Showing papers on "Iterative reconstruction published in 1984"

EM reconstruction algorithms for emission and transmission tomography.

Abstract: Two proposed likelihood models for emission and transmission image reconstruction accurately incorporate the Poisson nature of photon counting noise and a number of other relevant physical features As in most algebraic schemes, the region to be reconstructed is divided into small pixels For each pixel a concentration or attenuation coefficient must be estimated In the maximum likelihood approach these parameters are estimated by maximizing the likelihood (probability of the observations) EM algorithms are iterative techniques for finding maximum likelihood estimates In this paper we discuss the general principles behind all EM algorithms and derive in detail the specific algorithms for emission and transmission tomography The virtues of the EM algorithms include (a) accurate incorporation of a good physical model, (b) automatic inclusion of non-negativity constraints on all parameters, (c) an excellent measure of the quality of a reconstruction, and (d) global convergence to a single vector of parameter estimates We discuss the specification of necessary physical features such as source and detector geometries Actual reconstructions are deferred to a later time

Limitations of Imaging with First-Order Diffraction Tomography

Abstract: In this paper, the results of computer simulations used to determine the domains of applicability of the first-order Born and Rytov approximations in diffraction tomography for cross-sectional (or three-dimensional) imaging of biosystems are shown. These computer simulations were conducted on single cylinders, since in this case analytical expressions are available for the exact scattered fields. The simulations establish the first-order Born approximation to be valid for objects where the product of the relative refractive index and the diameter of the cylinder is less than 0.35 lambda. The first-order Rytov approximation is valid with essentially no constraint on the size of the cylinders; however, the relative refractive index must be less than a few percent. We have also reviewed the assumptions made in the first-order Born and Rytov approximations for diffraction tomography. Further, we have reviewed the derivation of the Fourier Diffraction projection Theorem, which forms the basis of the first-order reconstruction algorithms. We then show how this derivation points to new FFT-based implementations for the higher order diffraction tomography algorithms that are currently being developed.

The feasible solution in signal restoration

Abstract: The feasible solution to the signal restoration problem is defined as the one which satisfies all constraints which can be imposed on the true solution. A very important set of constraints can be obtained by examining the statistics of the noise. These and other constraints can be described as closed convex sets. Thus, projection onto closed convex sets is the numerical method used to obtain a feasible solution. Examples of this method demonstrate its usefulness in one-and two-dimensional signal restoration. The limitations of the method are discussed.

Modulation-transfer-function analysis for sampled image systems.

Abstract: Sampling generally causes the response of a digital imaging system to be locally shift-variant and not directly amenable to Modulation Transfer Function (MTF) analysis. However, this paper demonstrates that a meaningful system response can be calculated by averaging over an ensemble of point-source system inputs to yield an MTF which accounts for the combined effects of image formation, sampling, and image reconstruction. As an illustration, the MTF of the Landsat MSS system is analyzed to reveal an average effective instantaneous field of view which is significantly larger than the commonly accepted value, particularly in the along-track direction where undersampling contributes markedly to an MTF reduction and resultant increase in image blur.

A new fast algorithm for the evaluation of regions of interest and statistical uncertainty in computed tomography

Abstract: A new algorithm for region of interest evaluation in computed tomography has been developed. Region of interest evaluation is a technique used to improve quantitation of the tomographic imaging process by summing (or averaging) the reconstructed quantity throughout a volume of particular significance. An important application of this procedure arises in the analysis of dynamic emission computed tomographic data, in which the uptake and clearance of radiotracers are used to determine the blood flow and/or physiologic function of tissue within the significant volume. The new algorithm replaces the conventional technique of repeated image reconstructions with one in which projected regions are convolved and then used to form multiple vector inner products with the raw tomographic data sets. Quantitation of regions of interest is made without the need for reconstruction of tomographic images. The computational advantage of the new algorithm over conventional methods is between a factor of 20 and a factor of 500 for typical applications encountered in medical science studies. The greatest benefit of the new algorithm (and the motivation for its development) is the ease with which the statistical uncertainty of the result is computed. The entire covariance matrix for the evaluation of regions of interest can be calculated with relatively few operations.

