Data redundancy and reduced-scan reconstruction in reflectivity tomography

In reflectivity tomography, conventional reconstruction approaches require that measurements be acquired at view angles that span a full angular range of 2/spl pi/. It is often, however, advantageous to reduce the angular range over which measurements are acquired, in order, for example, to minimize artifacts due to movements of the imaged object. Moreover, in certain situations, it may not be experimentally possible to collect data over a 2/spl pi/ angular range. We investigate the problem of reconstructing images from reduced-scan data in reflectivity tomography. By exploiting symmetries in the data function of reflectivity tomography, we demonstrate heuristically that an image function can be uniquely specified by reduced-scan data that correspond to measurements taken over an angular interval (possibly disjoint) that spans at least /spl pi/ radians. We also identify sufficient conditions that permit for a stable reconstruction of image boundaries from reduced-scan data. Numerical results in computer-simulation studies indicate that images can be reconstructed accurately from reduced-scan data.     

Time-domain reconstruction for thermoacoustic tomography in a spherical geometry

Reconstruction-based microwave-induced thermoacoustic tomography in a spherical configuration is presented. Thermoacoustic waves from biological tissue samples excited by microwave pulses are measured by a wide-band unfocused ultrasonic transducer, which is set on a spherical surface enclosing the sample. Sufficient data are acquired from different directions to reconstruct the microwave absorption distribution. An exact reconstruction solution is derived and approximated to a modified backprojection algorithm. Experiments demonstrate that the reconstructed images agree well with the original samples. The spatial resolution of the system reaches 0.5 mm.     

Feasibility of enhanced microwave image resolution using a superdirective aperture

Microwave imaging systems with small numerical apertures have low resolution. It is shown that substantial enhancement of resolution is possible if the recorded data can be loaded with a superdirective function. The criterion for use of this technique is that the recorded data are sufficiently accurate.     

Fast fully 3-D image reconstruction in PET using planograms

We present a method of performing fast and accurate three-dimensional (3-D) backprojection using only Fourier transform operations for line-integral data acquired by planar detector arrays in positron emission tomography. This approach is a 3-D extension of the two-dimensional (2-D) linogram technique of Edholm. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used to index a LOR for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2-D plane in the four-dimensional (4-D) data space. Thus, backprojection of all the LORs passing through a point in the FOV corresponds to integration of a 2-D plane through the 4-D "planogram." The key step is that the integration along a set of parallel 2-D planes through the planogram, that is, backprojection of a plane of points, can be replaced by a 2-D section through the origin of the 4-D Fourier transform of the data. Backprojection can be performed as a sequence of Fourier transform operations, for faster implementation. In addition, we derive the central-section theorem for planogram format data, and also derive a reconstruction filter for both backprojection-filtering and filtered-backprojection reconstruction algorithms. With software-based Fourier transform calculations we provide preliminary comparisons of planogram backprojection to standard 3-D backprojection and demonstrate a reduction in computation time by a factor of approximately 15.     

Pattern tracking and 3-D motion reconstruction of a rigid body from a 2-D image sequence

This paper presents an integrated method to identify an object pattern from an image, and track its movement over a sequence of images. The sequence of images comes from a single perspective video source, which is capturing data from a precalibrated scene. This information is used to reconstruct the scene in three-dimension (3-D) within a virtual environment where a user can interact and manipulate the system. The steps that are performed include the following: i) Identify an object pattern from a two-dimensional perspective video source. The user outlines the region of interest (ROI) in the initial frame; the procedure builds a refined mask of the dominant object within the ROI using the morphological watershed algorithm. ii) The object pattern is tracked between frames using object matching within the mask provided by the previous and next frame, computing the motion parameters. iii) The identified object pattern is matched with a library of shapes to identify a corresponding 3-D object. iv) A virtual environment is created to reconstruct the scene in 3-D using the 3-D object and the motion parameters. This method can be applied to real-life application problems, such as traffic management and material flow congestion analysis.     

