Quantitative and Qualitative Evaluation of Geometric Deconvolution of Distortion in Limited-View Computed Tomography

Images reconstructed using a set of a few projections spanning a narrow angular range suffer from a systematic geometric distortion due to the point spread function of the reconstruction process. This distortion can be removed by deconvolving a complementary set of projections calculated from the initial reconstruction. Homomorphic deconvolution and inverse filtering techniques were used for this purpose. A second reconstruction is computed from the union of both sets of projections. Although the distortion is removed, the results are noisy due to problems associated with inverse filtering. Two-dimensional (2-D) filtering of the second reconstruction is performed to reduce the noise, while preserving the reduction in geometric distortion. Results obtained using several 2-D filters were compared visually and by point noise content, distortion, and projection error measures. Quantitative measures of geometric distortion removal for test images are also described.     

Derivation and analysis of a filtered backprojection algorithm for cone beam projection data

The authors address the problem of three-dimensional image reconstruction from cone beam projections. Modifying a result due to A.A. Kirillov (Soviet Math. Dokl., vol. 2, p.268-9, 1961), the authors derive an inversion formula for the case where the cone vertices form an unbounded curve. For the special case in which the cone vertices form a circle, an approximate reconstruction formula is developed and shown to be essentially equivalent to the practical cone-beam algorithm of L.A. Feldkamp et al. (1984). For this approximate inverse, the authors derive the resulting spatially varying point spread function, examine the effect of bandlimiting due to sampling, and compare the resulting image quality as a function of the radius of the circle formed by the cone vertices.     

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.     

Resolution enhancement of biomagnetic images using the method ofalternating protections

Resolution of biomagnetic images using the technique of alternating projections is proposed. The image reconstruction procedure is divided into two steps. First, the biomagnetic inverse problem is solved by using the projection theorem to reconstruct an initial image of the current distribution from a given magnetic field profile. Although the current distribution thus obtained has poor resolution, it can resemble the original shape of the current distribution. The second step improves the resolution of the reconstructed image by using the method of alternating projections. The procedure assumes that images can be represented by linelike elements and involves finding such elements based on the initial image and projecting back onto the original solution space. Simulation studies were performed on a set of parallel conductors and conductors shaped in the form of the letters, U, W, and B and of the `at' symbol, and all of linelike thickness. Restored images closely resemble the original shape of the conductors     

Reply to "Comments on Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography"2

We have developed two new "meta-algorithms" for computed tomography that give significantly improved images through deconvolution of the two-dimensional point spread function of standard, quasi-linear algorithms. In geometric deconvolution the projections of the point spread function provide the basis for a set of one-dimensional deconvolutions. In two-dimensional Wiener deconvolution, the two-dimensional point spread function is deconvoluted directly. The criticism that there is no data available for these deconvolutions is met here by showing that the "missing data" is partly provided by incorporation of a priori information, as is the practice in other superresolution work.     

Hilbert transform based FBP algorithm for fan-beam CT full and partial scans

This paper presents a new type of filtered backprojection (FBP) algorithm for fan-beam full- and partial-scans. The filtering is shift-invariant with respect to the angular variable. The backprojection does not include position-dependent weights through the Hilbert transform and the one-dimensional transformation between the fan- and parallel-beam coordinates. The strong symmetry of the filtered projections directly leads to an exact reconstruction for partial data. The use of the Hilbert transform avoids the approximation introduced by the nonuniform cutoff frequency required in the ramp filter-based FBP algorithm. Variance analysis indicates that the algorithm might lead to a better uniformity of resolution and noise in the reconstructed image. Numerical simulations are provided to evaluate the algorithm with noise-free and noisy projections. Our simulation results indicate that the algorithm does have better stability over the ramp-filter-based FBP and circular harmonic reconstruction algorithms. This may help improve the image quality for in place computed tomography scanners with single-row detectors.     

Noniterative compensation for the distance-dependent detector response and photon attenuation in SPECT imaging

A filtering approach is described, which accurately compensates for the 2D distance-dependent detector response, as well as for photon attenuation in a uniform attenuating medium. The filtering method is based on the frequency distance principle (FDP) which states that points in the object at a specific source-to-detector distance provide the most significant contribution to specified frequency regions in the discrete Fourier transform (DFT) of the sinogram. By modeling the detector point spread function as a 2D Gaussian function whose width is dependent on the source-to-detector distance, a spatially variant inverse filter can be computed and applied to the 3D DFT of the set of all sinogram slices. To minimize noise amplification the inverse filter is rolled off at high frequencies by using a previously published Wiener filter strategy. Attenuation compensation is performed with Bellini's method. It was observed that the tomographic point response, after distance-dependent filtering with the FDP, was approximately isotropic and varied substantially less with position than that obtained with other correction methods. Furthermore, it was shown that processing with this filtering technique provides reconstructions with minimal degradation in image fidelity.     