III The Radon Transform and Its Applications

Abstract: Publisher Summary This chapter discusses the Radon transform, its applications, present state of knowledge about the Radon transform, and some of its lesser-known applications. Although x-ray projections and tomographic reconstruction are used in the chapter as a starting point, no consideration is given to such things as fan-beam geometries, iterative reconstruction algorithms, polyenergetic X-rays, detector noise, or clinical applications. It is undoubtedly medical computed tomography (CT) that has attracted more attention than any other application of the Radon transform. The basic data obtained in a CT procedure are x-ray transmission measurements through a two-dimensional (2D) slice of the patient's body. Because of the overwhelming clinical and commercial success of CT, the 2D Radon transform is studied in exhaustive detail.

Tomographic Image Reconstruction from Incomplete View Data by Convex Projections and Direct Fourier Inversion

Abstract: We consider the problem of reconstructing CAT imagery by the direct Fourier method (DFM) when not all view data are available. To restore the missing information we use the method of projections onto convex sets (POCS). POCS is a recursive image restoration technique that finds a solution consistent with the measured data and a priori known constraints in both the space and Fourier domain. Because DFM reconstruction is a frequency-domain technique it is ideally matched to POCS restoration when, for one reason or another, we are forced to generate an image from a less than complete set of view data. We design and apply an algorithm (PRDF) which interpolates/extrapolates the missing Fourier domain information by POCS and reconstructs an image by DFM. A simulated human thorax cross section is restored and reconstructed. The restorations using POCS are compared with the Gerchberg-Papoulis extrapolation method and shown to be superior. Applications of PRDF to other types of medical imaging modalities are discussed.

Reconstruction from projections based on detection and estimation of objects--Parts I and II: Performance analysis and robustness analysis

Abstract: The problem of reconstructing a multidimensional field from noisy, limited projection measurements is approached using an object-based stochastic field model. Objects within a cross section are characterized by a finite-dimensional set of parameters, which are estimated directly from limited, noisy projection measurements using maximum likelihood estimation. In Part I, the computational structure and performance of the ML estimation procedure are investigated for the problem of locating a single object in a deterministic background; simulations are also presented. In Part II, the issue of robustness to modeling errors is addressed.

Image reconstruction from frequency-offset Fourier data

Abstract: Motivated by the ability of synthetic-aperture radar and related imaging systems to produce images of surprisingly high quality, we consider the problem of reconstructing the magnitude of a complex signal f from samples of the Fourier transform of f located in a small region offset from the origin. It is shown that high-quality speckle reconstructions are possible so long as the phase of f is highly random. In this case, the quality of the reconstruction is insensitive to the location of the known Fourier data, and edges at all orientations are reproduced equally well. A large number of computer examples are presented demonstrating these attributes. Methods for improving image quality are also briefly discussed.

Real-Time Digital Image Reconstruction: A Description of Imaging Hardware and an Analysis of Quantization Errors

Abstract: On decrit un systeme de formation d'image acoustique numerique en temps reel (appele DAISY) capable de reconstruire plus de 30 nouvelles images par seconde. Effets des erreurs de quantification dans les systemes de formation d'image numeriques

Method for reducing image artifacts due to projection measurement inconsistencies

Abstract: A method is provided for reducing streak artifacts in images reconstructed from projections having significant discrepancies between the first and last scan views due to subject motion or to scan geometry aberrations during a typical 360° scan such as that utilized in computerized tomography. The views taken at the beginning and end of the 360° scan are taken far apart in time, but in the image reconstruction process, they are treated as being adjacent. The method recognizes that in a 360° scan each ray in a projection is scanned twice so that the data set contains redundant information. To reduce the inconsistencies, weights less than the nominal weight are assigned to original projections at the beginning and end of the scan, and the views near the middle of the scan containing corresponding redundant data are compensated so that the combined weights of all ray pairs are constant. In this manner, the inconsistency between the first and last views is feathered out, and the resulting image exhibits significantly reduced sensitivity to errors caused by the discrepancies. The method is effective regardless of the modality (for example, ultrasound, emission nuclear tomography, computerized tomography, nuclear magnetic resonance) used to obtain the projection data.