单幅高分辨率SAR图像建筑物三维模型重构

提出了一种利用高分辨率SAR图像进行建筑物提取和三维重构的方法.首先,分析了高分辨率SAR图像建筑物产生的电磁散射的类型,给出了不同类型散射区域的后向散射计算方法,并在此基础上给出了一种利用建筑物三维CAD模型进行SAR建筑物特征区域图像仿真的方法;其次,给出了利用建筑物的二次散射结构确定建筑物底部轮廓位置和方向的方法,并提出了一种基于分布密度函数差异的仿真图像迭代匹配方法,进行建筑物高度的反演.仿真SAR图像后向散射系数用来划分建筑物不同的散射区域,通过计算特征区域之间的分布密度函数差异,以取得最大匹配度值的仿真图像对应的检验高度作为建筑物的反演高度;最后,选用了两幅不同屋顶类型的实际机载高分辨率SAR图像进行建筑物提取和三维重构实验,试验结果较为理想,验证了所提方法的可行性和有效性.     

Computing reconstruction kernels for circular 3-D cone beam tomography

In this paper, we present techniques for deriving inversion algorithms in 3-D computer tomography. To this end, we introduce the mathematical model and apply a general strategy, the so-called approximate inverse, for deriving both exact and numerical inversion formulas. Using further approximations, we derive a 2-D shift-invariant filter for circular-orbit cone-beam imaging. Results from real data are presented.      

Microwave image reconstruction from 3-D fields coupled to 2-D parameter estimation

An efficient Gauss-Newton iterative imaging technique utilizing a three-dimensional (3-D) field solution coupled to a two-dimensional (2-D) parameter estimation scheme (3-D/2-D) is presented for microwave tomographic imaging in medical applications. While electromagnetic wave propagation is described fully by a 3-D vector field, a 3-D scalar model has been applied to improve the efficiency of the iterative reconstruction process with apparently limited reduction in accuracy. In addition, the image recovery has been restricted to 2-D but is generalizable to three dimensions. Image artifacts related primarily to 3-D effects are reduced when compared with results from an entirely two-dimensional inversion (2-D/2-D). Important advances in terms of improving algorithmic efficiency include use of a block solver for computing the field solutions and application of the dual mesh scheme and adjoint approach for Jacobian construction. Methods which enhance the image quality such as the log-magnitude/unwrapped phase minimization were also applied. Results obtained from synthetic measurement data show that the new 3-D/2-D algorithm consistently outperforms its 2-D/2-D counterpart in terms of reducing the effective imaging slice thickness in both permittivity and conductivity images over a range of inclusion sizes and background medium contrasts.     

3-D model localization using high-resolution reconstruction ofmonocular image sequences

In this paper, we present a complete system for the recognition and localization of a three-dimensional (3-D) model from a sequence of monocular images with known motion. The originality of this system is twofold. First, it uses a purely 3-D approach, starting from the 3-D reconstruction of the scene and ending by the 3-D matching of the model. Second, unlike most monocular systems, we do not use token tracking to match successive images. Rather, subpixel contour matching is used to recover more precisely complete 3-D contours. In contrast with the token tracking approaches, which yield a representation of the 3-D scene based on disconnected segments or points, this approach provides us with a denser and higher level representation of the scene. The reconstructed contours are fused along successive images using a simple result derived from the Kalman filter theory. The fusion process increases the localization precision and the robustness of the 3-D reconstruction. Finally, corners are extracted from the 3-D contours. They are used to generate hypotheses of the model position, using a hypothesize-and-verify algorithm that is described in detail. This algorithm yields a robust recognition and precise localization of the model in the scene. Results are presented on infrared image sequences with different resolutions, demonstrating the precision of the localization as well as the robustness and the low computational complexity of the algorithms.     

