport equation and is applicable to a wide variety of object and detector configurations. Approximate correlations for point-kernels are presented which allow considerable savings in computer time and storage requirements. Results for simulated images show that the approach is effective for suppressing scatter background and distortion from sources both in and out of the tomographic slice of interest.

Iterative Procedures For Signal Reconstruction From Phase

Abstract: Recently, a set of conditions has been developed under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform. These conditions are distinctly different from the minimum or maximum phase requirement and are applicable to both one-dimensional and multi-dimensional sequences. Under the specified conditions, several numerical algorithms have been developed to reconstruct a sequence from its phase. In this paper, we review the recent theoretical results pertaining to the phase-only reconstruction problem and we discuss in detail two iterative numerical algorithms for performing the reconstruction.© (1980) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Comparison of some algorithms for reconstructing space-limited images

Abstract: This paper deals with the long-standing problem of reconstructing an optical object of known finite spatial extent from an image that is a noisy low-pass-filtered version of the object. The development of a number of iterative reconstruction algorithms in recent years has created a resurgence of interest in this topic. We consider several reconstruction algorithms from a point of view that illuminates their performance in the presence of noise. We also introduce a new iterative reconstruction algorithm and compare its performance with that of an earlier algorithm proposed by Gerchberg.

Limited Angle 3-D Reconstructions from Continuous and Pinhole Projections

Abstract: The propagation of errors incurred in 3-D reconstructions with limited angular input performed by deconvolution and matrix inversion algorithms is analyzed. The convergence rate and noise properties of an iterative scheme that utilizes the finite extent of the object to recover the missing Fourier components in deconvolution are studied. Methods are developed to stabilize the performance of the reconstruction algorithms in the presence of noise. An analysis is given for the necessary condition for complete reconstruction in imaging situations involving a number of discrete inputs confined to limited angular range.

On the optimality of the filtered backprojection algorithm.

Abstract: It is shown that under certain conditions the filtered backprojection algorithm produces a computed tomographic reconstruction for which the statistical accuracy attainable in the amplitude estimation of large-area objects meets the general lower bound derived by Tretiak. In this sense, filt

Ectomography-A New Radiographic Reconstruction Method-II. Computer Simulated Experiments

Abstract: In a special radiographic process, ectomography, an image of a slice is produced by simple summation of a set of specially filtered component images, of which each represents one of at least 60 different projections of the object. After being digitized, they are stored, filtered, and summed in a computer. Images representing any slice of any thickness in the object may be produced from the same set of component images. All details within the slice are pictured correctly while details outside are almost completely eliminated.

Holocamera for 3-D micrography of the alert human eye

Abstract: A holocamera that safely records holograms of the full depth of the alert human eye with a spatial resolution of ∼20 μm is described. A single-mode argon-ion laser generating 2 W at 5145 A serves as the illuminating source. Holographic exposure times of 0.3 msec are achieved by means of a fail-safe electromechanical shutter system. Integrated retinal irradiance levels are well under the American National Standards Institute safety standards. Reconstructed real images are projected directly onto the vidicon faceplate of a closed-circuit TV system, enabling convenient scanning in the x-y-z dimensions of the reconstructed eyeball. Serially reconstructed holograms of cataractous rabbit eyes and normal human eyes are presented.

On the electromagnetic imaging using linear reconstruction techniques

Abstract: The feasibility of using the presently available linear reconstruction techniques [1], [2] in microwave imaging is examined using a two-dimensional cross section model of the thorax. The electromagnetic field problem describing the wave transmission between a transmitter and a receiver located across the thorax was solved numerically using the method of moments. The obtained results, particularly at higher frequencies, suggest the possible use of the linear reconstruction algorithms in microwave imaging. As expected better resolution is obtained at higher frequencies.

Data Recording And Processing For Speckle Image Reconstruction

Abstract: Image reconstruction from astronomical speckle data using the Knox-Thompson algorithm has now been extensively demonstrated as feasible through analysis and computer simulations. Experimental verification of the technique and its implementation for astronomy places stringent constraints on the recording system and requires complex processing algorithms to handle the many experimental details. In this paper we describe a video recording system specifically designed for the requirements of speckle imaging. This system has been built and tested, yielding high quality image reconstructions from a laboratory-atmospheric simulator for a wide range of input light levels and test objects.

Optimisation techniques for digital image reconstruction from their projections

Abstract: A method is proposed for the digital reconstruction of images from their projections based on optimising specified performance criteria. The reconstruction problem is embedded into the framework of constrained optimisation and its solution is shown to lead to a relationship between the image and the one-dimensional Lagrange functions associated with each cost criterion. Two types of geometries (the parallel-beam and fan-beam systems) are considered for the acquisition of projection data and the constrained-optimisation problem is solved for both. The ensuing algorithms allow the reconstruction of multidimentional objects from one-dimensional functions only. For digital data a fast reconstruction algorithm is proposed which exploits the symmetries inherent in both a circular domain of image reconstruction and in projections obtained at equispaced angles. Computational complexity is significantly reduced by the use of fast-Fourier-transform techniques, as the underlying relationship between the available projection data and the associated Lagrange multipliers is shown to possess a block circulant matrix structure.

Hills and valleys analysis in optical mapping and its application to moiré contouring

Abstract: The information content of a contour map is calculated and compared with the information required for determining the relative position of the contours. We have found that usually the information required for arranging the contours in the right order is small as compared with that of producing the map. To demonstrate this finding we introduce two novel methods for ordering the contours. The first makes use of two colors, double exposure, moire mapping. The second analyzes the relative motion of hills and valleys, while the relative angle of two transparencies photographed in the grid projection technique is changed.

Industrial Applications Of Computed Tomography At Los Alamos Scientific Laboratory

Abstract: A research and development program was begun two years ago at the Los Alamos Scientific Laboratory (LASL) to study nonmedical applications of computed tomography. This program has several goals. The first goal was to develop the necessary reconstruction algorithms to accurately reconstruct cross sections of nonmedical industrial objects. The second goal was to be able to perform extensive tomographic simulations to determine the efficacy of tomographic reconstruction with a variety of hardware configurations. The final goal was to construct an inexpensive industrial prototype scanner with a high degree of design flexibility. This paper will describe the implementation of these program goals.

Adaptive nonlinear image restoration by a modified Kalman filtering approach

Abstract: An adaptive nonlinear Kalman-type filter is presented for the restoration of two-dimensional images degraded by general image formation system degradations and additive white noise. A vector difference equation model is used to represent the degradation process. Due to the nonstationarity of an image the object plane distribution function, i.e. the original image, is partitioned into disjoint regions based on the amount of spatial activity in the image. Difference equation models are used to characterize each of the regions of this nonstationary object plane distribution function. Features of the restoration filter include the ability to account for the response of the human visual system to additive noise in the image; a two-dimensional interpolation scheme to improve the estimates of the initial states in each region; and a nearest neighbor algorithm to choose the previous state vector for the state of pixel (i,j).

Astronomical Imaging By Processing Stellar Speckle Interferometry Data

Abstract: Diffraction-limited images, of resolution many times finer than what is ordinarily obtainable through large earth-bound telescopes, can be obtained by first measuring the modulus of the Fourier transform of an object by the method of Labeyrie's stellar speckle interferometry, and then reconstructing the object by an iterative method. Before reconstruction is performed, it is first necessary to compensate for weighting functions and noise in order to arrive at a good estimate of the object's Fourier modulus. A simple al-ternative to Worden's method of compensation for the MTF of the speckle process is described. Experimental reconstruction results are shown for the binary star system SAO 94163.