Restoration of Digital Multiplane Tomosynthesis by a Constrained Iteration Method

Abstract: Tomosynthetic reconstructions suffer from the disadvantage that blurred images of object detail lying outside the plane of interest are superimposed over the desired image of structures in the tomosynthetic plane. It is proposed to selectively reduce these undesired superimpositions by a constrained iterative restoration method, suitably generalized to permit simultaneous deconvolution of multiple planes. Sufficient conditions are derived ensuring the convergence of the iterations to the exact solution in the absence of noise and constraints. Although in practice the restoration process must be left incomplete because of inescapable noise and quantization artifacts, the experimental results demonstrate that for reasons of stability the convergence conditions derived for the noise-free, unconstrained case should be satisfied. In order to establish a basis for a formal stopping criterion of the iteration procedure, the buildup of noise in the sequence of iterative restorations arising from white noise in the original radiographs is investigated theoretically and experimentally. This results in the derivation of an approximation to the limiting noise variance in the reconstructions which is verified experimentally.

Prospects for three‐dimensional projective and tomographic imaging radar networks

Abstract: Results of a study demonstrating the feasibility of broadband and speckle-free projective imaging of a complex shaped scattering object in the 6-17 GHz range with centimeter resolution are presented. It is shown how angular, spectral, and polarization diversities can be combined in the data acquisition process with a unique target-derived reference technique to access the three-dimensional Fourier space of the scatterer cost-effectively. Imagea retrieval algorithms, based on the projection slice theorem and knowledge of object symmetry, are utilized in obtaining images of a model aircraft with near optical resolution. The implications for high-resolution three-dimensional tomographic imaging radar networks are discussed.

Parameter Estimation for Dynamic Studies in Emission-Tomography Systems Having List-Mode Data

Abstract: Maximum-likelihood parameter estimation for dynamic tracer-studies is investigated for emission-tomography systems having time-of-flight measurements in the form of list-mode data. It is shown how the EM iterative algorithm of statistics can be used to estimate compartmental parameters just as it is also used to reconstruct images of activity distributions. Retrospective processing of list-mode data for dynamic studies requires that the influence of each measurement point to the region of interest in the reconstructed images be identified; a procedure for accomplishing this is given.

A unified description of NMR imaging, data-collection strategies, and reconstruction

Abstract: In nuclear magnetic resonance (NMR) imaging by the zeugmatographic methods, there is a common and unified theoretical description. All forms of two‐dimensional and three‐dimensional imaging involve NMR data which trace various geometric representations, in reciprocal transform space, of the subject’s spatially blurred ‘‘effective’’ spin density. The effective density is proportional to the physical density modulated spatially by the several factors of receiver coil (B/I) ratio, rf pulse excitation terms, T 1‐relaxation terms, and T 2‐relaxation terms. These factors depend upon the rf pulse sequence and field‐gradient modulation sequence, and they may be calculated according to some model or directly measured. From this viewpoint, all different imaging modes appear as variations in data‐collection and image‐reconstruction strategies. The results are used here to describe slice‐oriented polar and Cartesian strategies, three‐dimensional Cartesian and two forms of spherical strategies, and multiecho strategies of the ‘‘planar‐echo’’ type.

Synthetic Aperature Diffraction Tomography and Its Interpolation-Free Computer Implementation

Abstract: A new tomographic imaging technique is presented that requires only two rotational positions of an object. Although ideally the angle between the two rotational positions should be 90°, theory predicts that valid results should be obtainable, albeit with reduced spatial resolution, even when this condition is not satisfied. For each rotational position of the object, the data is collected most efficiently by using arrays on both the transmit and the receive sides; the elements of the transmit array are fired sequentially, and for each such firing the received field is measured over all the elements of the receive array. It is shown thot this measurement strotegy firrs up the Fourier space, from which the object can be recovered by simple Fourier inversion. This imaging strategy was derived from the equations of propagation in an inhomogeneous medium with Born and Rytov approximations. A digital implementation is also presented of the proposed algorithm that requires no interpolations in either the frequency or the space domain, and can be carried out with only 2N FFT's for reconstructing an N X Nimage. Since no interpolations are carried out whatsoever, no computational errors are introduced by the algorithm itself. The total computational complexity of the procedure is of the order of Ow3) as compared to O(Ar4) for a filtered-backpropagation algorithm and O(NZ log N) for procedures based on interpolation in the frequency domain. Some computer simulation results have been included to demonstrate the numerical accuracy of the algorithm.

