Limited Angle Reconstruction in Tomography via Squashing

We give a new algorithm for reconstructing a density f in the plane from its projections along those lines making an angle greater than a fixed delta > 0 with the x axis. Of course, the performance of the algorithm depends on delta and on the smoothness of f, but it appears to give a practical and simple solution to the problem whenever one exists. The basic idea, which seems to be new, is to make an affine (squashing) scale change of f to g for which the projections are then known at n equally spaced angles, so that we know how to find g, and then we obtain f from g by inverting the scale change.     

O(N3 log N) backprojection algorithm for the 3-D radon transform

We present a novel backprojection algorithm for three-dimensional (3-D) radon transform data that requires O(N3 log2 N) operations for reconstruction of an N x N x N volume from O(N2) plane-integral projections. Our algorithm uses a hierarchical decomposition of the 3-D radon transform to recursively decompose the backprojection operation. Simulations are presented demonstrating reconstruction quality comparable to the standard filtered backprojection, which requires O(N5) computations under the same circumstances.     

Geometric deconvolution: a meta-algorithm for limited view computed tomography

Images reconstructed using a limited number of projections spanning a narrow angular range suffer from a systematic geometric distortion due to the two-dimensional point spread function of the reconstruction process. Applying the projection theorem, we show that the problem of removing this distortion reduces to that of estimating the one-dimensional spread function and deconvolving projections computed for a complementary set of new angles from the initial reconstruction. A second reconstruction is performed using the deconvolved projections along with the original set of projections, thus incorporating wider angular coverage. We present here initial results of such geometric deconvolution performed via inverse filtering using fast Fourier transform techniques. While the results are noisy due to well-known problems associated with inverse filtering, they illustrate the plausibility of the underlying ideas.     

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)     

Extrapolation of signals using the method of alternating projections in fractional Fourier domains

The need for extrapolation of signals in time domain or frequency domain often arises in many applications in the area of signal and image processing. One of the approaches used for the extrapolation of the signals is the method of alternating projections (MAP) in conventional Fourier domains (CFD). Here we propose an extension of this approach using the fractional Fourier transform (FRFT) called here as the method of alternating projections in the FRFT domains (MAPFD). It is shown through the simulation results that the mean square error (MSE) between the true signal and the extrapolated signal obtained from the given signal is a function of the angle parameter of the FRFT, and the MAPFD gives lower MSE than the MAP in the CFD for the class of signals bandlimited in the FRFT domains, e.g., chirp signals. Moreover, the performance of the extrapolation using the MAPFD is shown to be shift-variant along the time axis.     

Accurate centerline detection and line width estimation of thick lines using the radon transform.

Centerline detection and line width estimation are important for many computer vision applications, e.g., road network extraction from high resolution remotely sensed imagery. Radon transform-based linear feature detection has many advantages over other approaches: for example, its robustness in noisy images. However, it usually fails to detect the centerline of a thick line due to the peak selection problem. In this paper, several key issues that affect the centerline detection using the radon transform are investigated. A mean filter is proposed to locate the true peak in the radon image and a profile analysis technique is used to further refine the line parameters. The theta-boundary problem of the radon transform is also discussed and the erroneous line parameters are corrected. Intensive experiments have shown that the proposed methodology is effective in finding the centerline and estimating the line width of thick lines.     

Structure and motion from line correspondences: Representation,projection, initialization and sparse bundle adjustment

We address the problem of structure and motion from line correspondences, which ranges from the representation of lines, their projections and the initialization procedure to the final adjustment. The Cayley representation of spatial lines is developed, which is a nonlinear minimal parametrization circumventing the tiresome Plücker constraint. The relationships between different line representations are given. Based on these relationships, we derive a novel line projection function which is consistent with the previous results. After building the line observation model, we employ a closed-form solution for the first image triplet, then develop an incremental initialization approach to initialize the motion and structure parameters. Finally, the sparse bundle adjustment (SBA) is applied to refine the parameters, which updates the spatial lines by using the Cayley representation with an unconstrained optimization engine. The experiments show that the proposed algorithm outperforms the previous works both in efficiency and accuracy.     

3-D shape estimation of DNA molecules from stereo cryo-electron micro-graphs using a projection-steerable snake.