Half-time image reconstruction in thermoacoustic tomography

Thermoacoustic tomography (TAT) is an emerging imaging technique with great potential for a wide range of biomedical imaging applications. In this paper, we propose and investigate reconstruction approaches for TAT that are based on the half-time reflectivity tomography paradigm. We reveal that half-time reconstruction approaches permit for the explicit control of statistically complementary information that can result in the optimal reduction of image variances. We also show that half-time reconstruction approaches can mitigate image artifacts due to heterogeneous acoustic properties of an object. Reconstructed images and numerical results produced from simulated and experimental TAT measurement data are employed to demonstrate these effects.     

Parallelization of the EM algorithm for 3-D PET image reconstruction

The EM algorithm for PET image reconstruction has two major drawbacks that have impeded the routine use of the EM algorithm: the long computation time due to slow convergence and a large memory required for the image, projection, and probability matrix. An attempt is made to solve these two problems by parallelizing the EM algorithm on multiprocessor systems. An efficient data and task partitioning scheme, called partition-by-box, based on the message passing model is proposed. The partition-by-box scheme and its modified version have been implemented on a message passing system, Intel iPSC/2, and a shared memory system, BBN Butterfly GP1000. The implementation results show that, for the partition-by-box scheme, a message passing system of complete binary tree interconnection with fixed connectivity of three at each node can have similar performance to that with the hypercube topology, which has a connectivity of log(2) N for N PEs. It is shown that the EM algorithm can be efficiently parallelized using the (modified) partition-by-box scheme with the message passing model.     

3-D image reconstruction from averaged Fourier transform magnitudeby parameter estimation

An object model and estimation procedure for three-dimensional (3-D) reconstruction of objects from measurements of the spherically averaged Fourier transform magnitudes is described. The motivating application is the 3-D reconstruction of viruses based on solution X-ray scattering data. The object model includes symmetry, positivity and support constraints and has the form of a truncated orthonormal expansion and the parameters are estimated by maximum likelihood methods. Successful 3-D reconstructions based on synthetic and experimental measurements from Cowpea mosaic virus are described.     

An improved reconstruction algorithm for 3-D diffraction tomography using spherical-wave sources

Diffraction tomography (DT) is an inversion technique that reconstructs the refractive index distribution of a weakly scattering object. In this paper, a novel reconstruction algorithm for three-dimensional diffraction tomography employing spherical-wave sources is mathematically developed and numerically implemented. Our algorithm is numerically robust and is much more computationally efficient than the conventional filtered backpropagation algorithm. Our previously developed algorithm for DT using plane-wave sources is contained as a special case.     

Convolution backprojection image reconstruction for spotlight modesynthetic aperture radar

Convolution backprojection (CBP) image reconstruction has been proposed as a means of producing high-resolution synthetic-aperture radar (SAR) images by processing data directly in the polar recording format which is the conventional recording format for spotlight mode SAR. The CBP algorithm filters each projection as it is recorded and then backprojects the ensemble of filtered projections to create the final image in a pixel-by-pixel format. CBP reconstruction produces high-quality images by handling the recorded data directly in polar format. The CBP algorithm requires only 1-D interpolation along the filtered projections to determine the precise values that must be contributed to the backprojection summation from each projection. The algorithm is thus able to produce higher quality images by eliminating the inaccuracies of 2-D interpolation, as well as using all the data recorded in the spectral domain annular sector more effectively. The computational complexity of the CBP algorithm is O(N (3)).     

Aperture collimation correction and maximum-likelihood image reconstruction for near-field coded aperture imaging of single photon emission computerized tomography

Coded aperture (CA) imaging originally developed in X-ray astronomy has not been widely used in nuclear medicine due to the decoding complexity of near-field CA images. In this paper, we present a near-field CA imaging technique and image reconstruction method for high sensitivity and high resolution single photon emission computerized tomography (SPECT). Our approach makes three contributions. First, a correction method for the aperture collimation effect is used to eliminate the near-field artifacts without dual acquisitions of mask and anti-mask images. Second, a maximum-likelihood expectation-maximization (MLEM) deconvolution method is used to restore CA images. Finally, a new MLEM-based algorithm is used to partially reconstruct three-dimensional (3-D) objects from a single projection of CA images. Experiments conducted using a dual-head SPECT system equipped with a parallel-hole collimator and a CA module show a tenfold increase in count sensitivity and significant improvement in image resolution with CA collimation as compared to parallel-hole collimation. Experiments conducted using the same dual-head SPECT system equipped with a pinhole collimator show that when the object is closer to the pinhole collimator the CA image resolution is only slightly inferior to the pinhole collimated image. We found that the MLEM deconvolution method provides an inherent nonnegativity constraint on pixel values and remarkably reduces background activities of CA images. The MLEM reconstruction algorithm for CA images is capable of reconstructing 3-D objects from a single projection and can be potentially extended to full 3-D SPECT reconstruction for CA images.     