Increased sensitivity and field of view for a rotating positron camera

Abstract: Discusses two approaches towards improving the sensitivity and enlarging the useful field of view for a rotating positron camera by removing the constraint on phi . Weighted backprojection appears superior in that the camera response is more uniform and the images are less noisy than for the post-reconstruction scaling method. Fourier deconvolution reconstruction may be retained since the response function of the overall system is still shift invariant. In a typical imaging situation, the increase in sensitivity may be as much as a factor of 2.5, which represents a significant improvement when considering the poor statistics of nuclear medicine images. As a consequence of decoupling the sensitivity from the diameter of the field of view, transverse sections through internal organs with dimensions approaching those of the detectors may therefore be accurately imaged with good sensitivity. The weighted backprojection method is now applied in routine clinical imaging (Frey et al., 1984).

Experimental optical fan beam tomography.

Abstract: Optical tomography is used to map the iodine vapor density in a plane. Two-dimensional images are obtained with 1-cm spatial resolution using a fan beam geometry with a 28-cm radius fan source circle. The images are reconstructed using the convolution backprojection algorithm with data collected in 0.1 sec from 90 detectors on a full circle using 90–360 fan source positions. Experimental results quantitatively confirm a theoretical analysis of the noise in the reconstructed image, including the effects of correlated noise, position within the image, and spatial resolution. The noise amplitude–absorption length product for a 2-cm pixel size is 6 × 10−4 which is equivalent to an iodine concentration of 6 ppm.

A Reconstruction Algorithm from Truncated Projections

Abstract: A new tomographic reconstruction method is proposed which permits the reconstruction of a region of interest within a slice from partially truncated scanning data. This method utilizes two types of source data, namely a series of truncated projections and the outline of the object's cross section. The principle of this algorithm is to estimate the outside area of truncation in one projection from the projection data of the other viewing angles and the outline data of the object. The above estimation is accomplished by following two repeated procedures: 1) the modification of the calculated projection data compared each time with the already measured projection data of the truncated area, and 2) the modification of the reconstructed image compared also each time with the shape of the object. Computer simulation shows the convergence of the results obtained by this algorithm thus verifying its validity, and a reconstructed image after iterative processes exhibits good quality.

Reconstruction of Images from Neuromagnetic Fields

Abstract: In response to specific stimuli, the human brain emits a measurable magnetic field from regions actively involved in processing the stimulus. We have implemented an iterative algorithm to reconstruct images from the neuromagnetic field. Computer simulation studies performed to develop the algorithm are reported. Experimental measurements of a human visually-evoked field and images reconstructed therefrom are also reported. The results demonstrate, for the first time, the feasibility of imaging multiple sources within the brain that produce a magnetic field.

Convolutional image reconstruction for quantitative single photon emission computed tomography

Abstract: Two image reconstruction algorithms have been investigated. They are based on filtered backprojection, and are useful when the tissue attenuation is considered to be uniform in the object. The first method uses a weighted backprojection, the weighting factor being determined in such a way that the photon attenuation is compensated with low noise propagation. The parameters involved in the convolution kernel and the correction function were determined by a computer iteration program. The second method, which is a simplified version of the first, uses conventional backprojection, and takes a shorter computation time than the first method. The statistical noise of an image can be minimised by suitable positioning of the coordinate origin for the reconstruction. The theory of the two methods, their performance on statistical noise and some results of mathematical and experimental phantom studies are described.

Analysis of x-ray computed tomography images using the noise power spectrum and autocorrelation function.