We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; we choose the global model as a 3-D filament with a B-spline skeleton and a specified radial profile. The active contour algorithm iteratively updates the B-spline coefficients, which requires us to evaluate the projections and match them with the micrographs at every iteration. Since the evaluation of the projections of the global model is computationally expensive, we propose a fast algorithm based on locally approximating it by elongated blob-like templates. We introduce the concept of projection-steerability and derive a projection-steerable elongated template. Since the two-dimensional projections of such a blob at any 3-D orientation can be expressed as a linear combination of a few basis functions, matching the projections of such a 3-D template involves evaluating a weighted sum of inner products between the basis functions and the micrographs. The weights are simple functions of the 3-D orientation and the inner-products are evaluated efficiently by separable filtering. We choose an internal energy term that penalizes the average curvature magnitude. Since the exact length of the DNA molecule is known a priori, we introduce a constraint energy term that forces the curve to have this specified length. The sum of these energies along with the image energy derived from the matching process is minimized using the conjugate gradients algorithm. We validate the algorithm using real, as well as simulated, data and show that it performs well.     

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.     

Iterative reconstruction in X-ray fluorescence tomography based on radon inversion

We describe a new approach for the inversion of the generalized attenuated radon transform in X-ray fluorescence computed tomography (XFCT). The approach consists of using the radon inverse as an approximation for the actual one, followed by an iterative refinement. Also, we analyze the problem of retrieving the attenuation map directly from the emission data, giving rise to a novel alternating method for the solution. We applied our approach to real and simulated XFCT data and compared its performance to previous inversion algorithms for the problem, showing its main advantages: better images than those obtained by other analytic methods and much faster than iterative methods in the discrete setting.     

Resampling of data between arbitrary grids using convolutioninterpolation

For certain medical applications resampling of data is required. In magnetic resonance tomography (MRT) or computer tomography (CT), e.g., data may be sampled on nonrectilinear grids in the Fourier domain. For the image reconstruction a convolution-interpolation algorithm, often called gridding, can be applied for resampling of the data onto a rectilinear grid. Resampling of data from a rectilinear onto a nonrectilinear grid are needed, e.g., if projections of a given rectilinear data set are to be obtained. In this paper we introduce the application of the convolution interpolation for resampling of data from one arbitrary grid onto another. The basic algorithm can be split into two steps. First, the data are resampled from the arbitrary input grid onto a rectilinear grid and second, the rectilinear data is resampled onto the arbitrary output grid. Furthermore, we like to introduce a new technique to derive the sampling density function needed for the first step of our algorithm. For fast, sampling-pattern-independent determination of the sampling density function the Voronoi diagram of the sample distribution is calculated. The volume of the Voronoi cell around each sample is used as a measure for the sampling density. It is shown that the introduced resampling technique allows fast resampling of data between arbitrary grids. Furthermore, it is shown that the suggested approach to derive the sampling density function is suitable even for arbitrary sampling patterns. Examples are given in which the proposed technique has been applied for the reconstruction of data acquired along spiral, radial, and arbitrary trajectories and for the fast calculation of projections of a given rectilinearly sampled image.     

多准则图象重建的神经网络模型及实现

本文提出一种采用Ｈｏｐｆｉｅｌｅ神经网络（Ｈｏｐｆｉｅｌｄ Ｎｅｉｒａｌ Ｎｅｔｗｏｒｋ简称ＨＮＮ）优化的图象重建算法。将图象重建问题转化为ＨＮＮ优化问题,取重建图象的峰值函数最小以及原始投影与再投影之间的误差平方和最小作为图象重建的优化目标,作为能量函数构造连续型ＨＮＮ模型,由ＨＮＮ能量函数极小化可得到重建问题的优化解。这种方法具有简单、计算量小、收敛快、便于并行计算等特点。对照ＡＲＴ算法,用计算机模拟产生的无噪声投影数据检验新算法,验证了新算法的优越性。     

Time-domain reconstruction algorithms and numerical simulations for thermoacoustic tomography in various geometries

In this paper, we present time-domain reconstruction algorithms for the thermoacoustic imaging of biological tissues. The algorithm for a spherical measurement configuration has recently been reported in another paper. Here, we extend the reconstruction algorithms to planar and cylindrical measurement configurations. First, we generalize the rigorous reconstruction formulas by employing Green's function technique. Then, in order to detect small (compared with the measurement geometry) but deeply buried objects, we can simplify the formulas when two practical conditions exist: 1) that the high-frequency components of the thermoacoustic signals contribute more to the spatial resolution than the low-frequency ones, and 2) that the detecting distances between the thermoacoustic sources and the detecting transducers are much greater than the wavelengths of the high-frequency thermoacoustic signals (i.e., those that are useful for imaging). The simplified formulas are computed with temporal back projections and coherent summations over spherical surfaces using certain spatial weighting factors. We refer to these reconstruction formulas as modified back projections. Numerical results are given to illustrate the validity of these algorithms.     