Three-dimensional reconstruction using homocentric spherical spatiotemporal image analysis

This paper presents a new algorithm for reconstructing a scene of three-dimensional structures from an image sequence. Three-dimensional reconstruction using an image sequence, called the spatiotemporal image method, is robust against image noises. But in this method, camera motion is limited to only one direction translation. Our algorithm makes allowances for camera rotation in spatiotemporal image analysis. With this technique, the whole spatiotemporal image is transformed to spherical projection and three-dimensional structures are determined robustly using the Hough transformation. We call the technique Homocentric Spherical Spatiotemporal Image (HSSI) analysis. With HSSI, it is possible to distinguish objects with a rotating camera from a longer baseline and to measure them with much greater accuracy than previously possible. This algorithm is demonstrated through simulations and experiments with real images from a translating and rotating camera, and the three-dimensional structures in a static scene are reconstructed.     

Iterative image reconstruction using inverse fourier rebinning for fully 3-D PET

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully three-dimensional (3-D) positron emission tomography (PET). The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a two-dimensional (2-D) projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing line of responses (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation.     

Iterative image reconstruction using inverse Fourier rebinning for fully 3-D PET

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully 3-D positron emission tomography (PET). The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a 2-D projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing lines of response (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation.     

Practical considerations for 3-D image reconstruction using spherically symmetric volume elements

Spherically symmetric volume elements with smooth tapering of the values near their boundaries are alternatives to the more conventional voxels for the construction of volume images in the computer. Their use, instead of voxels, introduces additional parameters which enable the user to control the shape of the volume element (blob) and consequently to control the characteristics of the images produced by iterative methods for reconstruction from projection data. For images composed of blobs, efficient algorithms have been designed for the projection and discrete back-projection operations, which are the crucial parts of iterative reconstruction methods. The authors have investigated the relationship between the values of the blob parameters and the properties of images represented by the blobs. Experiments show that using blobs in iterative reconstruction methods leads to substantial improvement in the reconstruction performance, based on visual quality and on quantitative measures, in comparison with the voxel case. The images reconstructed using appropriately chosen blobs are characterized by less image noise for both noiseless data and noisy data, without loss of image resolution.     

Three-dimensional guide-wire reconstruction from biplane image sequences for integrated display in 3-D vasculature

Using three-dimensional rotational X-ray angiography (3DRA), three-dimensional (3-D) information of the vasculature can be obtained prior to endovascular interventions. However, during interventions, the radiologist has to rely on fluoroscopy images to manipulate the guide wire. In order to take full advantage of the 3-D information from 3DRA data during endovascular interventions, a method is presented that yields an integrated display of the position of the guide wire and vasculature in 3-D. The method relies on an automated method that tracks the guide wire simultaneously in biplane fluoroscopy images. Based on the calibrated geometry of the C-arm, the 3-D guide-wire position is determined and visualized in the 3-D coordinate system of the vasculature. The method is evaluated in an intracranial anthropomorphic vascular phantom. The influence of the angle between projections, distortion correction of the projection images, and accuracy of geometry knowledge on the accuracy of 3-D guide-wire reconstruction from biplane images is determined. If the calibrated geometry information is used and the images are corrected for distortion, a mean distance to the reference standard of 0.42 mm and a tip distance of 0.65 mm is found, which means that accurate guide-wire reconstruction from biplane images can be performed.