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.     

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.     

Reconstruction From Uniformly Attenuated SPECT Projection Data Using the DBH Method

An algorithm was developed for the 2-D reconstruction of truncated and nontruncated uniformly attenuated data acquired from single photon emission computed tomography (SPECT). The algorithm is able to reconstruct data from half-scan (180$^{circ}$ ) and short-scan (180$^{circ}$ +fan angle) acquisitions for parallel- and fan-beam geometries, respectively, as well as data from full-scan (360 $^{circ}$) acquisitions. The algorithm is a derivative, backprojection, and Hilbert transform (DBH) method, which involves the backprojection of differentiated projection data followed by an inversion of the finite weighted Hilbert transform. The kernel of the inverse weighted Hilbert transform is solved numerically using matrix inversion. Numerical simulations confirm that the DBH method provides accurate reconstructions from half-scan and short-scan data, even when there is truncation. However, as the attenuation increases, finer data sampling is required.      

Extension of the 3-D range migration algorithm to cylindrical andspherical scanning geometries

A near field three-dimensional (3-D) synthetic-aperture radar (SAR) algorithm specially tailored for cylindrical and spherical scanning geometries is presented. An imaging system with 3-D capability can be implemented by using a stepped-frequency radar which synthesizes a two-dimensional (2-D) aperture. Typical scanning geometries commonly used are planar, cylindrical, and spherical. The 3-D range migration algorithm (RMA) can be readily used with a planar scanning geometry. This algorithm is extremely accurate, preserves the phase, and corrects for the wavefront curvature. The RMA cannot be directly applied with nonplanar scanning geometries. However, as an alternative solution, we propose to backpropagate the backscattered data onto a planar aperture in the vicinity of the measurement aperture and then apply the 3-D RMA. The proposed imaging algorithm is validated both numerically and experimentally     

Feldkamp-type cone-beam tomography in the wavelet framework

X-ray computed tomography (CT) is in transition from fan-beam to cone-beam geometry. For cone-beam volumetric imaging, reduction of radiation exposure remains an important issue. Because the wavelet approach was shown to be effective and flexible for two-dimensional (2-D) local region reconstruction, we are motivated to perform wavelet local CT in cone-beam geometry. In this paper, we formulate the Feldkamp cone-beam reconstruction from the wavelet perspective, derive both full-scan and half-scan Feldkamp-type formulas for either global or local reconstruction, and demonstrate the feasibility and utility in synthetic and real data. It is found that using the wavelet Feldkamp approach, a three-dimensional (3-D) region of interest (ROI) can be reconstructed with neither severe image artifacts nor any significant constant bias in our simulation and experiments.     

A cone-beam reconstruction algorithm for circle-plus-arc data-acquisition geometry

In cone-beam computerized tomography (CT), projections acquired with the focal spot constrained on a planar orbit cannot provide a complete set of data to reconstruct the object function exactly. There are severe distortions in the reconstructed noncentral transverse planes when the cone angle is large. In this work, a new method is proposed which can obtain a complete set of data by acquiring cone-beam projections along a circle-plus-arc orbit. A reconstruction algorithm using this circle-plus-arc orbit is developed, based on the Radon transform and Grangeat's formula. This algorithm first transforms the cone-beam projection data of an object to the first derivative of the three-dimensional (3-D) Radon transform, using Grangeat's formula, and then reconstructs the object using the inverse Radon transform. In order to reduce interpolation errors, new rebinning equations have been derived accurately, which allows one-dimensional (1-D) interpolation to be used in the rebinning process instead of 3-D interpolation. A noise-free Defrise phantom and a Poisson noise-added Shepp-Logan phantom were simulated and reconstructed for algorithm validation. The results from the computer simulation indicate that the new cone-beam data-acquisition scheme can provide a complete set of projection data and the image reconstruction algorithm can achieve exact reconstruction. Potentially, the algorithm can be applied in practice for both a standard CT gantry-based volume tomographic imaging system and a C-arm-based cone-beam tomographic imaging system, with little mechanical modification required.     