A prototype rotating slat collimator for single photon emission computed tomography

A collimator consisting of a series of highly attenuating parallel slats has been constructed and used in conjunction with a gamma-camera to approximately measure planar projections of a given radionuclide distribution. The enlarged solid angle of acceptance afforded by the slat collimator gave rise to an increased geometric efficiency of between 12 and 28 times that observed with a low-energy high-resolution (LEHR) parallel-hole collimator. When the slats rotated over the face of the detector and the camera gantry turned about the object, sufficient projections were acquired to reconstruct a three-dimensional (3-D) image using the inversion of the 3-D radon transform. The noise behavior of an algorithm for implementing this inversion was studied analytically and the resulting relationship has been verified by computer simulation. The substantially improved geometric efficiency of the slat collimator translated to improvements in reconstructed signal-to-noise ratio (SNR) by, at best, up to a factor of 2.0 with respect to standard parallel-hole collimation. The spatial resolution achieved with the slat collimator was comparable to that obtained with a LEHR collimator and no significant differences were observed in terms of scatter response. Accurate image quantification was hindered by the spatially variant response of the slat collimator.     

Feasibility of tomography with unknown view angles

In the standard two-dimensional (2-D) parallel beam tomographic formulation, it is generally assumed that the angles at which the projections were acquired are known. We have previously demonstrated, however, that under fairly mild conditions these view angles can be uniquely recovered from the projections themselves. We address the question of reliability of such solutions to the angle recovery problem using moments of the projections. We demonstrate that under mild conditions, the angle recovery problem has unique solutions and is stable with respect to perturbations in the data. Furthermore, we determine the Cramer-Rao lower bounds on the variance of the estimates of the angles when the projection are corrupted by additive Gaussian noise. We also treat the case in which each projection is shifted by some unknown amount which must be jointly estimated with the view angles. Motivated by the stability results and relatively small values of the error bounds, we construct a simple algorithm to approximate the ML estimator and demonstrate that the problem can be feasibly solved in the presence of noise. Simulations using this simple estimator on a variety of phantoms show excellent performance at low to moderate noise levels, essentially achieving the Cramer-Rao bounds.     

Observability of permutations, and stream ciphers

We study the observability of a permutation on a finite set by a complex-valued function. The analysis is done in terms of the spectral theory of the unitary operator on functions defined by the permutation. Any function f can be written uniquely as a sum of eigenfunctions of this operator; we call these eigenfunctions the eigencomponents of f. It is shown that a function observes the permutation if and only if its eigencomponents separate points and if and only if the function has no nontrivial symmetry that preserves the dynamics. Some more technical conditions are discussed. An application to the security of stream ciphers is discussed.     

People,Places, Things: Web Presence for the Real World

The convergence of Web technology, wireless networks, and portable client devices provides new design opportunities for computer/communications systems. In the HP Labs' Cooltown project we have been exploring these opportunities through an infrastructure to support web presence for people, places and things. We put web servers into things like printers and put information into web servers about things like artwork; we group physically related things into places embodied in web servers. Using URLs for addressing, physical URL beaconing and sensing of URLs for discovery, and localized web servers for directories, we can create a location-aware but ubiquitous system to support nomadic users. On top of this infrastructure we can leverage Internet connectivity to support communications services. Web presence bridges the World Wide Web and the physical world we inhabit, providing a model for supporting nomadic users without a central control point.     

Graph laplacian tomography from unknown random projections

We introduce a graph Laplacian-based algorithm for the tomographic reconstruction of a planar object from its projections taken at random unknown directions. A Laplace-type operator is constructed on the data set of projections, and the eigenvectors of this operator reveal the projection orientations. The algorithm is shown to successfully reconstruct the Shepp-Logan phantom from its noisy projections. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.     

闪烁室和电离室法测氡的气压效应

使用闪烁室法和电离室法的测氡仪有气压效应。闪烁室和电流电离室注入恒量的氡气,改变其内的气压进行放射性计数测量;脉冲电离室的AlphaGUARD便携式氡监测仪则放入一有固体氡源的可调气压的氡室,改变氡室气压对其进行气压效应测试。通过实验表明,在低于常压时闪烁室法测氡的探测效率增高,而电流电离室法和脉冲电离室法测氡的探测效率降低。还对闪烁室法和电离室法测氡的气压效应实验结果进行了初步分析。     

Iterative methods based on polynomial interpolation filters to detect discontinuities and recover point values from Fourier data

In previous papers, we proposed new filters based on polynomial interpolation to approximate the point values of a piecewise smooth function f on [0,1] from its Fourier coefficients and derived error estimates. We proved that if all the discontinuity points of f are nodes, we can reconstruct point values of f accurately, even close to the discontinuities. We use the new filters to develop iterative methods for detecting the discontinuity points and, therefore, accurately approximate the point values of the function from its Fourier coefficients.