Investigation of fiber grating-based performance limits in pulse stretching and recompression schemes using bidirectional reflection from a linearly chirped fiber grating

We demonstrate the controlled stretching and recompression of ultrashort optical pulses using bidirectional reflection from both ends of a single linearly chirped fiber grating. We identify operating regimes for minimal pulse distortion due to the phase and filtering responses of a simple linear grating and experimentally demonstrate complete pulse reconstruction.     

Optimal scan for time-varying tomography. II. Efficient design andexperimental validation

For pt.I see ibid., vol.4, no.5, p.642-53 (1995). In pt.I the authors presented a theoretical analysis of tomographic reconstruction of objects with spatially localized temporal variation, such as a thorax cross section with a beating heart. That analysis showed that by using an optimally scrambled angular sampling order, the scan rate required to avoid motion artifacts in the reconstructed images can be lowered as much as four times while preserving image quality. Here, the authors present a simple design procedure for the optimum choice of angular sampling pattern, which depends only on pre-specified geometric and spectral parameters and the desired spatial resolution. The resulting patterns have a simple congruential structure. Reconstruction is accomplished by interpolation to standard time-invariant scan format, followed by conventional reconstruction. The interpolation only requires linear shift-invariant separable filtering, at a negligible computational cost. Simulation results demonstrate the technique and validate the analysis for both bandlimited and approximately bandlimited objects.     

微小区环境下角度扩散特性的仿真结果

智能天线及其他空间滤波技术的研究与应用为无线信道的研究提出了新的课题－需要对无线信道的时空联合扩散特性进行全面地分析和研究.本文利用射线跟踪技术对典型微小区下信道的时域扩散和角度扩散特性进行了大量仿真.作者按照时域扩散的研究方法,利用角度扩散的一阶矩和二阶中心矩来说明问题.通过典型环境下的仿真,得到了存在直达信号和无直达信号两种接收条件下的角度扩散结果.     

Optimal design of transform-based block digital filters using a quadratic criterion

Block digital filtering is a powerful tool to reduce the computational complexity of digital filtering systems. However, due to their block structure, block digital filters (BDFs) are time-varying linear systems, hence, their design is not easy. The most widely spread approaches to BDF design consist of constraining the BDF to be time-invariant (by restricting the design process to a specific subset of possible solutions) and then using conventional filter synthesis techniques. In this paper, we do not restrict the design process, and we propose a simple and optimal matrix-oriented approach to optimize the BDF coefficients. Furthermore, the proposed approach takes profit of the structure of transform-based BDFs to considerably reduce the computational complexity and memory requirements of the design process. Experimental results confirm that as expected, the obtained global distortion is lower than the distortion obtained with a traditional technique such as overlap-save.     

A stochastic continuation approach to piecewise constant reconstruction.

We address the problem of reconstructing a piecewise constant 3-D object from a few noisy 2-D line-integral projections. More generally, the theory developed here readily applies to the recovery of an ideal n-D signal (n > or =1) from indirect measurements corrupted by noise. Stabilization of this ill-conditioned inverse problem is achieved with the Potts prior model, which leads to a challenging optimization task. To overcome this difficulty, we introduce a new class of hybrid algorithms that combines simulated annealing with deterministic continuation. We call this class of algorithms stochastic continuation (SC). We first prove that, under mild assumptions, SC inherits the finite-time convergence properties of generalized simulated annealing. Then, we show that SC can be successfully applied to our reconstruction problem. In addition, we look into the concave distortion acceleration method introduced for standard simulated annealing and we derive an explicit formula for choosing the free parameter of the cost function. Numerical experiments using both synthetic data and real radiographic testing data show that SC outperforms standard simulated annealing.     

Novel Inverse S Transform With Equalization Filter

The S transform is a useful linear time-frequency distribution with a progressive resolution. Since it is linear, it filters efficiently in a time-frequency domain by multiplying a mask function. Several different inverse algorithms exist, which may result in different filtering effects. The conventional inverse S transform (IST) proposed by Stockwell is efficient but suffers from time leakage during filtering. The recent algorithm proposed by Schimmel and Gallart has better time localization during filtering but suffers from a reconstruction error and the frequency leakage during filtering. In this paper, two new IST algorithms are proposed that have better time-frequency localization in filtering than the previous two methods.     

Blind deconvolution of medical ultrasound images: a parametric inverse filtering approach.

The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a "hybridization" of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the "hybrid" approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolutioh algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.     

3D-Object Space Reconstruction from Planar Recorded Data of 3D-Integral Images

The paper presents a novel algorithm for object space reconstruction from the planar (2D) recorded data set of a 3D-integral image. The integral imaging system is described and the associated point spread function is given. The space data extraction is formulated as an inverse problem, which proves ill-conditioned, and tackled by imposing additional conditions to the sought solution. An adaptive constrained 3D-reconstruction regularization algorithm based on the use of a sigmoid function is presented. A hierarchical multiresolution strategy which employes the adaptive constrained algorithm to obtain highly accurate intensity maps of the object space is described. The depth map of the object space is extracted from the intensity map using a weighted Durbin–Willshaw algorithm. Finally, illustrative simulation results are given.     