A system model and inversion for synthetic aperture radar imaging

A system model and its corresponding inversion for synthetic aperture radar (SAR) imaging are presented. The system model incorporates the spherical nature of a radar's radiation pattern at far field. The inverse method based on this model performs a spatial Fourier transform (Doppler processing) on the recorded signals with respect to the available coordinates of a translational radar (SAR) or target (inverse SAR). It is shown that the transformed data provide samples of the spatial Fourier transform of the target's reflectivity function. The inverse method can be modified to incorporate deviations of the radar's motion from its prescribed straight line path. The effects of finite aperture on resolution, reconstruction, and sampling constraints for the imaging problem are discussed.     

Exact and approximate rebinning algorithms for 3-D PET data

This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18° axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard “exact” 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time     

Bistatic synthetic aperture radar inversion with application indynamic object imaging

An inversion method is presented for bistatic synthetic aperture radar imaging. The method is based on a Fourier analysis (Doppler processing) of the bistatic synthesized array's data followed by a phase modulation analysis of the Doppler data. The approach incorporates the phase information of the wavefront curvature in the transmitted waves as well as the resultant echoed signals. The Doppler data are shown to provide samples of the reflectivity function's spatial Fourier transform within a band that depends upon the bistatic angles and ranges. Associated resolution, reconstruction, and sampling constraints for the imaging problem are discussed. The bistatic SAR inversion is also utilized to formulate an inversion for multistatic measurements made along a physical linear array due to a single transmission to image a dynamic object     

Three-dimensional interferometric ISAR imaging for targetscattering diagnosis and modeling

Two-dimensional (2-D) inverse synthetic aperture radar (ISAR) imaging has been widely used in target scattering diagnosis, modeling and target identification. A major shortcoming is that a 2-D ISAR image cannot provide information on the relative altitude of each scattering center on the target. In this paper, we present an interferometric inverse synthetic aperture radar (IF-ISAR) image processing technique for three-dimensional (3-D) target altitude image formation. The 2-D ISAR images are obtained from the signature data acquired as a function of frequency and azimuthal angle. A 3-D IF-ISAR altitude image can then be derived from two 2-D images reconstructed from the measurements by antennas at different altitudes. 3-D altitude image formation examples from both indoor and outdoor test range data are demonstrated on complex radar targets.     

Three-dimensional near-field MIMO array imaging using range migration techniques

This paper presents a 3-D near-field imaging algorithm that is formulated for 2-D wideband multiple-input-multiple-output (MIMO) imaging array topology. The proposed MIMO range migration technique performs the image reconstruction procedure in the frequency-wavenumber domain. The algorithm is able to completely compensate the curvature of the wavefront in the near-field through a specifically defined interpolation process and provides extremely high computational efficiency by the application of the fast Fourier transform. The implementation aspects of the algorithm and the sampling criteria of a MIMO aperture are discussed. The image reconstruction performance and computational efficiency of the algorithm are demonstrated both with numerical simulations and measurements using 2-D MIMO arrays. Real-time 3-D near-field imaging can be achieved with a real-aperture array by applying the proposed MIMO range migration techniques.     

基于稀疏孔径干涉ISAR技术的复杂运动舰船目标三维坐标恢复方法

基于正交双基线的3维干涉逆合成孔径雷达(ISAR)成像技术可获得目标的3维坐标信息,这对目标的分类与识别是非常有利的。然而,实际情况下回波数据一般都是稀疏的,这对传统的干涉成像技术带来一定的挑战。该文提出一种稀疏孔径情况下的舰船目标3维干涉成像算法,并采用最小熵方法实现回波数据的运动补偿与图像配准,同时基于梯度算子实现对稀疏数据的精确恢复。通过对方位向数据进行参数估计与压缩处理,可获得目标的2维ISAR成像结果,进而基于干涉技术实现对复杂运动舰船目标的3维成像。仿真数据验证了文中方法的有效性。      