Abstract: A discrete representation of the reconstruction process, consistent with the method of data collection, has been used to derive expressions for the noise power spectrum, autocorrelation function and noise equivalent quanta (NEQ) of a computed tomography (CT) image. These parameters have been expressed in terms of basic scanning factors such as tube current, exposure time, slice width and number of detectors. Each of these factors affects the overall magnitude of the noise power spectrum, but the spatial frequency dependence is also determined by the type of reconstruction filter used in the computer algorithm. The noise power spectrum has been calculated for scanners employing either a ramp or Hanning weighted ramp filter. Predictions made from this theoretical analysis have been compared with experimental measurements made on various CT scanners. Measurements were made of the modulation transfer function (MTF) by techniques which permitted us to deduce the contributions of the algorithmic and non-algorithmic components to the overall MTF. NEQ values have been calculated for a number of CT scanners.

Method of satellite operation using synthetic aperture radar addition holography for imaging

Abstract: A method of satellite operation utilizing a paired-satellite configuration in which one satellite illuminates the imaged field of view and the other satellite receives the reflected energy using bistatic synthetic radar. This method enables the unambiguous detection of radar signals for imagery construction, improves stability for image quality, provides recording format linearity to minimize image reconstruction processing, provides orthogonal range-doppler pattern distribution at all points in the recording plane to minimize computer processing, provides a triangulated signal reference baseline to improve system calibratability, and enables conformal mapping and uniform sampling of zone plates to achieve three dimensional holography.

Representation of three-dimensionally reconstructed objects in electron microscopy by surfaces of equal density.

Abstract: SUMMARY A surface representation algorithm has been developed to visualize the results of three-dimensional reconstructions from projections in electron microscopy. It produces an easily recognizable image of the reconstructed particle and facilitates comprehension of the three-dimensional structure. Thus building of physical models can be avoided in many cases. If such a model is needed the algorithm can be used to establish the correct particle boundary in advance. Some further effort has been made to represent long fibres and visualize inner structures of objects, which are obscured by outer high-density regions. Shading may be used to enhance the depth perception from single views.

Noise and contrast detection in computed tomography images

Abstract: A discrete representation of the reconstruction process is used in an analysis of noise in computed tomography (CT) images. This model is consistent with the method of data collection in actual machines. An expression is derived which predicts the variance on the measured linear attenuation coefficient of a single pixel in an image. The dependence of the variance on various CT scanner design parameters such as pixel size, slice width, scan time, number of detectors, etc., is then described. The variation of noise with sampling area is theoretically explained. These predictions are in good agreement with a set of experimental measurements made on a range of CT scanners. The equivalent sampling aperture of the CT process is determined and the effect of the reconstruction filter on the variance of the linear attenuation coefficient is also noted, in particular, the choice and its consequences for reconstructing images and noise behaviour. The theory has been extended to include contrast detail behaviour, and these predictions compare favourably with experimental measurements.

Imaging through an inhomogeneous layer by least‐mean‐square error fitting

Abstract: A new active ultrasonic imaging method through an inhomogeneous layer is proposed. It has the special feature that its effectiveness does not depend on the class of the objects to be imaged. In this method, first, a set of data is acquired by repeating transmission and reception for all possible combinations of pairs of transducers on the array, then the spatial frequency components of the object and the structure of the inhomogeneous layer are estimated from these data by means of least‐mean‐square error fitting. Since the data have redundancy for the parameters to be estimated, this process gives an optimum and stable estimation algorithm even when measurement errors and noise are included. The image is reconstructed from the estimated spatial frequency components through inverse Fourier transform. The effectiveness of this method is ensured by several numerical analyses and experiments.

Results of a Comparative Study of a Reconstruction Procedure for Producing Improved Estimates of Radioactivity Distributions in Time-of-Flight Emission Tomography

Abstract: Several reconstruction algorithms for estimating distributions of radioactivity in an emission-tomography system having time-of-flight measurements have previously been identified. We present here a comparative study of various images reconstructed from data acquired with an emission-tomography system having time-of-flight data. Preliminary results indicate that a new recursive algorithm provides substantial improvements in image quality.