Markov random field modeling for three-dimensional reconstruction of the left ventricle in cardiac angiography

This paper reports on a method for left ventricle three-dimensional (3-D) reconstruction from two orthogonal ventriculograms. The proposed algorithm is voxel-based and takes into account the conical projection geometry associated with the biplane image acquisition equipment. The reconstruction process starts with an initial ellipsoidal approximation derived from the input ventriculograms. This model is subsequently deformed in such a way as to match the input projections. To this end, the object is modeled as a 3-D Markov-Gibbs random field, and an energy function is defined so that it includes one term that models the projections compatibility and another one that includes the space-time regularity constraints. The performance of this reconstruction method is evaluated by considering the reconstruction of mathematically synthesized phantoms and two 3-D binary databases from two orthogonal synthesized projections. The method is also tested using real biplane ventriculograms. In this case, the performance of the reconstruction is expressed in terms of the projection error, which attains values between 9.50% and 11.78 % for two biplane sequences including a total of 55 images.     

Truncated total least squares: a new regularization method for the solution of ECG inverse problems

The reconstruction of epicardial potentials (EPs) from body surface potentials (BSPs) can be characterized as an ill-posed inverse problem which generally requires a regularized numerical solution. Two kinds of errors/noise: geometric errors and measurement errors exist in the ECG inverse problem and make the solution of such problem more difficulty. In particular, geometric errors will directly affect the calculation of transfer matrix A in the linear system equation AX = B. In this paper, we have applied the truncated total least squares (TTLS) method to reconstruct EPs from BSPs. This method accounts for the noise/errors on both sides of the system equation and treats geometric errors in a new fashion. The algorithm is tested using a realistically shaped heart-lung-torso model with inhomogeneous conductivities. The h-adaptive boundary element method [h-BEM, a BEM mesh adaptation scheme which starts from preset meshes and then refines (adds/removes) grid with fixed order of interpolation function and prescribed numerical accuracy] is used for the forward modeling and the TTLS is applied for inverse solutions and its performance is also compared with conventional regularization approaches such as Tikhonov and truncated single value decomposition (TSVD) with zeroth-, first-, and second-order. The simulation results demonstrate that TTLS can obtain similar results in the situation of measurement noise only but performs better than Tikhonov and TSVD methods where geometric errors are involved, and that the zeroth-order regularization is the optimal choice for the ECG inverse problem. This investigation suggests that TTLS is able to robustly reconstruct EPs from BSPs and is a promising alternative method for the solution of ECG inverse problems.     

基于区域互信息的特征级多光谱图像配准

提出了一种基于点特征的多光谱图像配准方法.利用SUSAN算法提取角点特征,采用域互信息(RMI)作为相似性测度获取初始匹配特征点集;在精匹配阶段,首先计算初始匹配征点对的匹配强度和明确度,进行松弛迭代,得到匹配强度和明确度都较大的一一对应关系的特征点对,然后利用马氏距离的仿射不变性筛选出正确的点对,将不正确的点对从初始匹配特征点集中删除,重新进行松弛迭代,重复上面的步骤,直到筛选不出新的正确点对为止;获取了足够多的同名控制点后,用最小二乘法估计初始仿射变换参数并迭代修正.实验结果表明,算法可以达到亚像素级的配准精度.     

Digital reconstruction of images from their projections in polar coordinates

In a wide variety of applications, it is necessary to infer the structure of a three-dimensional object from its projections. Usually, the problem is reduced to the reconstruction of a series of two-dimensional (planar) sections from a set of one-dimensional (linear) projections. In this paper, starting from a polar representation of the density function, we present some closed form formulas, which can be successfully used in the reconstruction of images. The results of some numerical tests are also presented.     

Exact (spiral + circles) scan region-of-interest cone beam reconstruction via backprojection

We present a (spiral + circles) scan cone beam reconstruction algorithm in which image reconstruction proceeds via backprojection in the object space. In principle, the algorithm can reconstruct sectional region-of-interest (ROI) in a long object. The approach is a generalization of the cone beam backprojection technique developed by Kudo and Saito in two aspects: the resource-demanding normalization step in the Kudo and Saito's algorithm is eliminated through the technique of data combination that we published earlier, and the elimination of the restriction that the detector be big enough to capture the entire cone beam projection of the ROI. Restricting the projection data to the appropriate angular range required by data combination can be accomplished by a masking process. Because of the simplification resulting from the elimination of the normalization step, the most time-consuming operations of the algorithm can be approximated by the efficient step of line-by-line ramp filtering the cone beam image in the direction of the scan path, plus a correction image. The correction image, which can be computed exactly, is needed because data combination is not properly matched at the mask boundary when ramp filtering is involved. Empirical two-dimensional (2-D) point spread function (PSF) is developed to improve matching with the correction image which is computed with finite samplings. The use of transition region to further improve matching is introduced. The results of testing the algorithm on simulated phantoms are presented.