3-D radar imaging using range migration techniques

An imaging system with three-dimensional (3-D) capability can be implemented by using a stepped frequency radar which synthesizes a two-dimensional (2-D) planar aperture. A 3-D image can be formed by coherently integrating the backscatter data over the measured frequency band and the two spatial coordinates of the 2-D synthetic aperture. This paper presents a near-field 3-D synthetic aperture radar (SAR) imaging algorithm. This algorithm is an extension of the 2-D range migration algorithm (RMA). The presented formulation is justified by using the method of the stationary phase (MSP). Implementation aspects including the sampling criteria, resolutions, and computational complexity are assessed. The high computational efficiency and accurate image reconstruction of the algorithm are demonstrated both with numerical simulations and measurements using an outdoor linear SAR system     

Tomographic Reconstruction of Three-Dimensional Volumes Using the Distorted Born Iterative Method

Although real imaging problems involve objects that have variations in three dimensions, a majority of work examining inverse scattering methods for ultrasonic tomography considers 2-D imaging problems. Therefore, the study of 3-D inverse scattering methods is necessary for future applications of ultrasonic tomography. In this work, 3-D reconstructions using different arrays of rectangular elements focused on elevation were studied when reconstructing spherical imaging targets by producing a series of 2-D image slices using the 2-D distorted Born iterative method (DBIM). The effects of focal number f/#, speed of sound contrast Deltac, and scatterer size were considered. For comparison, the 3-D wave equation was also inverted using point-like transducers to produce fully 3-D DBIM image reconstructions. In 2-D slicing, blurring in the vertical direction was highly correlated with the transmit/receive elevation point-spread function of the transducers for low Deltac. The eventual appearance of overshoot artifacts in the vertical direction were observed with increasing Deltac. These diffraction-related artifacts were less severe for smaller focal number values and larger spherical target sizes. When using 3-D DBIM, the overshoot artifacts were not observed and spatial resolution was improved. However, results indicate that array configuration in 3-D reconstructions is important for good image reconstruction. Practical arrays were designed and assessed for image reconstruction using 3-D DBIM.     

On a limited-view reconstruction problem in diffraction tomography

Diffraction tomography (DT) is an inversion technique that reconstructs the refractive index distribution of a scattering object. We previously demonstrated that by exploiting the redundant information in the DT data, the scattering object could be exactly reconstructed using measurements taken over the angular range [0, phimin], where pi < phimin < or = 3pi/2. In this paper, we reveal a relationship between the maximum scanning angle and image resolution when a filtered backpropagation (FBPP) reconstruction algorithm is employed for image reconstruction. Based on this observation, we develop short-scan FBPP algorithms that reconstruct a low-pass filtered scattering object from measurements acquired over the angular range [0, phi(c)], where phi(c) < phimin.     

An efficient Fourier method for 3-D radon inversion in exactcone-beam CT reconstruction

The radial derivative of the three-dimensional (3-D) radon transform of an object is an important intermediate result in many analytically exact cone-beam reconstruction algorithms. The authors briefly review Grangeat's (1991) approach for calculating radon derivative data from cone-beam projections and then present a new, efficient method for 3-D radon inversion, i.e., reconstruction of the image from the radial derivative of the 3-D radon transform, called direct Fourier inversion (DFI). The method is based directly on the 3-D Fourier slice theorem. From the 3-D radon derivative data, which is assumed to be sampled on a spherical grid, the 3-D Fourier transform of the object is calculated by performing fast Fourier transforms (FFTs) along radial lines in the radon space. Then, an interpolation is performed from the spherical to a Cartesian grid using a 3-D gridding step in the frequency domain. Finally, this 3-D Fourier transform is transformed back to the spatial domain via 3-D inverse FFT. The algorithm is computationally efficient with complexity in the order of N ³ log N. The authors have done reconstructions of simulated 3-D radon derivative data assuming sampling conditions and image quality requirements similar to those in medical computed tomography (CT)     

The unifying role of the coarray in aperture synthesis for coherentand incoherent imaging

Systems of two-dimensional (2-D) imaging arrays and apertures are considered from the point of view of their performance in the imaging of spatially incoherent as well as coherent source distributions. Such systems find applications in radar, sonar, and ultrasound imaging, as well as in applications such as seismology and radio astronomy. For linear imaging techniques related to beamforming and based on the Fourier transform relationship between the source distribution and the aperture plane measurements, the point spread function of the system completely characterizes its performance. This function is determined by the geometry of the physical aperture or array as well as the weighting that can be applied to measurements. It is shown that the introduction of the concept of coarray, both for receive apertures in incoherent imaging and for transmit/receive systems in reflection-mode coherent imaging, provides a convenient and elegant framework within which many apparently isolated techniques for point-spread function or aperture synthesis can be understood. In addition to this unifying role, coarray concept gives new insight into the aperture synthesis process, which allows interesting new imaging techniques to be developed, especially in coherent imaging     

Efficient framework for model-based tomographic image reconstruction using wavelet packets

The use of model-based algorithms in tomographic imaging offers many advantages over analytical inversion methods. However, the relatively high computational complexity of model-based approaches often restricts their efficient implementation. In practice, many modern imaging modalities, such as computed-tomography, positron-emission tomography, or optoacoustic tomography, normally use a very large number of pixels/voxels for image reconstruction. Consequently, the size of the forward-model matrix hinders the use of many inversion algorithms. In this paper, we present a new framework for model-based tomographic reconstructions, which is based on a wavelet-packet representation of the imaged object and the acquired projection data. The frequency localization property of the wavelet-packet base leads to an approximately separable model matrix, for which reconstruction at each spatial frequency band is independent and requires only a fraction of the projection data. Thus, the large model matrix is effectively separated into a set of smaller matrices, facilitating the use of inversion schemes whose complexity is highly nonlinear with respect to matrix size. The performance of the new methodology is demonstrated for the case of 2-D optoacoustic tomography for both numerically generated and experimental data.     

Convolution backprojection formulas for 3-D vector tomography withapplication to MRI

Vector tomography is the reconstruction of vector fields from measurements of their projections. In previous work, it has been shown that the reconstruction of a general three-dimensional (3-D) vector field is possible from the so-called inner product measurements. It has also been shown how the reconstruction of either the irrotational or solenoidal component of a vector field can be accomplished with fewer measurements than that required for the full field. The present paper makes three contributions. First, in analogy to the two-dimensional (2-D) approach of Norton (1988), several 3-D projection theorems are developed. These lead directly to new vector field reconstruction formulas that are convolution backprojection formulas. It is shown how the local reconstruction property of these 3-D reconstruction formulas permits reconstruction of point flow or of regional flow from a limited data set. Second, simulations demonstrating 3-D reconstructions, both local and nonlocal, are presented. Using the formulas derived herein and those derived in previous work, these results demonstrate the reconstruction of the irrotational and solenoidal components, their potential functions, and the field itself from simulated inner product measurement data. Finally, it is shown how 3-D inner product measurements can be acquired using a magnetic resonance scanner     

Electrical impedance tomography

Electrical impedance tomography (EIT) is an imaging modality that estimates the electrical properties at the interior of an object from measurements made on its surface. Typically, currents are injected into the object through electrodes placed on its surface, and the resulting electrode voltages are measured. An appropriate set of current patterns, with each pattern specifying the value of the current for each electrode, is applied to the object, and a reconstruction algorithm uses knowledge of the applied current patterns and the measured electrode voltages to solve the inverse problem, computing the electrical conductivity and permittivity distributions in the object. This article focuses on the type of EIT called adaptive current tomography (ACT) in which currents are applied simultaneously to all the electrodes. A number of current patterns are applied, where each pattern defines the current for each electrode, and the subsequent electrode voltages are measured to generate the data required for image reconstruction. A ring of electrodes may be placed in a single plane around the object, to define a two-dimensional problem, or in several layers of such rings, to define a three-dimensional problem. The reconstruction problem is described and two algorithms are discussed, a one-step, two-dimensional (2-D) Newton-Raphson algorithm and a one-step, full three-dimensional (3-D) reconstructor. Results from experimental data are presented which illustrate the performance of the algorithms